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{{Short description|Decimal-based systems of measurement with 7 base units defined by physical constants}}
{{outline|Outline of the metric system}}
{{Use dmy dates|date=October 2015}}{{Use British English|date=August 2016}} {{Use dmy dates|date=December 2018}}
{{Use British English|date=August 2021}}
{{Good article}}
{{For outline|Outline of the metric system}}
] mass and three metric measuring devices: a ] in ]s, a ] in ], and a ] that measures potential in ]s, current in ]s and resistance in ]s.]]


The '''metric system''' is a ] that ] a set of base units and a ] for describing relatively large and small quantities via ]-based multiplicative ]es. Though the rules governing the metric system have changed over time, the modern definition, the ] (SI), defines the ]es and seven base units: ] (m), ] (kg), ] (s), ] (A), ] (K), ] (mol), and ] (cd).<ref name=SI2019>{{Cite web|url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-url=https://web.archive.org/web/20190530124226/https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-date=2019-05-30 |url-status=live|title=The International System of Units (SI), 9th Edition|date=2019|publisher=Bureau International des Poids et Mesures}}</ref>
{{good article}}
{{See introduction|Introduction to the metric system}}
]
], 1791). Four everyday measuring devices that have metric calibrations: a ] calibrated in ]s, a ] calibrated in ], a ] weight and an electrical ] that measures ]s, ]s and ]s.]]


An ] is a named combination of base units such as ] (cycles per second), ] (kg⋅m/s<sup>2</sup>), and ] (1 kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>) and in the case of ] a shifted scale from Kelvin. Certain units have been ]. Some of these are decimalised, like the ] and ], and are considered "metric". Others, like the ] are not. Ancient non-metric but SI-accepted multiples of time, ] and ], are base 60 (]). Similarly, the angular measure ] and submultiples,
The '''metric system''' is an internationally agreed ] ]. It was originally based on the {{lang|fr|'']''}} and the {{lang|fr|'']''}} introduced by the ] in 1799,<ref name=Alder /> but over the years the definitions of the metre and the kilogram have been refined, and the metric system has been extended to incorporate many more units. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries, the term is now often used as a synonym for "SI"<ref name=French group=Note>The following abbreviations are taken from the French rather than the English language
], and ], are also sexagesimal and SI-accepted.
* SI: ]
* CGPM: ]
* CIPM: ]
* BIPM: ]
* CIE: ]</ref> or the "]"—the official ] in almost every country in the world.


The SI system derives from the older ] (MKS) system of units, though the definition of the base units has evolved over time. Today, all base units are defined by ]s; not by example as physical objects as they were in the past.
The metric system has been officially sanctioned for use in the ] since 1866,<ref name="H.R. 596" /> but the U.S.A. remains the only ] that has not fully adopted the metric system as its official system of measurement (although, in 1988, the ] passed the ], which designates "the metric system of measurement as the preferred system of weights and measures for U.S. trade and commerce"). Among many other things, the act requires federal agencies to use metric measurements in nearly all of their activities, although there are still exceptions allowing traditional linear units to be used in documents intended for consumers. Many sources also cite the countries of ] and ] (]) as the only other countries not to have done so.<!-- A combination of the text in the CIA Handbook (the word "official") and the NIST website (the words "industrialised country". Both are cited in full later in the article --> Although the ] also uses the metric system for most administrative and trade purposes, ] are widely used by the public and are permitted or obligatory for some purposes, such as road signs.


Other metric system variants include the ], the ], and the ]. Each has ]. Some of these systems are still used in limited contexts.
Although the originators intended to devise a system that was equally accessible to all, it proved necessary to use ] units in the custody of national or local authorities as standards. Control of the prototype units of measure was maintained by the ] until 1875, when it was passed to an international ], the ] (CGPM).<ref name=French group=Note />


==Adoption==
From its beginning, the main features of the metric system were the standard set of interrelated ] and a standard set of prefixes in powers of ten. These base units are used to derive larger and smaller units that could replace a huge number of other units of measure in existence. Although the system was first developed for commercial use, the development of ] units of measure made it particularly suitable for science and engineering.
]


The SI system has been adopted as the official system of weights and measures by most countries in the world.
The uncoordinated use of the metric system by different scientific and engineering disciplines, particularly in the late 19th century, resulted in different choices of ]s even though all were based on the same definitions of the units of the ] and the ]. During the 20th century, efforts were made to rationalise these units, and in 1960, the CGPM published the ], which has since then been the ] metric system.


A notable outlier is the ] (US). Although used in some contexts, the US has resisted full adoption; continuing to use "a conglomeration of basically ]".<ref>{{cite book |last=Gullberg |first=Jan |author-link=Jan Gullberg |title=Mathematics from the Birth of Numbers |publisher=W. W. Norton and Company |location=New York and London |year=1997 |isbn=978-0-393-04002-9 |page=52 |chapter=2.4 Decimal Position System}}</ref>
== Features ==
Although the metric system has changed and developed since its inception, its basic concepts have hardly changed. Designed for transnational use, it consisted of a basic set of units of measurement, now known as ]. ] were built up from the base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal-based and identified by a ].


Adopting the metric system is known as ].
=== Universality ===
]. Although the primary text is in Chinese, the distances use internationally recognised characters.]]At the outbreak of the ] in 1789, most countries and even some cities had their own ]. Although different countries might have used units of measure with the same name, such as the ], or local language equivalents such as ''pied'', ''Fuß,'' and ''voet'', there was no consistency in the magnitude of those units, nor in the relationships with their multiples and submultiples,<ref name=Palaiseau>{{cite book
|url = https://books.google.com/books?id=ahjPAAAAMAAJ&printsec=frontcover&cad=0#v=onepage&q&f=false
|title = Métrologie universelle, ancienne et moderne: ou rapport des poids et mesures des empires, royaumes, duchés et principautés des quatre parties du monde
|first = JFG
|last = Palaiseau
|pages = 71–460
|location = Bordeaux
|date = October 1816
|accessdate =30 October 2011}}</ref> much like the modern-day differences between the US and the UK ]s and ]s.<ref>{{cite web
|url = http://www.britannica.com/EBchecked/topic/461186/pint
|title = pint
|publisher = Encyclopædia Britannica
|year = 2013
|accessdate = 4 April 2013}}</ref>


==Multiplicative prefixes==
The metric system was designed to be universal—in the words of the French philosopher ] it was to be "for all people for all time".<ref name=Alder />{{rp|1}} It was designed for ordinary people, for engineers who worked in human-related measurements and for astronomers and physicists who worked with numbers both small and large, hence the huge range of the prefixes that have been defined in SI.<ref name=SI_prefix>{{SIbrochure8th|pages=121,122}}</ref>
{{Main|Metric prefix}}


In the SI system and generally in older metric systems, multiples and fractions of a unit can be described via a prefix on a unit name that implies a decimal (base-10), multiplicative factor. The only exceptions are for the SI-accepted units of time (minute and hour) and angle (degree, arcminute, arcsecond) which, based on ancient convention, use base-60 multipliers.<ref>{{cite web |title=Non-SI units accepted for use with SI |url=https://metricsystem.net/non-si-units/accepted-for-use-with-si/ |website=Metric System |date=26 July 2018 |access-date=10 July 2023}}</ref>
When the French Government first investigated the idea of overhauling their system of measurement, the concept of universality was put into practice in 1789: ], acting on Condorcet's advice, invited ], a British parliamentarian and ], the American Secretary of State to ], to work with the French in producing an international standard by promoting legislation in their respective legislative bodies. However, these early overtures failed and the custody of the metric system remained in the hands of the French government until 1875.<ref name=Alder />{{rp|250–253}}
{{common metric prefixes}}
The prefix ''kilo'', for example, implies a factor of 1000 (10<sup>3</sup>), and the prefix ''milli'' implies a factor of 1/1000 (10<sup>-3</sup>). Thus, a ''kilometre'' is a thousand metres, and a ''milligram'' is one thousandth of a gram. These relations can be written symbolically as:<ref name=SI_prefix>{{SIbrochure8th|pages=121,122}}</ref>
{{block indent|1=1&nbsp;km = 1000&nbsp;m}}
{{block indent|1=1&nbsp;mg = 0.001&nbsp;g}}


==Base units==
In languages where the distinction is made, unit names are ]s (i.e. not proper nouns). They use the character set and follow the grammatical rules of the language concerned, for example ''"]"'', "'']''", but each unit has a symbol that is independent of language, for example "km" for "kilometer", "V" for "volts" etc.<ref name=noun />


The ] is based on the ], which had been introduced in ]. The historical development of these systems culminated in the definition of the ] (SI) in the mid-20th century, under the oversight of an international standards body.
=== Decimal multiples ===
{{Main|metric prefix}}
In the metric system, multiples and submultiples of units follow a decimal pattern,<ref group = Note>Non-SI units for time and plane angle measurement, inherited from existing systems, are an exception to the decimal-multiplier rule</ref> a concept identified as a possibility in 1586 by ], the Flemish mathematician who had introduced decimal fractions into Europe.<ref name=Stevin_MacTutor /> This is done at the cost of losing the simplicity associated with many traditional systems of units where division by 3 does not result in awkward fractions; for example one third of a foot is four inches, a simplicity that in 1790 was debated, but rejected by the originators of the metric system.<ref name=Glasser>{{cite book
|url = http://www.eipiphiny.org/books/history-of-binary.pdf
|pages = 71–72
|title = History of Binary and other Nondecimal Numeration
|first1 = Anton
|last1 = Glaser
|publisher = Tomash
|year = 1981
|isbn = 0-938228-00-5
|edition = Revised
|origyear = 1971
|accessdate = 5 April 2013}}</ref> In 1854, in the introduction to the proceedings of the Decimal Association, the mathematician ] summarised the advantages of a decimal-based system over a non-decimal system thus: "In the ''simple'' rules of ], we practice a pure decimal system, nowhere interrupted by the entrance of any other system: ''from column to column we never carry anything but tens''".<ref>{{cite book
|url = http://babel.hathitrust.org/cgi/pt?view=image;size=100;id=nnc1.cu01594990;page=root;seq=5
|first1 = Augustus
|last1 = de Morgan
|title = Decimal Association (formed Jun 12, 1854)—Proceedings with an introduction by Professor de Morgan
|page = 2
|location = London
|year = 1854
|accessdate = 21 April 2012}}</ref>
{{common metric prefixes}}
A common set of decimal-based prefixes that have the effect of multiplication or division by an integer power of ten can be applied to units which are themselves too large or too small for practical use. The concept of using consistent classical (] or ]) names for the prefixes was first proposed in a report by the ]] Commission on Weights and Measures in May 1793.<ref name=Alder>{{cite book
|title = The Measure of all Things—The Seven-Year-Odyssey that Transformed the World
|last= Alder
|first= Ken
|year= 2002
|publisher= Abacus
|location= London
|isbn= 0-349-11507-9}}</ref>{{rp|89–96}} The prefix ''kilo'', for example, is used to multiply the unit by 1000, and the prefix ''milli'' is to indicate a one-thousandth part of the unit. Thus the '']'' and '']'' are a thousand ]s and ]s respectively, and a '']'' and '']'' are one thousandth of a gram and metre respectively. These relations can be written symbolically as:<ref name=SI_prefix />
:1&nbsp;mg = 0.001&nbsp;g
:1&nbsp;km = 1000&nbsp;m


The historical evolution of metric systems has resulted in the recognition of several principles. A set of independent dimensions of nature is selected, in terms of which all natural quantities can be expressed, called base quantities. For each of these dimensions, a representative quantity is defined as a ] of measure. The definition of base units has increasingly been ] in terms of fundamental natural phenomena, in preference to copies of physical artefacts. A unit ] from the base units is used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which is derived from length. These derived units are ], which means that they involve only products of powers of the base units, without any further factors. For any given quantity whose unit has a name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the ]; the unit of ] should be either the metre or a decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it.
In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as ''kilo-'' and ''mega-'', and those that were negative powers of ten were given Latin-derived prefixes such as ''centi-'' and ''milli-''. However, 1935 extensions to the prefix system did not follow this convention: the prefixes ''nano-'' and ''micro-'', for example have Greek roots.<ref>{{cite book

|title = The Basis of Measurement: Volume 2—Metrication and Current Practice
Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, other metric systems include: the ] and the ] systems, which are the direct forerunners of the SI; the ] system and its subtypes, the ] (cgs-esu) system, the ] (cgs-emu) system, and their still-popular blend, the ]; the ] system; and the ]s, which can be based on either the metre or the centimetre, and either the gram, gram-force, kilogram or kilogram-force.
|isbn = 0-948251-84-0

|publisher = Picton Publishing
==Attributes==
|location = Chippenham

|year = 1997
===Ease of learning and use===
|first1 = Thomas
The metric system is intended to be easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units.
|last1 = McGreevy

|editor1-first = Peter
It is a ] with ] built from base units using logical rather than empirical relationships and with multiples and submultiples of both units based on decimal factors and identified by a ].<ref name=":0" />{{Rp|pages=15–18}}
|editor1-last = Cunningham

|pages = 222–223}}</ref> During the 19th century the prefix ], derived from the Greek word μύριοι (''mýrioi''), was used as a multiplier for {{val|10000}}.<ref>{{cite book
===Extensibility===
|url=https://books.google.com/books?id=h6miHpDMjXEC&pg=PA494
The metric system is extensible since the governing body reviews, modifies and extends it needs arise. For example, the ], a derived unit for catalytic activity equivalent to one ] per second (1&nbsp;mol/s), was added in 1999.<ref>{{Cite journal |last=Dybkær |first=René |date=2002-03-01 |title=The Tortuous Road to the Adoption of katal for the Expression of Catalytic Activity by the General Conference on Weights and Measures |journal=Clinical Chemistry |volume=48 |issue=3 |pages=586–590 |doi=10.1093/clinchem/48.3.586 |issn=0009-9147 |pmid=11861460|doi-access=free }}</ref>
|title=The Edinburgh Encyclopædia

|first1=D
=== Realisation ===
|last1=Brewster
{{See also|Realisation (metrology)}}
|page=494

|year=1830
The base units used in a measurement system must be ]. To that end, the definition of each SI base unit is accompanied by a ''mise en pratique'' (practical realisation) that describes at least one way that the unit can be measured.<ref>{{cite web |url = http://www.bipm.org/en/si/new_si/mise-en-pratique.html |title = What is a ''mise en pratique''? |publisher = ] |year=2011 |access-date = 11 March 2011}}</ref> Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country. In practice, such realisation is done under the auspices of a ].<ref>{{cite web |url=http://www.oiml.org/maa/ |title=OIML Mutual Acceptance Arrangement (MAA) |publisher=] |access-date=23 April 2013 |url-status=dead |archive-url=https://web.archive.org/web/20130521131225/http://www.oiml.org/maa/ |archive-date=21 May 2013}}</ref>
}}</ref>

] was originally defined to be ''one ten millionth'' of the distance between the ] and the ] through ].<ref name="Alder">{{cite book |last=Alder |first=Ken |title=The Measure of all Things—The Seven-Year-Odyssey That Transformed the World |publisher=Abacus |year=2002 |isbn=978-0-349-11507-8 |location=London}}</ref>]]

In 1791 the commission originally defined the ] based on the size of the earth, equal to one ten-millionth of the distance from the equator to the North Pole. In the SI, the standard ] is now defined as exactly {{frac|1|{{val|299,792,458}}}} of the distance that light travels in a ].<ref>{{cite web |url=https://www.bipm.org/en/committees/cg/cgpm/17-1983/resolution-1 |title=17th General Conference on Weights and Measures (1983), Resolution 1. |access-date=17 June 2023}}</ref><ref>{{Cite web|date=20 May 2019|title=Mise en pratique for the definition of the metre in the SI|url=https://www.bipm.org/documents/20126/41489670/SI-App2-metre.pdf/0e011055-9736-d293-5e56-b8b1b267fd68?version=1.8&t=1637238031486&download=false|website=BIPM |access-date=17 June 2023}}</ref> The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency.<ref>{{cite conference |last1=Lewis |first1=A. |title=1983 realisation of the metre definition |publisher=National Physical Laboratory |conference=Varenna Summer School |url=https://static.sif.it/SIF/resources/public/files/va2019/Lewis2.pdf |access-date=10 July 2023 |page=15 |date=4 July 2019}}</ref>

The ] was originally defined as the mass of one cubic decimetre of water at 4&nbsp;°C, standardised as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a ]. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the ] serve as ''de facto'' standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention. The replicas were subject to periodic validation by comparison to the original, called the ]. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50&nbsp;μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of {{val|5|e=-8}}. The ] replaced the IPK with an exact definition of the ] as expressed in SI units, which defines the kilogram in terms of fundamental constants.<ref>{{cite web |date=16 November 2018 |title=The Latest: Landmark Change to Kilogram Approved |url=https://apnews.com/e6991383703e4ad5a9570d97b0e57822 |access-date=17 June 2023 |website=AP News |publisher=Associated Press}}</ref><ref>{{Cite web |date=7 July 2021 |title=Mise en pratique for the definition of the kilogram in the SI |url=https://www.bipm.org/documents/20126/41489673/SI-App2-kilogram.pdf/5881b6b5-668d-5d2b-f12a-0ef8ca437176?version=1.9&t=1637237674882&download=false |access-date=17 June 2023 |website=BIPM}}</ref><ref>{{cite news |last1=Resnick |first1=Brian |title=The new kilogram just debuted. It's a massive achievement. |url=https://www.vox.com/science-and-health/2019/5/17/18627757/kilogram-redefined-world-metrology-day-explained |work=Vox |date=20 May 2019 |access-date=17 June 2023}}</ref>

=== Base and derived unit structure ===
{{Main|Base unit (measurement)}}
{{See also|SI derived unit}}
A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. A base unit is a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has the unit metre and time has the unit second, and speed has the derived unit metre per second.<ref name=":0" />{{Rp|page=15}} Density, or mass per unit volume, has the unit kilogram per cubic metre.<ref name=":0" />{{Rp|page=434}}

=== Decimal ratios ===
A significant characteristic of the metric system is its use of decimal multiples {{endash}} powers of 10. For example, a length that is significantly longer or shorter than 1 metre can be represented in units that are a power of 10 or 1000 metres. This differs from many older systems in which the ratio of different units varied. For example, 12 ]es is one ], but the larger unit in the same system, the ] is not a power of 12 feet. It is 5,280 feet {{endash}} which is hard to remember for many.<ref name=":0" />{{Rp|page=17}}

In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as ''kilo-'' and ''mega-'', and those that were negative powers of ten were given Latin-derived prefixes such as ''centi-'' and ''milli-''. However, 1935 extensions to the prefix system did not follow this convention: the prefixes ''nano-'' and ''micro-'', for example have Greek roots.<ref name="McGreevy v2">{{cite book |title = The Basis of Measurement: Volume 2—Metrication and Current Practice |isbn = 978-0-948251-84-9 |publisher = Picton Publishing |location = Chippenham |year = 1997 |first1 = Thomas |last1 = McGreevy |editor1-first = Peter |editor1-last = Cunningham}}</ref>{{rp|222–223}} During the 19th century the prefix ], derived from the Greek word μύριοι (''mýrioi''), was used as a multiplier for {{val|10000}}.<ref>{{cite book |url=https://archive.org/details/edinburghencyclo07brew |title=The Edinburgh Encyclopædia |first1=D. |last1=Brewster |page= |year=1830 }}</ref>


When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below.<ref name=SI_prefix /> When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below.<ref name=SI_prefix />
{| style="margin-left:3em !important; white-space:nowrap"
:{|
|- |-
|1&nbsp;mm<sup>2</sup> (square millimetre) ||= (1&nbsp;mm)<sup>2</sup>&nbsp;||= (0.001&nbsp;m)<sup>2</sup>&nbsp;||= {{val|0.000001|u=m2}} |1&nbsp;mm<sup>2</sup> (square millimetre) ||= (1&nbsp;mm)<sup>2</sup>&nbsp;||= (0.001&nbsp;m)<sup>2</sup>&nbsp;||= {{val|0.000001|u=m2}}
Line 112: Line 84:
|} |}


Prefixes are not usually used to indicate multiples of a second greater than 1; the non-SI units of ], ] and ] are used instead. On the other hand, prefixes are used for multiples of the non-SI unit of volume, the ] (l, L) such as millilitres (ml).<ref name=SI_prefix /> For the most part, the metric prefixes are used uniformly for SI base, derived and accepted units. A notable exception is that for a large measure of seconds, the non-SI units of ], ] and ] are customary instead. Units of duration longer than a day are problematic since both month and year have varying number of days. Sub-second measures are often indicated via submultiple prefixes. For example, ].<ref name=SI_prefix />

=== Realisability and replicable prototypes ===
] and the ] through Paris.<ref name=Alder />]]
{{Main|Realisation (metrology)}}
The base units used in the metric system must be ], ideally with reference to natural ] rather than unique ]. <!-- Artifact is US spelling; artefact is UK spelling --> Each of the base units in SI is accompanied by a ''mise en pratique'' published by the BIPM that describes in detail at least one way in which the base unit can be measured.<ref>{{cite web
|url = http://www.bipm.org/en/si/new_si/mise-en-pratique.html
|title = What is a ''mise en pratique''?
|publisher = ]
|year = 2011
|accessdate = 11 March 2011}}</ref> Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country. In practice, such realisation is done under the auspices of a ] (MAA).<ref>{{cite web
|url=http://www.oiml.org/maa/
|title=OIML Mutual Acceptance Arrangement (MAA)
|publisher=]
|accessdate=23 April 2013
|deadurl=yes
|archiveurl=https://web.archive.org/web/20130521131225/http://www.oiml.org/maa/
|archivedate=21 May 2013
|df=
}}</ref>

==== Metre and kilogram ====
In the original version of the metric system the base units could be derived from a specified length (the metre) and the weight of a specified volume ({{frac|{{val|1000}}}} of a cubic metre) of pure water. Initially the ''de facto'' French Government of the day, the ], considered defining the metre as the length of a ] that has a period of one second at 45°N and an ] equal to ]. The altitude and latitude were specified to accommodate variations in ]; the specified latitude was a compromise between the latitude of {{nowrap|London (51° 30'N)}}, {{nowrap|Paris (48° 50'N)}} and the median parallel of the United States (38°N) to accommodate variations.<ref name=Alder />{{rp|94}} However the mathematician ] persuaded the assembly that a survey having its ends at sea level and based on a meridian that spanned at least 10% of the earth's quadrant would be more appropriate for such a basis.<ref name=Alder />{{rp|96}}
] with edges of 10&nbsp;cm and the '''kilogram''' was originally designed to be one litre of water at the ] of ].<ref name=Nelson />]]
The available technology of the 1790s made it impracticable to use these definitions as the basis of the kilogram and the metre, so prototypes that represented these quantities insofar as was practicable were manufactured. On 22 June 1799 these prototypes were adopted as the definitive reference pieces, deposited in the ] and became known as the {{lang|fr|'']''}} and the {{lang|fr|'']''}}. Copies were made and distributed around France.<ref name=Alder />{{rp|266–269}} These artefacts were replaced in 1889 by the new prototypes manufactured under international supervision. Insofar as was possible, the new prototypes were exact copies of the original prototypes, but used a later technology to ensure better stability. One of each of the kilogram and metre prototypes were chosen by lot to serve as the definitive international reference piece with the remainder being distributed to signatories of the ].<ref>{{cite web
|url = http://www.britannica.com/EBchecked/topic/378767/Treaty-of-the-Metre
|title = Treaty of the Metre
|publisher = ]
|accessdate = 28 March 2013
|year = 2013}}</ref>
In 1889 there was no generally accepted theory regarding the nature of light but by 1960 the wavelength of specific ] could give a more accurate and reproducible value than a prototype metre. In that year the prototype metre was replaced by a formal definition which defines the metre in terms of the ] of specified light spectra. By 1983 it was accepted that the ] in vacuum was ] and that this constant provided a more ] procedure for measuring length. Therefore, the metre was redefined in terms of the speed of light. These definitions give a much better reproducibility and also allow anyone, anywhere with a suitably equipped laboratory, to make a standard metre.<ref>{{cite web
|url=http://www.bipm.org/en/si/history-si/evolution_metre.html
|title=The BIPM and the evolution of the definition of the metre
|publisher=]
|accessdate=11 March 2011
|deadurl=yes
|archiveurl=https://web.archive.org/web/20110607152538/http://www1.bipm.org/en/si/history-si/evolution_metre.html
|archivedate=7 June 2011
|df=
}}</ref>

==== Other base units ====
None of the other base units rely on a prototype – all are based on phenomena that are directly observable and had been in use for many years before formally becoming part of the metric system.

The ] first became a ''de facto'' base unit within the metric system when, in 1832, ] used it, the centimetre and the gram to derive the units associated with values of absolute measurements of the ].<ref name=SI_1_8 /> The second, if based on the ], is not a constant as the Earth's rotation is slowing down—in 2008 the solar day was 0.002&nbsp;s longer than in 1820.<ref>{{cite web
|url = http://tycho.usno.navy.mil/leapsec.html
|title = Leap Seconds
|publisher = Time Service Dept., U.S. Naval Observatory
|location = Washington, DC
|accessdate = 11 March 2011}}</ref> This had been known for many years; consequently in 1952 the ] (IAU) defined the second in terms of the Earth's rotation in the year 1900. Measurements of time were made using ] from readings based on ]. With the launch of SI in 1960, the 11th CGPM adopted the IAU definition.<ref>{{cite journal
|url = http://www.cl.cam.ac.uk/~mgk25/time/metrologia-leapsecond.pdf
|title = The leap second: its history and possible future
|first1 = R.A
|last1 = Nelson
|first2 = D.D
|last2 = McCarthy
|first3 = S
|last3 = Malys
|first4 = J
|last4 = Levine
|first5 = B
|last5 = Guinot
|first6 = H.F
|last6 = Fliegel
|first7 = R.L
|last7 = Beard
|first8 = T.R
|last8 = Bartholomew
|journal = Metrologia
|year = 2001
|number = 6
|volume = 38
|pages = 509–529
|doi=10.1088/0026-1394/38/6/6
|accessdate = 4 April 2013|bibcode = 2001Metro..38..509N }}</ref> In the years that followed, ]s became significantly more reliable and precise; and in 1968 the 13th CGPM redefined the second in terms of a specific frequency from the ] of the ] atom, a component of atomic clocks. This provided the means to measure the time associated with astronomical phenomena rather than using astronomical phenomena as the basis from which time measurements were made.<ref name=SI_units /><ref>{{cite web
|title=Caesium Atoms at Work
|publisher=Time Service Department—U.S. Naval Observatory—Department of the Navy
|url=http://tycho.usno.navy.mil/cesium.html
|accessdate=21 October 2012
|deadurl=yes
|archiveurl=https://web.archive.org/web/20150223231150/http://tycho.usno.navy.mil/cesium.html
|archivedate=23 February 2015
|df=
}}</ref>

The ] absolute unit of ], the ], had been defined in terms of the ] between two parallel current-carrying wires in 1881.<ref>{{cite book
|url = https://books.google.com/books?id=m7c6AAAAIAAJ&pg=PA322&lpg=PA322&dq=cgs+unit+of+current+1881&source=bl&ots=Lw5kV5-jd4&sig=mytqNION410y2qYnGEGn-Hcbu6o&hl=en&sa=X&ei=qaWkUKfiFeeZ0QXpvYC4CA&ved=0CCAQ6AEwADgK#v=onepage&q=cgs%20unit%20of%20current%201881&f=false
|page = 322
|title = Magnetism and Electricity
|last1 = McKenzie
|first1 = A.E.E
|publisher = ]
|year = 1961}}</ref> In the 1940s, the ] adopted an ] variant of this definition for the ] which was adopted in 1948 by the ].<ref>{{cite book
|url = https://books.google.com/books?id=Bokc0XY-gS8C&pg=PA226&lpg=PA226&dq=abampere+dynes+per+centimetre+iec&source=bl&ots=p4Ix16p2c2&sig=1Zz3ALWdjsRl_e_DBctX9UuqteQ&hl=en&sa=X&ei=X2llUcW0BovVPI3igSA&ved=0CDIQ6AEwAA#v=onepage&q=abampere&f=false
|title = Metric Units in Engineering: Going SI
|edition = Revised
|first1 = Cornelius
|last1 = Wandmacher
|first2 = Arnold Ivan
|last2 = Johnson
|pages = 225–226
|year = 1995
|isbn = 0-7844-0070-9
|publisher = American Society of Civil Engineers}}</ref><ref>{{SIBrochure8th|pages=113, 144}}</ref>

] has always been based on observable phenomena—in 1744 the ]<ref group = Note>Now called the ''degree Celsius''</ref> was based on the freezing and boiling points of water.<ref>{{cite web
|url = http://www.linnaeus.uu.se/online/life/6_32.html
|title = Linnaeus' thermometer
|publisher = ]
|year = 2008
|editor1-first = Roland
|editor1-last = Mopberg
|accessdate = 7 April 2013}}</ref> In 1948 the ] adopted the Centigrade scale, renamed it the "Celsius" temperature scale name and defined it in terms of the ] of water.<ref>{{SIBrochure8th|pages=113, 114, 144}}</ref>

When the ] and the ] were accepted by the CGPM in 1971 and 1975 respectively, both had been defined by third parties by reference to phenomena rather than artefacts.<ref name=BIPM1975>{{cite book
|url = https://books.google.com/books?id=nOG0SxxEu64C&pg=PA240&lpg=PA240&dq=gram-atom+IUPAP&source=bl&ots=31G9ZoFX7w&sig=glQv9TS6dbSISJXCPk6cX1p6-mw&hl=en&sa=X&ei=Iw2kUJaCMoHO0QXc8oGgCg&ved=0CDkQ6AEwBA#v=onepage&q=gram-atom%20&f=false
|pages = 238–244
|title = The International Bureau of Weights and Measures 1875–1975: NBS Special Publication 420
|date = 20 May 1975
|editor1-last = Page
|editor1-first = Chester H
|editor2-last = Vigoureux
|editor2-first = Paul
|publisher = National Bureau of Standards
|location = ]}}</ref>


=== Coherence === === Coherence ===
{{Main|Coherence (units of measurement)}} {{Main|Coherence (units of measurement)}}
] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.]] ] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.]]
Each variant of the metric system has a degree of coherence—the various derived units are directly related to the base units without the need for intermediate conversion factors.<ref>{{citation Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors.<ref>{{citation
| author = Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2). | author = Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2).
| publisher = ] (BIPM) on behalf of the Joint Committee for Guides in Metrology | publisher = ] (BIPM) on behalf of the Joint Committee for Guides in Metrology
| year = 2008 | year = 2008
| url = http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf | url = http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
| title = International vocabulary of metrology — Basic and general concepts and associated terms (VIM) | title = International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
| edition = 3rd | edition = 3rd
| at = 1.12 | at = 1.12
|accessdate = 12 April 2012}}</ref> For example, in a coherent system the units of ], ] and ] are chosen so that the equations |access-date = 12 April 2012}}</ref> For example, in a coherent system the units of ], ], and ] are chosen so that the equations
{| style="margin-left:3em !important"
:{|
|- |-
|''force'' ||''= mass'' ||''× acceleration'' | ''force'' || = || ''mass'' || × || ''acceleration''
|- |-
|''energy''&nbsp;||''= force'' ||''× distance'' | ''energy'' || = || ''force'' || × || ''distance''
|- |-
|''power'' ||''= energy''&nbsp;||''÷ time'' | ''energy'' || = || ''power'' || × || ''time''
|} |}
hold without the introduction of unit conversion factors. Once a set of coherent units have been defined, other relationships in physics that use those units will automatically be true. Therefore, ] ], ''E''&nbsp;=&nbsp;''mc''<sup>2</sup>, does not require extraneous constants when expressed in coherent units.<ref>{{cite web hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, ]'s ], {{nowrap|1=''E'' = ''mc''{{i sup|2}}}}, does not require extraneous constants when expressed in coherent units.<ref>{{cite web
|url=http://www.unc.edu/~mgood/research/RestEnergy.pdf |url=http://www.unc.edu/~mgood/research/RestEnergy.pdf
|title=Some Derivations of E = mc<sup>2</sup> |title=Some Derivations of ''E'' = ''mc''<sup>2</sup>
|first1=Michael |first1=Michael
|last1=Good |last1=Good
|accessdate=18 March 2011 |access-date=18 March 2011
|url-status=dead
|deadurl=yes
|archiveurl=https://web.archive.org/web/20111107023429/https://www.unc.edu/~mgood/research/RestEnergy.pdf |archive-url=https://web.archive.org/web/20111107023429/https://www.unc.edu/~mgood/research/RestEnergy.pdf
|archivedate=7 November 2011 |archive-date=7 November 2011
|df=
}}</ref> }}</ref>


The ] had two units of energy, the ] that was related to ] and the ] that was related to ]; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI resulting in only one unit of energy being defined – the ].<ref name=SI_units /> The ] had two units of energy, the ] that was related to ] and the ] that was related to ]; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the ].<ref name=SI_units>{{SIbrochure8th|pages = 111–120}}</ref>


=== Rationalisation ===
In SI, which is a coherent system, the unit of power is the "]" which is defined as "{{em|one}} joule per second".<ref name=SI_units /> In the ] of measurement, which is non-coherent, the unit of power is the "]" which is defined as "550 foot-pounds per second" (the pound in this context being the ]).<ref>{{cite web
Maxwell's equations of electromagnetism contained a factor of <math>1/(4\pi)</math> relating to ]s, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor made equations more awkward than necessary, and so ] suggested adjusting the system of units to remove it.<ref name=":1" />
|url = http://www.britannica.com/EBchecked/topic/272384/horsepower
|title = Horsepower
|publisher = Encyclopædia Britannica Online
|year = 2013
|accessdate = 5 April 2013}}</ref> Similarly, neither the US gallon nor the imperial gallon is {{em|one}} cubic foot or {{em|one}} cubic yard— the US gallon is 231&nbsp;cubic inches and the imperial gallon is 277.42&nbsp;cubic inches.<ref>{{cite book
|page = 47
|chapter = A Central Program for Weights and Measures in Canada
|first1 = RW
|last1 = MacLean
|conference = 42nd National Conference on Weights and Measures 1957
|title = Report of the 42nd National Conference on Weights and Measures 1957
|date = 20 December 1957
|id = Miscellaneous publication 222
|publisher = National Bureau of Standards
|url = https://books.google.com/books?id=CEgJAQAAMAAJ&pg=PA47&lpg=PA47&dq=imperial+US+gallon+231+277.42&source=bl&ots=EvuGYTULgG&sig=3alwe-MkLpQerD8wEah0DUUV1nA&hl=en&sa=X&ei=XWaKUfmWCPHM0AWM84GoBA&ved=0CDUQ6AEwATgU#v=onepage&q=imperial%20US%20gallon%20231%20277.42&f=false
|accessdate = 8 May 2013}}</ref>


==Everyday notions==
The concept of coherence was only introduced into the metric system in the third quarter of the 19th century;<ref name=Maxwell2>{{cite book
The basic units of the metric system have always represented commonplace quantities or relationships in nature; even with modern refinements of definition and methodology. In cases where laboratory precision may not be required or available, or where approximations are good enough, the commonplace notions may suffice.
|title = A treatise on electricity and magnetism
|volume = 2
|author = J C Maxwell
|year = 1873
|publisher = Clarendon Press
|location = Oxford
|url = https://archive.org/stream/electricandmag02maxwrich
|pages = 242–245
|accessdate = 12 May 2011}}</ref> in its original form the metric system was non-coherent—in particular the ] was 0.001&nbsp;m<sup>3</sup> and the ] (from which the ] derives) was 100&nbsp;m<sup>2</sup>. However the units of mass and length were related to each other through the physical properties of water, the gram having been designed as being the mass of one cubic centimetre of water at its freezing point.<ref name=France1795 />


== History == ===Time===
The second is readily determined from the Earth's rotation period. Unlike other units, time multiples are not decimal. A second is {{sfrac|1|60}} of a minute, which is {{sfrac|1|60}} of an hour, which is {{sfrac|1|24}} of a day, so a second is {{sfrac|1|{{val|86400}}}} of a day.
{{Main|History of the metric system}}
{{See also|Metrication}}
] who, in 1668, published an essay proposing a decimal system of measurement]]


===Length===
In 1585 the Flemish mathematician ] published a small pamphlet called ''De Theinde'' ("the tenth"). Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but nobody used decimal numbers in daily life. Stevin declared that using decimals was so important that the universal introduction of decimal weights, measures and coinage was only a matter of time.<ref name=Stevin_MacTutor>{{MacTutor|id=Stevin|title = Simon Stevin|date=January 2004}}</ref>
The length of the ] is close to {{val|40000000|u=metres}} (more precisely {{val|40075014.2|u=metres}}).<ref>{{cite web |last1=Science |first1=Tim Sharp 2017-09-15T15:47:00Z |last2=Astronomy |title=How Big Is Earth? |url=https://www.space.com/17638-how-big-is-earth.html |access-date=22 October 2019 |website=Space.com}}</ref> In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre.<ref>{{cite web |title=Metre {{!}} measurement |url=https://www.britannica.com/science/metre-measurement |access-date=22 October 2019 |website=Encyclopedia Britannica}}</ref> A dining tabletop is typically about 0.75 metres high.<ref>{{cite web |title=Standard Table Sizes |url=https://www.bassettfurniture.com/blog/standard-table-sizes.aspx |access-date=22 October 2019 |website=Bassett Furniture}}</ref> A very tall human is about 2 metres tall.<ref>{{cite web |date=9 December 2018 |title=The Average Height of NBA Players – From Point Guards to Centers |url=https://www.thehoopsgeek.com/average-nba-height/ |access-date=22 October 2019 |website=The Hoops Geek}}</ref>


===Mass===
One of the earliest proposals for a decimal system in which ], ], ] and ] were linked to each other was made by ], first secretary of the ] of London in his 1668 essay "'']''". His proposal used a pendulum that had a beat of one second as the basis of the unit of length.<ref>{{cite web
A ] weighs 7.5&nbsp;g;<ref>{{cite web |title=RUBINGHSCIENCE.ORG / Using Euro coins as weights |url=http://www.rubinghscience.org/surv/euroweights1.html |access-date=22 October 2019 |website=www.rubinghscience.org}}</ref> a ] weighs 8.1&nbsp;g;<ref>{{cite web |date=20 September 2016 |title=Coin Specifications {{!}} U.S. Mint |url=https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications |access-date=22 October 2019 |website=www.usmint.gov}}</ref> a ] weighs 8.0&nbsp;g.<ref>{{cite web |title=Fifty Pence Coin |url=https://www.royalmint.com/discover/uk-coins/coin-design-and-specifications/fifty-pence-coin/ |access-date=22 October 2019 |website=www.royalmint.com}}</ref>
|title = Celebrating metrology: 51 years of SI units
|url = http://www.iop.org/activity/branches/south_east/scentral/news/11/page_51247.html
|date = 20 June 2011
|publisher = Institute of Physics
|accessdate = 30 December 2012}}</ref><ref>{{cite journal
|first1 = John
|last1 = Wilkins
|date = 1668
|publisher = ]
|title = An Essay towards a Real Character and a Philosophical Language
|pages = 190–194}}
,
</ref><ref>{{cite conference
|conference = Baroque Science workshop
|date = 15–17 February 2008
|title = The Hive and the Pendulum: Universal Metrology and Baroque Science
|url = http://sydney.edu.au/science/hps/baroque_science/docs/February_2008_papers/Dew_The_Hive_and_the_Pendulum.pdf
|first1 = Nicholas
|last1 = Dew
|page = 5}}</ref> Two years later, in 1670, ], a French abbot and scientist, proposed a decimal system of length based on the circumference of the Earth. His suggestion was that a unit, the milliare, be defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima. His ideas attracted interest at the time, and were supported by both ] and ] in 1673, and also studied at the Royal Society in London. In the same year, ] independently made proposals similar to those of Mouton.<ref name=Mouton_MacTutor>{{MacTutor|id=Mouton|title = Gabriel Mouton| date=January 2004}}</ref>


===Temperature===
In pre-revolutionary Europe, each state had its own system of units of measure.<ref name=Palaiseau /> Some countries, such as Spain and Russia, saw the advantages of harmonising their units of measure with those of their trading partners.<ref name = metricSpain>{{cite web
In every day use, Celsius is more commonly used than Kelvin, however a temperature difference of one Kelvin is the same as one degree Celsius and that is defined as {{sfrac|1|100}} of the temperature differential between the freezing and boiling points of water at ]. A temperature in Kelvin is the temperature in Celsius plus about 273. ] is about 37&nbsp;°C or 310&nbsp;K.
|url = http://www.2iceshs.cyfronet.pl/2ICESHS_Proceedings/Chapter_16/R-8_Navarro_Merino.pdf
|title = The units of length in the Spanish treatises of military engineering
|first1 = Juan Navarro
|last1 = Loidi
|first2 = Pilar Merino
|last2 = Saenz
|work = The Global and the Local: The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS
|location = Cracow, Poland
|date = 6–9 September 2006
|publisher = The Press of the Polish Academy of Arts and Sciences
|accessdate = 17 March 2011}}</ref> However, vested interests who profited from variations in units of measure opposed this. This was particularly prevalent in France where the huge inconsistency in the size of units of measure was one of the causes that, in 1789, led to the outbreak of the ].<ref name=Alder />{{rp|2}} During the early years of the revolution, ]<ref group=Note>An extremely learned or scholarly person – </ref> including the ], ], ], ] and ] set up a Commission of Weights and Measures. The commission was of the opinion that the country should adopt a completely new system of measure based on the principles of logic and natural phenomena.<ref>{{cite web|last1=Anticole|first1=Matt|title=Why the metric system matters|url=http://ed.ted.com/lessons/why-the-metric-system-matters-matt-anticole|website=]|publisher=]|accessdate=25 July 2016|ref=TedEd}}</ref> Logic dictated that such a system should be based on the ] used for counting. Their report of March 1791 to the ''Assemblée nationale constituante'' considered but rejected the view of Laplace that a ] system of counting should replace the existing decimal system; the view such a system was bound to fail prevailed. The commission's final recommendation was that the assembly should promote a decimal-based system of measurement. The leaders of the assembly accepted the views of the commission.<ref name=Alder />{{rp|99–100}}<ref name=Glasser />


===Length, mass, volume relationship===
Initially France attempted to work with other countries towards the adoption of a common set of units of measure.<ref name=Alder />{{rp|99–100}} Among the supporters of such an international system of units was ] who, in 1790, presented a document '']'' to Congress in which he advocated a decimal system that used traditional names for units (such as ten inches per foot).<ref>{{cite web
The mass of a litre of cold water is 1 kilogram. 1 millilitre of water occupies 1 cubic centimetre and weighs 1 gram.
|url = http://avalon.law.yale.edu/18th_century/jeffplan.asp
|title = Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States
|date = 4 July 1790
|author = Thomas Jefferson
|accessdate = 19 April 2011}}</ref> The report was considered but not adopted by Congress.<ref name=Alder />{{rp| 249–250}}


===Candela and Watt relationship===
]
Candela is about the luminous intensity of a moderately bright candle, or 1 candle power. A 60&nbsp;] tungsten-filament ] has a luminous intensity of about 800 lumens<ref>{{cite web|title=Lumens and the Lighting Facts Label|url=https://www.energy.gov/energysaver/save-electricity-and-fuel/lighting-choices-save-you-money/lumens-and-lighting-facts|access-date=11 June 2020|website=Energy.gov|language=en}}</ref> which is radiated equally in all directions (i.e. 4{{pi}} steradians), thus is equal to {{math|''I''<sub>v</sub> {{=}} {{sfrac|800 lm|4{{pi}} sr}} ≈ 64 cd}}.


=== Original metric system === ===Watt, Volt and Ampere relationship===
A 60&nbsp;W incandescent light bulb consumes 0.5&nbsp;A at 120&nbsp;V (US mains voltage). A 60&nbsp;W bulb rated at 230&nbsp;V (European mains voltage) consumes 0.26&nbsp;A at this voltage. This is evident from the formula {{math|''P'' {{=}} ''I'' ''V''}}.
The French law of 18 Germinal, Year III (7 April 1795) defined five units of measure:<ref name=France1795 />
* The '']'' for length
* The ]&nbsp;(100&nbsp;m<sup>2</sup>) for area
* The '']''&nbsp;(1&nbsp;m<sup>3</sup>) for volume of stacked<ref>{{cite web
|url = http://www.utc.fr/~tthomass/Themes/Unites/unites/infos/stere/Le%20stere.pdf
|title = Le stère
|work = Tout sur les unités de mesure
|language = French
|author = Thierry Thomasset
|publisher = Université de Technologie de Compiègne
|accessdate = 21 March 2011}}</ref> firewood
* The '']''&nbsp;(1&nbsp;dm<sup>3</sup>) for volumes of liquid
* The '']me'' for mass.
This system continued the tradition of having separate base units for geometrically related dimensions, e.g., '']'' for lengths, ]<!--not ''acre''--> (100&nbsp;m<sup>2</sup>) for areas, '']'' (1&nbsp;m<sup>3</sup>) for dry capacities, and '']'' (1 dm<sup>3</sup>) for liquid capacities. The '']'', equal to a hundred '']'', the area of a square 100 metres on a side (about 2.47 ]s), is still in use. The early metric system included only a few ] from '']'' (one thousandth) to '']'' (ten thousand).<ref name=France1795>{{cite web
|url= http://aviatechno.free.fr/unites/nouveausys.php
|title =La loi du 18 Germinal an 3 ''la mesure de superficie pour les terrains, égale à un carré de dix mètres de côté''
|language = french|trans_title = The law of 18 Germanial year 3 "The republican measures of land area equal to a square with sides of ten metres"
|publisher = Le CIV (Centre d'Instruction de Vilgénis) – Forum des Anciens
|accessdate = 2 March 2010}}</ref>


===Mole and mass relationship===
Originally the ], defined as being one ''pinte'' (later renamed the ''litre'') of water at the melting point of ice, was called the ''grave'';<ref name=Nelson>{{cite web
A mole of a substance has a mass that is its ] expressed in units of grams. The mass of a mole of carbon is 12.0&nbsp;g, and the mass of a mole of table salt is 58.4&nbsp;g.
|url = http://www.aticourses.com/international_system_units.htm
| author = Nelson, Robert A
|date=February 2000
| accessdate = 12 April 2007
| work = Applied Technology Institute
| title = The International System of Units: Its History and Use in Science and Industry }}</ref> the ''gramme'' being an alternative name for a thousandth of a ''grave''. However, the word ''grave'', being a synonym for the title "]", had aristocratic connotations and was renamed the ''kilogramme''. The name ''mètre'' was suggested by ] in May 1790.<ref name=Alder />{{rp| 92}}


Since all gases have the same volume per mole at a given temperature and pressure far from their points of liquefaction and solidification (see ]), and air is about {{sfrac|1|5}} oxygen (molecular mass 32) and {{sfrac|4|5}} nitrogen (molecular mass 28), the density of any near-perfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because {{nowrap|{{sfrac|4|5}} × 28 + {{sfrac|1|5}} × 32 {{=}} 28.8 ≈ 29}}). For example, ] (molecular mass 28) has almost the same density as air.
France officially adopted the metric system on 10 December 1799. Although it was decreed that its use was to be mandatory in Paris that year and across the provinces the following year, the decree was not universally observed across France.<ref name = NICB>{{cite book|author=National Industrial Conference Board|title=The metric versus the English system of weights and measures|url=https://archive.org/stream/metricversuseng00boargoog#page/n52/mode/2up|accessdate=5 April 2013|year=1921|publisher=The Century Co|pages=10–11}}</ref>


==History==
=== International adoption ===
{{Main|History of the metric system}}
{{main|Metrication}}
], Saint-Cloud, France, the home of the metric system since 1875]]
Areas ] during the Napoleonic era were the first to inherit the metric system. In 1812, Napoleon introduced a system known as '']'' which used the names of pre-metric units of measure, but defined them in terms of metric units – for example, the ''livre metrique'' (metric pound) was 500&nbsp;g and the ''toise metrique'' (metric fathom) was 2&nbsp;metres.<ref name=Fevier>{{cite web
The ] (1789–99) enabled France to reform its many outdated systems of various local weights and measures. In 1790, ] proposed a new system based on natural units to the ], aiming for global adoption. With the ] not responding to a request to collaborate in the development of the system, the ] established a commission to implement this new standard alone, and in 1799, the new system was launched in France.<ref name="McGreevy v1">{{cite book |title=The Basis of Measurement: Volume 1—Historical Aspects |isbn=978-0-948251-82-5 |publisher=Picton Publishing |location=Chippenham |year=1995 |first1=Thomas |last1=McGreevy |editor1-first=Peter |editor1-last=Cunningham}}</ref>{{rp|145–149}}
|url = http://www.dgcis.redressement-productif.gouv.fr/files/files/archive/www.industrie.gouv.fr/metro/aquoisert/metre.html
|title = Un historique du mètre
|language = French
|author = Denis Février
|publisher = Ministère de l'Economie, des Finances et de l'Industrie
|accessdate = 10 March 2011}}</ref> After the ] in 1815, France lost the territories that she had annexed; some, such as the ] reverted to their pre-revolutionary units of measure, others such as ] adopted a modified version of the ''mesures usuelles'', but France kept her system of measurement intact.<ref name=europa1842 />


A number of different metric system have been developed, all using the ''Mètre des Archives'' and ''Kilogramme des Archives'' (or their descendants) as their base units, but differing in the definitions of the various derived units.
In 1817, the ] reintroduced the metric system, but used ]—for example 1&nbsp;centimetre became the ''duim'' (thumb), the ''ons'' (ounce) became 100&nbsp;g and so on.<ref>{{cite book
|url = https://books.google.com/books?id=XYVbAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false
|title = Allereerste Gronden der Cijferkunst
|author = Jacob de Gelder
|location = 's Gravenhage and Amsterdam
|language = Dutch
|year = 1824
|pages = 163–176
|publisher = de Gebroeders van Cleef
|trans_title = Introduction to Numeracy
|accessdate = 2 March 2011}}</ref> Certain German states adopted similar systems<ref name=europa1842>{{cite web
|url = http://www.spasslernen.de/geschichte/groessen/mas1.htm
|title = Amtliche Maßeinheiten in Europa 1842
|language = German
|trans_title = Official units of measure in Europe 1842
|accessdate = 26 March 2011}}</ref><ref>{{cite book
|url = http://www.bsb-muenchen-digital.de/~web/web1008/bsb10082343/images/index.html?digID=bsb10082343&pimage=00001&v=pdf&nav=0&l=de
|title = Theoretisch-practischer Unterricht im Rechnen
|language = German
|trans_title = Theoretical and practical instruction in arithmetic
|author = Ferdinand Malaisé
|place = München
|year = 1842
|pages = 307–322
|accessdate = 26 March 2011}}</ref> and in 1852 the German ] (customs union) adopted the zollpfund (customs pound) of 500&nbsp;g for intrastate commerce.<ref name=Zollmuseum>{{cite web
|url=http://www.zoll.de/SharedDocs/Textbausteine/DE/Zollmuseum/Archiv-der-Fundstuecke/2006/fundstueck_november_06.html?nn=163392
|title=Fundstück des Monats November 2006
|language=German
|trans_title=Exhibit of the month – November 2006
|publisher=Bundesministerium der Finanzen '' Federal Ministry of Finance''
|date=4 June 2009
|accessdate=7 March 2011
|deadurl=yes
|archiveurl=https://web.archive.org/web/20130508051037/http://www.zoll.de/SharedDocs/Textbausteine/DE/Zollmuseum/Archiv-der-Fundstuecke/2006/fundstueck_november_06.html?nn=163392
|archivedate=8 May 2013
|df=
}}</ref> In 1872 the newly formed ] adopted the metric system as its official system of weights and measures<ref>{{cite book
|title = Measures for Progress: A History of the National Bureau of Standards
|url = https://books.google.com/books?id=w073Vc3ZRCoC&pg=PA530&lpg=PA530&dq=1872+german+empire+adopts+metric+system&source=bl&ots=SzFUQeyKKe&sig=Ncd1fHYVUmryTxc8mgWQ935K-Hs&hl=en&sa=X&ei=2Hq-ULuvO-iX0QWJgIGQDQ&ved=0CGAQ6AEwCA#v=onepage&q=1872%20german%20empire%20adopts%20metric%20system&f=false
|page = 530
|first = Rexmond Canning
|last = Cochrane
|lccn = 65-62472
|year = 1966
|accessdate = 4 December 2012
|publisher = National Bureau of Standards}}</ref> and the newly formed ] likewise, following the lead given by ], adopted the metric system in 1861.<ref name = metricItaly>{{cite web
|url = http://www.2iceshs.cyfronet.pl/2ICESHS_Proceedings/Chapter_16/R-8_Borgato.pdf
|title = The first applications of the metric system in Italy
|author = Maria Teresa Borgato
|work = The Global and the Local: The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS
|location = Cracow, Poland
|date = 6–9 September 2006
|publisher = The Press of the Polish Academy of Arts and Sciences
|accessdate = 17 March 2011}}</ref>


{| class="wikitable floatright" style="font-size: 95%; width:230px;"
The '']'' (Paris Exhibition) devoted a stand to the metric system and by 1875, two thirds of the European population and close to half the world's population had adopted the metric system. By 1872, the only principal European countries not to have adopted the metric system were Russia and the United Kingdom.<ref>{{cite journal
|+Variants of the metric system<!-- without gravitational ones, mechanical units-->
|journal = Report of the forty second meeting of the British Association for the Advancement of Science held at Brighton, August 1872
! Measure
|year = 1873
! SI/MKS
|title = Report on the best means of providing a Uniformity of Weights and Measures, with reference to the Interests of Science
|author = Secretary, the Metric committee
|publisher = British Association for the Advancement of Science
|pages= 25–28
|url = https://archive.org/stream/report44sciegoog
|accessdate = 12 May 2011}}</ref>

By 1920, countries comprising 22% of the world's population, mainly English-speaking, used the imperial system or the closely related US customary system; 25% used mainly the metric system and the remaining 53% used neither.<ref name = NICB />

In 1927, several million people in the United States sent over 100,000 petitions backed by the Metric Association and The General Federation of Women's Clubs urging Congress to adopt the metric system. The petition was opposed by the manufacturing industry, citing the cost of the conversion.<ref> ''Popular Science Monthly'', January 1928, p. 53.</ref>

=== International standards ===
In 1861 a committee of the ] including William Thomson (later ]), ] and ] introduced the concept of a coherent system of units based on the metre, gram and second which, in 1873, was extended to include electrical units.<ref>{{cite book
|title = A treatise on electricity and magnetism
|volume = 2
|first1 = J C
|last1 =Maxwell
|year = 1873
|publisher = Clarendon Press
|location = Oxford
|url = https://archive.org/stream/electricandmag02maxwrich
|pages = 242–245
|accessdate = 12 May 2011}}</ref><ref>{{cite journal
|journal = Report on the Forty-third Meeting of the British Association for the Advancement of Science held at Bradford in September 1873
|year = 1874
|title = First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units
|editor = Professor Everett|publisher = British Association for the Advancement of Science
|pages= 222–225
|url = http://www.biodiversitylibrary.org/item/94452
|accessdate = 10 May 2011|display-editors=etal}}</ref>
] (BIPM)]]
On 20 May 1875 an international treaty known as the ''Convention du Mètre'' (])<ref>{{cite web
|url = http://www.bipm.org/utils/en/pdf/metre_convention.pdf
|title = Convention du mètre
|language = French
|publisher = ] (BIPM)
|postscript = 1875 text plus 1907 and 1921 amendments
|accessdate = 22 March 2011}}</ref> was signed by 17 states. This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:<ref>{{cite web
|url = http://www.bipm.org/en/convention/
|title = The metre convention
|publisher = ] (BIPM)
|accessdate = 22 March 2011}}</ref>
* ] (CGPM),<ref name=French group=Note /> an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
* ] (CIPM),<ref name=French group=Note /> consisting of selected scientists and ]s, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures (BIPM);
* ] (BIPM),<ref name=French group=Note /> a permanent laboratory and world centre of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities and maintenance of the international prototype standards.

In 1881 first International Electrical Congress adopted the BAAS recommendations on electrical units, followed by a series of congresses in which further units of measure were defined and the ] (IEC) was set up with the specific task of overseeing electrical units of measure.<ref name=ieeeghn /> This was followed by the ] (ISR) who, at their inaugural meeting in 1926, initiated the definition of radiological-related units of measure.<ref name=ISR_History>{{cite web
|title=History
|first=Otha W
|last=Linton
|url=http://www.isradiology.org/isr/about_02.php
|accessdate=25 May 2012
|publisher=International Society of Radiology
|deadurl=yes
|archiveurl=https://web.archive.org/web/20120424025448/http://www.isradiology.org/isr/about_02.php
|archivedate=24 April 2012
|df=
}}</ref>
In 1921 the Metre Convention was extended to cover all units of measure, not just length and mass and in 1933 the 8th CGPM resolved to work with other international bodies to agree standards for electrical units that could be related back to the international prototypes.<ref>{{cite web
|url = http://www.bipm.org/en/CGPM/db/8/10/
|title = Résolution 10 de la 8e réunion de la CGPM (1933)—Substitution des unités électriques absolues aux unités dites " internationales "
|trans_title = Resolution 10 of the 8th meeting of the CGPM (1933)—Substitution of the so-called "International" electrical units by absolute electrical units
|language = French
|year = 1935
|publisher = Bureau International des Poids et Meseures
|accessdate = 2 October 2012}}</ref> Since 1954 the CIPM committee that oversees the definition of units of measurement, the ],<ref group=Note>The CCU was set up in 1964 to replace the Commission for the System of Units—a commission established in 1954 to advise on the definition of SI.</ref> has representatives from many international organisations including the ISR, IEC and ] under the chairmanship of the CIPM.<ref>{{cite web
|url=http://www.bipm.org/en/committees/cc/ccu/ccu_criteria.html
|title=Criteria for membership of the CCU
|publisher=]
|accessdate=9 April 2013
|deadurl=yes
|archiveurl=https://web.archive.org/web/20130514063919/http://www.bipm.org/en/committees/cc/ccu/ccu_criteria.html
|archivedate=14 May 2013
|df=
}}</ref>

== Variants ==
A number of variants of the metric system evolved, all using the ''Mètre des Archives'' and ''Kilogramme des Archives'' (or their descendants) as their base units, but differing in the definitions of the various derived units.
{| class="infobox bordered" style="font-size: 95%;"
|- style="border-bottom-width=0; background:lightblue;"
!align="center"|Variants of the metric system<!-- without gravitational ones, mechanical units-->
|-
|
{| class="wikitable"
! Quantity
! {{abbrlink|CGS|Centimetre–gram–second system of units}} ! {{abbrlink|CGS|Centimetre–gram–second system of units}}
! {{abbrlink|MKS|Metre–kilogram–second system of units}}
! {{abbrlink|MTS|Metre–tonne–second system of units}} ! {{abbrlink|MTS|Metre–tonne–second system of units}}
|- |-
|distance, displacement, |]
| metre {{br}}(m)
:length, height, etc.
| centimetre {{br}}(cm)
:(''d'', '''x''', ''l'', ''h'', etc.)
| metre {{br}}(m)
| ] (cm)
| ] (m)
| metre
|- |-
|mass (''m'') |]
| ] (g) | kilogram {{br}}(kg)
| gram {{br}}(g)
| ] (kg)
| ] (t) | ] {{br}}(t)
|- |-
|time (''t'') |]
| ] (s) | second {{br}}(s)
| second | second {{br}}(s)
| second | second {{br}}(s)
|- |-
|speed, velocity (''v'', '''v''') |]
| m/s
| cm/s | cm/s
| m/s
| m/s | m/s
|- |-
|acceleration (''a'') |]
| ]
| m/s<sup>2</sup> | m/s<sup>2</sup>
| ]
| m/s<sup>2</sup> | m/s<sup>2</sup>
|- |-
|force (''F'') |]
| ] (dyn)
| ] | ]
| ] (sn) | ] {{br}}(dyn)
| ] {{br}}(sn)
|- |-
|pressure (''P'' or ''p'') |]
| ] (Ba)
| ] | ]
| ] (pz) | ] {{br}}(Ba)
| ] {{br}}(pz)
|- |-
|]
|energy (''E'', ''Q'', ''W'')
| ] (erg) | ] {{br}}(J)
| ] (J) | ] {{br}}(erg)
| kilojoule (kJ) | kilojoule {{br}}(kJ)
|- |-
|]
|power (''P'')
| ] {{br}}(W)
| erg/s
| ] (W) | erg/s {{br}}(erg/s)
| kilowatt (kW) | kilowatt {{br}}(kW)
|- |-
|viscosity (''µ'') |]
| Pa⋅s
| ] (p)
| ] {{br}}(P)
| Pa·s
| pz·s | pz⋅s
|}
|} |}


=== Centimetre-gram-second systems === === 19th century ===
The ] (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874, this system was formally promoted by the ] (BAAS).<ref name=SI_1_8>{{SIBrochure8th|page=109}}</ref> The system's characteristics are that density is expressed in {{nowrap|g/cm<sup>3</sup>}}, force expressed in ]s and mechanical energy in ]s. Thermal energy was defined in ]s, one calorie being the energy required to raise the temperature of one gram of water from 15.5&nbsp;°C to 16.5&nbsp;°C. The meeting also proposed ] – the electrostatic set of units and the electromagnetic set of units.<ref>{{cite book In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the Earth, and together with the milligram and millimetre, this became ]. He showed that the strength of a magnet could also be quantified in terms of these units, by measuring the oscillations of a magnetised needle and finding the quantity of "magnetic fluid" that produces an acceleration of one unit when applied to a unit mass.<ref>{{Cite journal |last=O'Hara |first=James Gabriel |date=1983 |title=Gauss and the Royal Society: The Reception of His Ideas on Magnetism in Britain (1832-1842) |url=https://www.jstor.org/stable/531344 |journal=Notes and Records of the Royal Society of London |volume=38 |issue=1 |pages=17–78 |doi=10.1098/rsnr.1983.0002 |jstor=531344 |s2cid=145724822 |issn=0035-9149}}</ref><ref>{{Cite journal |last=Van Baak |first=D. A. |date=October 2013 |title=Re-creating Gauss's method for non-electrical absolute measurements of magnetic fields and moments |url=https://pubs.aip.org/aapt/ajp/article/81/10/738-744/1057517 |journal=American Journal of Physics |language=en |volume=81 |issue=10 |pages=738–744 |doi=10.1119/1.4816806 |bibcode=2013AmJPh..81..738V |issn=0002-9505}}</ref> The ] (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874, this system was formally promoted by the ] (BAAS).<ref name=SI_1_8>{{SIBrochure8th|page=109}}</ref> The system's characteristics are that density is expressed in {{nowrap|g/cm<sup>3</sup>}}, force expressed in ]s and mechanical energy in ]s. Thermal energy was defined in ]s, one calorie being the energy required to raise the temperature of one gram of water from 15.5&nbsp;°C to 16.5&nbsp;°C. The meeting also recognised ] – the electrostatic set of units and the electromagnetic set of units.<ref>{{cite book |title = Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science |chapter-url = https://archive.org/stream/reportscommitte00maxwgoog |chapter = First Report – Cambridge 3 October 1862 |pages = 1–3 |first1 = William |last1 =Thomson |first2 =James Prescott |last2 =Joule |first3 = James Clerk |last3 =Maxwell |first4 =Flemming |last4 =Jenkin |editor1-first = Flemming |editor1-last =Jenkin |location = London |year =1873 |access-date = 12 May 2011}}</ref>
|title = Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science
|url = https://archive.org/stream/reportscommitte00maxwgoog
|chapter = First Report – Cambridge 3 October 1862
|pages = 1–3
|first1 = William
|last1 =Thomson
|first2 =James Prescott
|last2 =Joule
|first3 = James Clerk
|last3 =Maxwell
|first4 =Flemming
|last4 =Jenkin
|editor1-first = Flemming
|editor1-last =Jenkin
|location = London
|year =1873
|accessdate = 12 May 2011}}</ref>


The CGS units of electricity were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the ], ] and ], in the ].<ref>{{cite web |url = http://physics.nist.gov/cuu/Units/ampere.html |title = Historical context of the SI—Unit of electric current (ampere) |publisher = The NIST Reference on Constants, Units and Uncertainty |access-date = 10 April 2011}}</ref> During the same period in which the CGS system was being extended to include electromagnetism, other systems were developed, distinguished by their choice of coherent base unit, including the ], or QES (quad–eleventhgram–second) system, was being used. Here, the base units are the quad, equal to {{val|e=7|u=m}} (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to {{val|e=-11|u=g}}, and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude.{{refn|{{citation |author=James Clerk Maxwell |year=1954 |orig-year=1891 |title=A Treatise on Electricity & Magnetism |volume=2 |edition=3rd | publisher=]}}}}{{rp|268}}{{refn|name="Carron Babel"|{{cite arXiv |last=Carron |first=Neal |eprint=1506.01951 |title= Babel of Units. The Evolution of Units Systems in Classical Electromagnetism |class= physics.hist-ph |date=2015 }}}}{{rp|17}}
=== Metre-kilogram-second systems ===
The CGS units of electricity were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the ], ] and ].<ref>{{cite web
|url = http://physics.nist.gov/cuu/Units/ampere.html
|title = Historical context of the SI—Unit of electric current (ampere)
|publisher = The NIST Reference on Constants, Units and Uncertainty
|accessdate = 10 April 2011}}</ref> In 1901, ] showed that by adding an electrical unit as a fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre-kilogram-second-] (MKSC) and metre-kilogram-second-] (MKSA) systems are examples of such systems.<ref name=IECGiorgi>{{cite web
|url = http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm
|title = In the beginning... Giovanni Giorgi
|year = 2011
|publisher = ]
|accessdate = 5 April 2011}}</ref>


=== 20th century ===
The ] (''Système international d'unités'' or SI) is the current international standard metric system and is also the system most widely used around the world. It is an extension of Giorgi's MKSA system—its base units are the metre, kilogram, second, ampere, ], ] and ].<ref name=SI_units />
In 1901, ] showed that by adding an electrical unit as a fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre–kilogram–second–] (MKSC) and metre–kilogram–second–] (MKSA) systems are examples of such systems.<ref name=IECGiorgi>{{cite web|url = http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm|title = In the beginning... Giovanni Giorgi|year = 2011
|publisher = ]|access-date = 5 April 2011|archive-date = 15 May 2011|archive-url = https://web.archive.org/web/20110515134553/http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm|url-status = dead}}</ref><ref name=":1">{{Cite journal |last=Jayson |first=Joel S. |date=January 2014 |title=The Daniell cell, Ohm's law, and the emergence of the International System of Units |url=https://pubs.aip.org/aapt/ajp/article/82/1/60-65/1058039 |journal=American Journal of Physics |language=en |volume=82 |issue=1 |pages=60–65 |arxiv=1512.07306 |doi=10.1119/1.4826445 |bibcode=2014AmJPh..82...60J |s2cid=119278961 |issn=0002-9505}}</ref>


The ] (MTS) was based on the metre, ] and second – the unit of force was the ] and the unit of pressure was the ]. It was invented in France for industrial use and from 1933 to 1955 was used both in France and in the ].<ref name=ieeeghn>{{cite web |url=http://www.ieeeghn.org/index.php/System_of_Measurement_Units |title = System of Measurement Units |work = IEEE Global History Network |publisher= ] (IEEE) |access-date = 21 March 2011}}</ref><ref>{{cite web |url = http://www.hydrelect.info/articles.php?lng=fr&pg=3 |title = Notions de physique – Systèmes d'unités |language = fr |trans-title=Symbols used in physics – units of measure |access-date = 21 March 2011 |publisher = Hydrelect.info}}</ref> ]s use the ] (kilopond) as a base unit of force, with mass measured in a unit known as the ], ''Technische Masseneinheit'' (TME), mug or ].<ref>
=== Metre-tonne-second systems ===
{{cite web
The ] (MTS) was based on the metre, ] and second – the unit of force was the ] and the unit of pressure was the ]. It was invented in France for industrial use and from 1933 to 1955 was used both in France and in the ].<ref name=ieeeghn>{{cite web
|url = http://www.ieeeghn.org/wiki/index.php/System_of_Measurement_Units |url = http://www.numericana.com/answer/units.htm#slug
|title = System of Measurement Units |title = Final Answers
|first1 = Gérard P
|work = IEEE Global History Network
|last1 = Michon
|publisher = ] (IEEE)
|publisher = Numericana.com
|accessdate = 21 March 2011}}</ref><ref>{{cite web
|date = 9 September 2000
|url = http://www.hydrelect.info/articles.php?lng=fr&pg=3
|access-date = 11 October 2012
|title = Notions de physique – Systèmes d'unités
}}</ref> Although the CGPM passed a resolution in 1901 defining the standard value of ] to be 980.665&nbsp;cm/s<sup>2</sup>, gravitational units are not part of the ] (SI).<ref>{{cite web
|language = French
|trans_title = Symbols used in physics – units of measure
|accessdate = 21 March 2011
|publisher = Hydrelect.info}}</ref>

=== Gravitational systems ===
]s use the ] (kilopond) as a base unit of force, with mass measured in a unit known as the ], ''Technische Mass Einheit'' (TME), mug or ].<ref>{{cite web
|url = http://www.numericana.com/answer/units.htm#slug
|title = Final Answers
|first1 = Gérard P
|last1 = Michon
|publisher = Numericana.com
|date = 9 September 2000
|accessdate = 11 October 2012}}</ref> Although the CGPM passed a resolution in 1901 defining the standard value of ] to be 980.665&nbsp;cm/s<sup>2</sup>, gravitational units are not part of the ] (SI).<ref>{{cite web
|url = http://www.bipm.org/en/CGPM/db/3/2/ |url = http://www.bipm.org/en/CGPM/db/3/2/
|title = Resolution of the 3rd meeting of the CGPM (1901) |title = Resolution of the 3rd meeting of the CGPM (1901)
|publisher = General Conference on Weights and Measures |publisher = General Conference on Weights and Measures
|accessdate = 11 October 2012}}</ref> |access-date = 11 October 2012}}</ref>


===Current===
=== International System of Units ===
The International System of Units is the modern metric system. It is based on the metre–kilogram–second–ampere (MKSA) system of units from early in the 20th century.<ref name=SI_units /> It also includes numerous coherent derived units for common quantities like power (watt) and irradience (lumen). Electrical units were taken from the International system then in use. Other units like those for energy (joule) were modelled on those from the older CGS system, but scaled to be coherent with MKSA units. Two additional base units – the ''kelvin'', which is equivalent to degree Celsius for change in thermodynamic temperature but set so that 0&nbsp;K is ], and the ''candela'', which is roughly equivalent to the ] unit of illumination – were introduced. Later, another base unit, the ''mole'', a unit of ] equivalent to the ] number of specified molecules, was added along with several other derived units.<ref name="Gold Book mole">{{Cite book |url=https://goldbook.iupac.org/terms/view/M03980 |title=IUPAC – mole (M03980) |author=IUPAC Gold Book |publisher=]|doi=10.1351/goldbook.M03980 |s2cid=241546445 }}</ref>
{{Main|International System of Units|List of physical quantities}}
'']]
The 9th CGPM met in 1948, three years after the end of the ] and fifteen years after the 8th CGPM. In response to formal requests made by the ] and by the ] to establish a practical system of units of measure, the CGPM requested the CIPM to prepare recommendations for such a system, suitable for adoption by all countries adhering to the Metre Convention. The recommendation also catalogued symbols for the most important ] and ] units of measure and for the first time the CGPM made recommendations concerning derived units.<ref>{{cite conference
|url = http://www.bipm.org/en/CGPM/db/9/6/
|title = Resolution 6—Proposal for establishing a practical system of units of measurement
|conference = 9th Conférence Générale des Poids et Mesures (CGPM)
|date = 12–21 October 1948
|accessdate = 8 May 2011}}</ref> At the same time the CGPM formally adopted a recommendation for the writing and printing of unit symbols and of numbers.<ref>{{cite conference
|url = http://www.bipm.org/en/CGPM/db/9/7/
|title = Resolution 7—Writing and printing of unit symbols and of numbers
|conference = 9th Conférence Générale des Poids et Mesures (CGPM)
|date = 12–21 October 1948
|accessdate = 8 May 2011}}</ref>


The system was promulgated by the General Conference on Weights and Measures (French: ''Conférence générale des poids et mesures'' – CGPM) in 1960. At that time, the metre was redefined in terms of the wavelength of a spectral line of the ] atom (krypton-86 being a stable isotope of an inert gas that occurs in undetectable or trace amounts naturally), and the standard metre artefact from 1889 was retired.<ref name=":0">{{cite book|last1=Urone |first1=Peter Paul |last2=Hinrichs |first2=Roger |last3=Dirks |first3=Kim |last4=Sharma |first4=Manjula |title=College Physics |publisher=OpenStax |isbn=978-1-947172-01-2 |year=2020 |url=https://openstax.org/details/books/college-physics}}</ref>{{rp|16}}
The CIPM's draft proposal, which was an extensive revision and simplification of the metric unit definitions, symbols and terminology based on the MKS system of units, was put to the 10th CGPM in 1954. In accordance with Giorgi's proposals of 1901, the CIPM also recommended that the ampere be the base unit from which electromechanical units would be derived. The definitions for the ohm and volt that had previously been in use were discarded and these units became derived units based on the metre, ampere, second and kilogram. After negotiations with the ] (CIE)<ref name=French group=Note /> and IUPAP, two further base units, the degree kelvin and the candela were also proposed as base units.<ref>{{cite conference
|url = http://www.bipm.org/en/CGPM/db/10/6/
|title = Resolution 6 – Practical system of units
|conference = 10th Conférence Générale des Poids et Mesures (CGPM)
|date = 5–14 October 1954
|accessdate = 8 May 2011}}</ref> The full system and name "Système International d'Unités" were adopted at the 11th CGPM in October 1960.<ref>{{cite conference
|url = http://www.bipm.org/en/CGPM/db/11/12/
|title = Resolution 12—Système International d'Unités
|conference = 11th Conférence Générale des Poids et Mesures (CGPM)
|date = 11–20 October 1960
|accessdate = 8 May 2011}}</ref> During the years that followed the definitions of the base units and particularly the methods of applying these definitions have been refined.<ref>{{cite web
|url = http://www.bipm.org/en/si/si_brochure/appendix2/
|title = Practical realization of the definitions of some important units
|work = SI brochure, Appendix 2
|publisher = BIPM
|date = 9 September 2010
|accessdate = 5 May 2011}}</ref>


Today, the International system of units consists of 7 base units and innumerable coherent derived units including 22 with special names. The last new derived unit, the ''katal'' for catalytic activity, was added in 1999. All the base units except the second are now defined in terms of exact and invariant constants of physics or mathematics, barring those parts of their definitions which are dependent on the second itself. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as {{frac|299,792,458}} of the distance light travels in a second. The kilogram was defined by a ] until a ] in terms of ] was adopted in 2019. As of 2022, the range of decimal prefixes has been extended to those for 10<sup>30</sup> (''quetta–'') and 10<sup>−30</sup> (''quecto–'').<ref>{{cite web |url=https://www.theregister.com/2022/11/22/new_si_prefixes_clear_the/|title=New SI prefixes clear the way for quettabytes of storage|date=22 November 2022|publisher=The Register|access-date=23 Nov 2022|df=dmy-all}}</ref>
The formal definition of International System of Units (SI) along with the associated resolutions passed by the CGPM and the CIPM are published by the BIPM in brochure form at regular intervals. The eighth edition of the brochure ''Le Système International d'Unités—The International System of Units'' was published in 2006 and is available on the internet.<ref>{{SIbrochure8th}}</ref>
In October 2011, at the 24th ] proposals were made to change the ] of four of the base units. These changes should not affect the average person.<ref name="draft">{{cite web
|url = http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf
|title = Draft Chapter 2 for SI Brochure, following redefinitions of the base units
|author = Ian Mills
|publisher = CCU
|date = 29 September 2010
|accessdate = 1 January 2011}}</ref>

== Relating SI to the real world ==
{{Main|Non-SI units mentioned in the SI}}
Although SI, as published by the CGPM, should, in theory, meet all the requirements of commerce, science and technology, certain units of measure have acquired such a position within the world community that it is likely they will be used for many years to come. In order that such units are used consistently around the world, the CGPM catalogued such units in Tables 6 to 9 of the SI brochure. These categories are:<ref>{{SIBrochure8th|pages=124–129}}</ref>
* '''Non-SI units accepted for use with the International System of Units (Table 6)'''. This list includes the hour and minute, the angular measures (degree, minute and second of arc) and the historic metric units, the ], ] and ] (originally agreed by the CGPM in 1879)
* '''Non-SI units whose values in SI units must be obtained experimentally (Table 7)'''. This list includes various units of measure used in atomic and nuclear physics and in astronomy such as the ], the ], the ], the ], the ], and a number of other units of measure that are well-established, but dependent on experimentally-determined physical quantities.
* '''Other non-SI units (Table 8)'''. This list catalogues a number of units of measure that have been used internationally in certain well-defined spheres including the ] for pressure, the ] for ], the ] and the ] in ].
* '''Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9)'''. This table catalogues a number of units of measure based on the CGS system and dating from the nineteenth century. They appear frequently in the literature, but their continued use is discouraged by the CGPM.

== Usage around the world ==
{{further|Metrication}}
{{Overcolored|date=February 2015}}
]
The usage of the metric system varies around the world. According to the US Central Intelligence Agency's '']'' (2007), the International System of Units has been adopted as the official system of weights and measures by all nations in the world except for ] (Burma), ] and the United States,<ref name="World Factbook">{{cite web
|title = The World Factbook
|year = 2007 <!-- as per https://www.cia.gov/library/publications/the-world-factbook/docs/history.html -->
|location = Washington
|publisher = ]
|accessdate = 15 February 2013
|url = https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html
|quote = At this time, only three countries – Burma, Liberia, and the US – have not adopted the International System of Units (SI, or metric system) as their official system of weights and measures.}}</ref> while the ] has identified the United States as the only industrialised country where the metric system is not the predominant system of units.<ref>{{cite web |url=http://www.nist.gov/pml/wmd/metric/upload/1136a.pdf
|title=The United States and the metric system
|accessdate=2 November 2011
|quote=The United States is now the only industrialized country in the world that does not use the metric system as its predominant system of measurement.
|publisher=]}}</ref> However, reports published since 2007 hold this is no longer true of Myanmar or Liberia.<ref>{{cite web
|url = http://www.cl.cam.ac.uk/~mgk25/metric-system-faq.txt
|first1 = Markus
|last1 = Kuhn
|title = Metric System FAQ
|publisher = misc.metric-system Newsgroup
|date = 1 December 2009
|accessdate = 20 September 2011|authorlink1 = Markus Kuhn (computer scientist)
}}</ref> An ] report from 2010 stated that ] had passed a law to replace the ] with the metric system thereby aligning its system of measurement with that used by its ] (MRU) neighbours ] and Liberia.<ref group = Note>According to the ] report (2010) Liberia was metric, but Sierra Leone was not metric—a statement that conflicted with the CIA statement (2007).</ref><ref>{{cite web|url=https://www.google.com/hostednews/afp/article/ALeqM5jOO4s5CJG1MDuclJeYKyPmNlrBww |archive-url=https://archive.is/20130125081623/http://www.google.com/hostednews/afp/article/ALeqM5jOO4s5CJG1MDuclJeYKyPmNlrBww |dead-url=yes |archive-date=25 January 2013 |title=S.Leone goes metric after 49 years |date=11 June 2010 |publisher=] |accessdate=22 October 2011 }}</ref> Reports from Myanmar suggest that the country is also planning to adopt the metric system.<ref>{{cite news |title= Ditch the viss, govt urges traders
|author= Ko Ko Gyi
|url= http://www.mmtimes.com/2011/business/584/biz58401.html
|archiveurl=https://web.archive.org/web/20111118000916/http://www.mmtimes.com/2011/business/584/biz58401.html
|newspaper= ]
|date= 18–24 July 2011
|accessdate=23 July 2011
|archivedate=18 November 2011
}}</ref>

In the United States metric units, authorised by ] in 1866,<ref name="H.R. 596">{{cite web
|url=http://lamar.colostate.edu/~hillger/laws/metric-act-bill.html
|title=H.R. 596, An Act to authorize the use of the metric system of weights and measures
|author=29th Congress of the United States, Session 1
|date=13 May 1866
|accessdate=27 October 2011
|deadurl=yes
|archiveurl=https://web.archive.org/web/20150705015307/http://lamar.colostate.edu/~hillger/laws/metric-act-bill.html
|archivedate=5 July 2015
|df=
}}</ref> are widely used in science, medicine, military, and partially in industry, but ] predominate in household use. At retail stores the litre is a commonly used unit for volume, especially on bottles of beverages, and milligrams are used to denominate the amounts of medications, rather than grains.<ref>{{cite news
|url = http://chronicle.augusta.com/life/life-style/2013-04-04/metric-system-use-rise-us
|title = Metric system use on the rise in the U.S.
|first1 = Kelly
|last1 = Jasper
|date = 4 April 2013
|accessdate = 24 April 2013
|newspaper = ]}}</ref><ref>{{cite book
|url = https://books.google.com/?id=ZlKqGHGNrtIC&pg=PA55&lpg=PA55&dq=grams+grains+medication#v=onepage&q=grams%20grains%20medication&f=false
|title = Henke's Med-Math: Dosage Calculation, Preparation & Administration
|first1 = Susan
|last1 = Buchholz
|first2 = Grace
|last2 = Henke
|page = 55
|edition = Sixth
|year = 2009
|isbn = 978-0-7817-7628-8
|publisher = Wolters Kluwer and Lippincott Williams & Wilkins
|accessdate = 24 April 2013}}</ref> On the other hand, non-metric units are used in certain regulated environments such as ]s and ] in international aviation. Resistance to metrication, particularly in the UK and the US, has been connected to the perceived cost involved, a sense of patriotism and lack of desire to conform internationally.<ref name="BBC2011"/><ref>. Time. Retrieved 6 October 2015</ref><ref>. CNBC. Retrieved 6 October 2015</ref>

In the countries of the ] the metric system has replaced the ] by varying degrees: ], ] and Commonwealth countries in Africa are almost totally metric, ] while ]. In the United Kingdom, ], the use of which was first permitted for trade in 1864, is used in much government business, in most industries including building, health and engineering and for pricing by measure or weight in most trading situations, both wholesale and retail.<ref>{{cite web
|url=http://lamar.colostate.edu/~hillger/internat.htm
|title=Metric usage and metrication in other countries
|publisher=U.S. Metric Association
|date=22 July 2009
|accessdate=9 September 2011
|deadurl=yes
|archiveurl=https://web.archive.org/web/19990221223050/http://lamar.colostate.edu/~hillger/internat.htm
|archivedate=21 February 1999
|df=
}}</ref> However the imperial system is widely used by the British public, such as feet and inches as a measurement of height, weight in stone and pounds, and is legally mandated in various cases, such as road-sign distances, which must be given in yards and miles.<ref name=Alder /><ref name="BBC2011">{{cite news
|title=Will British people ever think in metric?
|url=http://www.bbc.co.uk/news/magazine-16245391
|publisher=BBC
|date=21 December 2011
|first1=Jon
|last1=Kelly
|quote=...but today the British remain unique in Europe by holding onto imperial weights and measures. Call it a proud expression of national identity or a stubborn refusal to engage with the neighbours, the persistent British preference for imperial over metric is particularly noteworthy...}}</ref><ref name=WMroads>{{cite web |url=http://www.bwmaonline.com/Transport%20-%20DfT%20memo.htm |title=Department for Transport statement on metric road signs |accessdate=24 August 2009|date=12 July 2002 |format=online |publisher=BWMA }}</ref> In 2007, the European Commission announced that it was to abandon the requirement for metric-only labelling on packaged goods in the UK, and to allow dual metric–imperial marking to continue indefinitely.<ref>{{Cite news |url=http://news.bbc.co.uk/1/hi/uk/6988521.stm |title=EU gives up on 'metric Britain
|publisher=BBC News
|accessdate=8 March 2015
|date=11 September 2007}}</ref>

Some other jurisdictions, such as Hong Kong, have laws mandating or permitting other systems of measurement in parallel with the metric system in some or all contexts.<ref name="HK">{{cite web
|url = http://www.legislation.gov.hk/blis_ind.nsf/d2769881999f47b3482564840019d2f9/ca7c0e7895c7f088c82564760077b0c9?OpenDocument
|title = HK Weights and Measures Ordinance
|accessdate = 20 September 2011}}</ref>

{{anchor|Symbol|Symbols}}<!--linked-->
=== Variations in spelling ===
The SI symbols for the metric units are intended to be identical, regardless of the language used<ref name=noun>{{SIBrochure8th|page=130}}</ref> but unit names are ] and use the character set and follow the grammatical rules of the language concerned. For example, the SI unit symbol for kilometre is "km" everywhere in the world, even though the local language word for the unit name may vary. Language variants for the kilometre unit name include: ''{{lang|it|chilometro}}'' (Italian), ''{{lang|de|Kilometer}}'' (German),<ref group=Note>In German all nouns start with an upper-case letter</ref> ''{{lang|nl|kilometer}}'' (Dutch), ''{{lang|fr|kilomètre}}'' (French), ''{{lang|el|χιλιόμετρο}}'' (Greek), ''{{lang|pt|quilómetro/quilômetro}}'' (Portuguese), ''{{lang|es|kilómetro}}'' (Spanish) and ''{{lang|bg|километр}}'' (Russian).<ref>{{cite web
|url = http://translation.babylon.com/
|title = Online Translation—Offering hundreds of dictionaries and translation in more than 800 language pairs
|publisher = Babylon
|accessdate = 5 February 2011}}</ref><ref>{{citation
| author = Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2).
| publisher = ] (BIPM) on behalf of the Joint Committee for Guides in Metrology
| year = 2008
| url = http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
| title = International vocabulary of metrology — Basic and general concepts and associated terms (VIM)
| edition = 3rd
|accessdate = 5 March 2011
| page = 9}}</ref>

Variations are also found with the spelling of unit names in countries using the same language, including differences in ]. For example, ''meter'' and ''liter'' are used in the United States whereas ''metre'' and ''litre'' are used in other English-speaking countries. In addition, the official US spelling for the rarely used ] is ''deka''. In American English the term ''metric ton'' is the normal usage whereas in other varieties of English ''tonne'' is common. ''Gram'' is also sometimes spelled ''gramme'' in English-speaking countries other than the United States, though this older usage is declining.<ref>{{cite web
|url=http://www.statutelaw.gov.uk/content.aspx?activeTextDocId=2191980
|title=Weights and Measures Act 1985 (c. 72)
|work=The UK Statute Law Database
|publisher=Office of Public Sector Information
|quote=§&nbsp;92.
|accessdate=26 January 2011
|deadurl=yes
|archiveurl=https://web.archive.org/web/20080912105635/http://www.statutelaw.gov.uk/content.aspx?activeTextDocId=2191980
|archivedate=12 September 2008
|df=
}}</ref>

=== Conversion and calculation incidents ===
The dual usage of or confusion between metric and non-metric units has resulted in a number of serious incidents. These include:
* Flying an overloaded American International Airways aircraft from ], ] to ], ] on 26 May 1994. The degree of overloading was consistent with ground crew reading the kilogram markings on the cargo as pounds.<ref>{{cite web
|url = http://www.ntsb.gov/alj/O_n_O/docs/AVIATION/4510.pdf
|title = NTSB Order No. EA-4510
|year = 1996
|location = Washington, D.C.
|publisher = ]
|accessdate = 3 August 2008}}</ref>
* In 1999 the ] reported that confusion between ] and grams led to a patient receiving ] 0.5&nbsp;grams instead of 0.5 grains (0.03&nbsp;grams) after the practitioner misread the prescription.<ref>{{cite web
|url = http://www.ismp.org/Newsletters/acutecare/articles/A3Q99Action.asp
|title = ISMP Medication Safety Alert''
|date = 14 July 1999
|publisher = ]
|accessdate = 3 August 2008}}</ref>
* The Canadian "]" accident in 1983, when a ] jet ran out of fuel in mid-flight because of two mistakes made when calculating the fuel supply of ]'s first aircraft to use metric measurements: mechanics miscalculated the amount of fuel required by the aircraft as a result of their unfamiliarity with metric units.<ref>{{cite journal
|url = http://www.skybrary.aero/bookshelf/books/1116.pdf
|title = The 156-tonne Gimli Glider
|first1 = Merran
|last1 = Williams
|pages= 22–27
|journal = Flight Safety Australia
|date = July–August 2003
|accessdate = 4 December 2012}}</ref>
* The root cause of the loss in 1999 of ]'s US$125 million ] was a mismatch of units – the spacecraft engineers calculated the thrust forces required for velocity changes using US customary units (lbf·s) whereas the team who built the thrusters were expecting a value in metric units (N·s) as per the agreed specification.<ref>{{cite news |title=NASA's metric confusion caused Mars orbiter loss |url=http://www.cnn.com/TECH/space/9909/30/mars.metric/
|publisher=CNN |date=30 September 1999
|accessdate=21 August 2007 }}</ref><ref>{{cite web
|url = ftp://ftp.hq.nasa.gov/pub/pao/reports/1999/MCO_report.pdf
|title = Mars Climate Orbiter; Mishap Investigation Board; Phase I Report
|date = 10 November 1999
|publisher = ]
|accessdate=25 August 2011}}</ref>

== Conversion between SI and legacy units ==
{{Main|Conversion of units}}
During its evolution, the metric system has adopted many units of measure. The introduction of SI rationalised both the way in which units of measure were defined and also the list of units in use. These are now catalogued in the official SI Brochure.<ref name=SI_units>{{SIbrochure8th|pages = 111–120}}</ref> The table below lists the units of measure in this catalogue and shows the conversion factors connecting them with the equivalent units that were in use on the eve of the adoption of SI.<ref>{{cite web
|url=http://sizes.com/units/index.php
|title=Index to Units & Systems of Units
|publisher=sizes.com
|accessdate=9 April 2011
|deadurl=yes
|archiveurl=https://web.archive.org/web/20120826122354/http://www.sizes.com/units/index.php
|archivedate=26 August 2012
|df=
}}</ref><ref>{{cite web
|url = http://physics.nist.gov/Pubs/SP811/appenB8.html
|title = Factors for Units Listed Alphabetically
|work = NIST Guide to the SI
|date = 2 July 2009
|accessdate = 14 April 2011}}</ref><ref>{{GreenBook2nd|pages=110–116}}.</ref><ref>{{cite book
|title = Oxford Dictionary of Weights, Measures and Units
|first1 = Donald
|last1 = Fenna
|publisher = ]
|year = 2002
|location = ]
|isbn = 0-19-860522-6}}</ref>

{| class="wikitable" style="margin:1em auto 1em auto;line-height:1.4"
!Quantity
!Dimension
!SI unit and symbol
!Legacy unit and symbol
!Conversion <br />{{nowrap|factor}}
|-
| ]
|align="center"|''T''
| ] (s)
| second (s)
|align="center"|1
|-
| ]
|align="center"|''L''
| ] (m)
| ] (cm)<br />] (Å)
|align="center"|0.01 <br />10<sup>−10</sup>
|-
| ]
|align="center"|''M''
| ] (kg)
| ] (g)
|align="center"|0.001
|-
|]
|align="center"|''I''
|] (A)
|]<br />] or ]<br />]
|align="center"|{{val|1.000022}}<br />10.0<br />{{val|3.335641|e=-10}}
|-
|]
|align="center"|''Θ''
| ] (K)<br /> ] (°C)
| ] (°C)
|align="center"| = + 273.15<br />1
|-
|]
|align="center"|''J''
| ] (cd)
| ]
|align="center"|0.982
|-
|]
|align="center"|''N''
|] (mol)
|No legacy unit
|align="center"|n/a
|-
| ]
|align="center"|''L''<sup>2</sup>
| ] (m<sup>2</sup>)
| ] (are)
|align="center"|100
|-
| ]
|align="center"|''LT''<sup>−2</sup>
| (m·s<sup>−2</sup>)
| gal (gal)
|align="center"|10<sup>−2</sup>
|-
|]
|align="center"|''T''<sup>−1</sup>
| ] (Hz)
| cycles per second
|align="center"| 1
|-
|]
|align="center"|''L''<sup>2</sup>''MT''<sup>−2</sup>
| ] (J)
| ] (erg)
|align="center"|10<sup>−7</sup>
|-
|]
|align="center"|''L''<sup>2</sup>''MT''<sup>−3</sup>
| ] (W)
| (erg/s)<br />] (HP)<br />Pferdestärke (PS)
|align="center"|10<sup>−7</sup><br />745.7<br />735.5
|-
|]
|align="center"|''LMT''<sup>−2</sup>
| ] (N)
| ] (dyn)<br /> ] (sn)<br />] (kp)
|align="center"|10<sup>−5</sup><br /> 10<sup>3</sup><br /> {{val|9.80665}}
|-
|]
|align="center"|''L''<sup>−1</sup>''MT''<sup>−2</sup>
| ] (Pa)
| ] (Ba)<br /> ] (pz)<br /> ] (at)
|align="center"|0.1<br /> 10<sup>3</sup><br />{{val|1.01325|e=5}}
|-
|]
|align="center"|''IT''
| ] (C)
| ]<br />] or franklin
|align="center"|10<br />{{val|3.335641|e=-10}}
|-
|]
|align="center"|''L''<sup>2</sup>''MT''<sup>−3</sup>''I''<sup>−1</sup>
| ] (V)
| ]<br />]<br />]
|align="center"|{{val|1.00034}}<br />10<sup>−8</sup><br />{{val|2.997925|e=2}}
|-
|]
|align="center"|''L''<sup>−2</sup>''M''<sup>−1</sup>''T''<sup>4</sup>''I''<sup>2</sup>
| ] (F)
| abfarad<br />statfarad
|align="center"|10<sup>9</sup><br />{{val|1.112650|e=-12}}
|-
|]
|align="center"|''L''<sup>2</sup>''MT''<sup>−2</sup>''I''<sup>−2</sup>
| ] (H)
| ]<br />]
|align="center"|10<sup>−9</sup><br />{{val|8.987552|e=11}}
|-
|]
|align="center"|''L''<sup>2</sup>''MT''<sup>−3</sup>''I''<sup>−2</sup>
| ] (Ω)
| international ohm<br />]<br />]
|align="center"|{{val|1.00049}}<br />10<sup>−9</sup><br />{{val|8.987552|e=11}}
|-
|]
|align="center"|''L''<sup>−2</sup>''M''<sup>−1</sup>''T''<sup>3</sup>''I''<sup>2</sup>
| ] (S)
| ] (℧)<br />]<br />]
|align="center"|{{val|0.99951}}<br />10<sup>9</sup><br />{{val|1.112650|e=-12}}
|-
|]
|align="center"|''L''<sup>2</sup>''MT''<sup>−2</sup>''I''<sup>−1</sup>
| ] (Wb)
| ] (Mx)
|align="center"|10<sup>−8</sup>
|-
|]
|align="center"|''MT''<sup>−2</sup>''I''<sup>−1</sup>
| ] (T)
| ] (G)
|align="center"|10<sup>−4</sup>
|-
|] strength
|align="center"|''IL''<sup>−1</sup>
| (A/m)
| ] (Oe)
|align="center"|{{frac|10<sup>3</sup>|4''π''}} = {{val|79.57747}}
|-
|]
|align="center"|''ML''<sup>−1</sup>''T''<sup>−1</sup>
| (Pa·s)
| ] (P)
|align="center"|0.1
|-
|]
|align="center"|''L''<sup>2</sup>''T''<sup>−1</sup>
| (m<sup>2</sup>·s<sup>−1</sup>)
| ] (St)
|align="center"|10<sup>−4</sup>
|-
| ]
|align="center"|''J''
| ] (lm)
| ] (sb)
|align="center"|10<sup>4</sup>
|-
|]
|align="center"|''JL''<sup>−2</sup>
| ] (lx)
| ] (ph)
|align="center"|10<sup>4</sup>
|-
| ]
|align="center"|''T''<sup>−1</sup>
| ] (Bq)
| ] (Ci)
|align="center"|{{val|3.70|e=10}}
|-
| dose]]
|align="center"|''L''<sup>2</sup>''T''<sup>−2</sup>
| ] (Gy)
| ] (R)<br />] (rad)
|align="center"|≈0.01<ref group=Note>] is a measure of ionisation (charge per mass), not of absorbed dose, so there is no well-defined conversion factor. However, a radiation field of gamma rays that produces 1 roentgen of ionisation in dry air would deposit 0.0096 gray in soft tissue, and between 0.01 and 0.04 grays in bone. Since this unit was often used in radiation detectors, a factor of 0.01 can be used to convert the detector reading in roentgens to the approximate absorbed dose in grays.</ref><br />0.01
|-
|]
|align="center"|''L''<sup>2</sup>''T''<sup>−2</sup>
| ]
| ] (rem)
|align="center"|0.01
|-
|]
|align="center"|''NT''<sup>−1</sup>
|] (kat)
| No legacy unit
|align="center"|n/a
|-
|}

The SI Brochure also catalogues certain non-SI units that are widely used with the SI in matters of everyday life or units that are exactly defined values in terms of SI units and are used in particular circumstances to satisfy the needs of commercial, legal, or specialised scientific interests. These units include:<ref name=SI_units />

{| class="wikitable" style="margin:1em auto 1em auto;line-height:1.4"
!Quantity
!Dimension
!Unit and symbol
!Equivalence
|-
| ]
|align="center"|''M''
| ] (t)
|align="center"|{{val|1000|u=kg}}
|-
| ]
|align="center"|''L''<sup>2</sup>
| ] (ha)
|align="center"|0.01&nbsp;km<sup>2</sup><br />10<sup>4</sup> m<sup>2</sup>
|-
| ]
|align="center"|''L''<sup>3</sup>
| ] (L or l)
|align="center"|0.001 m<sup>3</sup>
|-
| ]
|align="center"|''T''
| ] (min)<br />] (h)<br />] (d)
|align="center"|60&nbsp;s<br />{{val|3600|u=s}}<br />{{val|86400|u=s}}
|-
| ]
|align="center"|''L''<sup>−1</sup>''MT''<sup>−2</sup>
| ]
| 100 kPa
|-
| ]
|align="center"|''none''
| ] (°)<br />] (ʹ)<br />second (″)
|align="center"|({{frac|''π''|180}}) rad<br />({{frac|''π''|{{val|10800}}}}) rad<br />({{frac|''π''|{{val|648000}}}}) rad
|}

== Future developments ==
{{Main|Proposed redefinition of SI base units}}
]

After the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artefact. After the 1996–1998 recalibrations a clear divergence between the international and various national prototype kilograms was observed.<ref>{{cite web
|url = http://physics.vniim.ru/SI50/files/mohr.pdf
|author = Peter Mohr
|title = Recent progress in fundamental constants and the International System of Units
|work = Third Workshop on Precision Physics and Fundamental Physical Constants
|date = 6 December 2010
|accessdate = 2 January 2011}}</ref>

At the 23rd CGPM (2007), the CIPM was mandated to investigate the use of natural constants as the basis for all units of measure rather than the artefacts that were then in use. At a meeting of the CCU held in ] in September 2010, a resolution<ref>{{cite web
|url = http://www.bipm.org/utils/en/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf
|title = On the possible future revision of the International System of Units, the SI
|author = Ian Mills
|publisher = CCU
|date = 29 September 2010
|accessdate = 1 January 2011}}</ref> and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle.<ref name="draft" /> The CCU proposed to
* in addition to the speed of light, define four constants of nature—], an ], ] and ] – to have exact values
* retire the international prototype kilogram
* revise the current definitions of the kilogram, ], ] and ] to make use of the above four constants of nature
* tighten the wording of the definitions of all the base units

The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time".<ref>{{cite web
|url = http://www.bipm.org/en/si/new_si/
|title = Towards the "new SI"
|publisher = ] (BIPM)
|accessdate = 20 February 2011}}</ref> The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed in principle and which were expected to be finalised at the 25th CGPM in 2014.<ref>{{cite conference
|url= http://www.bipm.org/utils/en/pdf/24_CGPM_Resolution_1.pdf
|title= Resolution 1—On the possible future revision of the International System of Units, the SI
|conference= 24th meeting of the General Conference on Weights and Measures
| location = Sèvres, France
| date = 17–21 October 2011
| accessdate = 25 October 2011}}</ref>


== See also == == See also ==
* ], used in computer science * {{Annotated link|Binary prefix}}
* ] * {{Annotated link|Electrostatic units}}
* ] * {{Annotated link|History of measurement}}
* {{Annotated link|ISO 31}}
* ], style manual for measurements metric and non-metric, superseding ]
* {{Annotated link|ISO/IEC 80000}}
* ], the process of introducing the SI metric system as the worldwide standard for physical measurements
* {{Annotated link|List of metric units}}
** ]
* ] * {{Annotated link|Metrology}}
* {{Annotated link|Non-SI units mentioned in the SI}}
* ]
* {{Annotated link|Outline of metrology and measurement}}

* {{Annotated link|Preferred metric sizes}}
== Notes ==
* {{Annotated link|Unified Code for Units of Measure}}
{{Reflist|group=Note}}


== References == == References ==
{{Reflist|30em}} {{reflist}}


== External links == == External links ==
{{Wikiversity|Using the Metric System}} * {{Wikiversity inline|Using the Metric System}}
* For Good Measure: Canada Converts to Metric
* Metrication in other countries


{{systems of measurement}} {{systems of measurement}}
{{systems}}
{{French Revolution navbox}} {{French Revolution navbox}}


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]
] ]
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Latest revision as of 18:31, 2 January 2025

Decimal-based systems of measurement with 7 base units defined by physical constants

For a topical guide, see Outline of the metric system.
A kilogram mass and three metric measuring devices: a tape measure in centimetres, a thermometer in degrees Celsius, and a multimeter that measures potential in volts, current in amperes and resistance in ohms.

The metric system is a system of measurement that standardizes a set of base units and a nomenclature for describing relatively large and small quantities via decimal-based multiplicative unit prefixes. Though the rules governing the metric system have changed over time, the modern definition, the International System of Units (SI), defines the metric prefixes and seven base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).

An SI derived unit is a named combination of base units such as hertz (cycles per second), newton (kg⋅m/s), and tesla (1 kg⋅s⋅A) and in the case of Celsius a shifted scale from Kelvin. Certain units have been officially accepted for use with the SI. Some of these are decimalised, like the litre and electronvolt, and are considered "metric". Others, like the astronomical unit are not. Ancient non-metric but SI-accepted multiples of time, minute and hour, are base 60 (sexagesimal). Similarly, the angular measure degree and submultiples, arcminute, and arcsecond, are also sexagesimal and SI-accepted.

The SI system derives from the older metre, kilogram, second (MKS) system of units, though the definition of the base units has evolved over time. Today, all base units are defined by physical constants; not by example as physical objects as they were in the past.

Other metric system variants include the centimetre–gram–second system of units, the metre–tonne–second system of units, and the gravitational metric system. Each has unaffiliated metric units. Some of these systems are still used in limited contexts.

Adoption

Units in everyday use by country as of 2019

The SI system has been adopted as the official system of weights and measures by most countries in the world.

A notable outlier is the United States (US). Although used in some contexts, the US has resisted full adoption; continuing to use "a conglomeration of basically incoherent measurement systems".

Adopting the metric system is known as metrication.

Multiplicative prefixes

Main article: Metric prefix

In the SI system and generally in older metric systems, multiples and fractions of a unit can be described via a prefix on a unit name that implies a decimal (base-10), multiplicative factor. The only exceptions are for the SI-accepted units of time (minute and hour) and angle (degree, arcminute, arcsecond) which, based on ancient convention, use base-60 multipliers.

Metric prefixes in everyday use
Prefix Symbol Factor Power
tera T 1000000000000 10
giga G 1000000000 10
mega M 1000000 10
kilo k 1000 10
hecto h 100 10
deca da 10 10
(none) (none) 1 10
deci d 0.1 10
centi c 0.01 10
milli m 0.001 10
micro μ 0.000001 10
nano n 0.000000001 10
pico p 0.000000000001 10

The prefix kilo, for example, implies a factor of 1000 (10), and the prefix milli implies a factor of 1/1000 (10). Thus, a kilometre is a thousand metres, and a milligram is one thousandth of a gram. These relations can be written symbolically as:

1 km = 1000 m 1 mg = 0.001 g

Base units

The decimalised system is based on the metre, which had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body.

The historical evolution of metric systems has resulted in the recognition of several principles. A set of independent dimensions of nature is selected, in terms of which all natural quantities can be expressed, called base quantities. For each of these dimensions, a representative quantity is defined as a base unit of measure. The definition of base units has increasingly been realised in terms of fundamental natural phenomena, in preference to copies of physical artefacts. A unit derived from the base units is used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which is derived from length. These derived units are coherent, which means that they involve only products of powers of the base units, without any further factors. For any given quantity whose unit has a name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the second; the unit of length should be either the metre or a decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it.

Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, other metric systems include: the MKS system of units and the MKSA systems, which are the direct forerunners of the SI; the centimetre–gram–second (CGS) system and its subtypes, the CGS electrostatic (cgs-esu) system, the CGS electromagnetic (cgs-emu) system, and their still-popular blend, the Gaussian system; the metre–tonne–second (MTS) system; and the gravitational metric systems, which can be based on either the metre or the centimetre, and either the gram, gram-force, kilogram or kilogram-force.

Attributes

Ease of learning and use

The metric system is intended to be easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units.

It is a coherent system with derived units built from base units using logical rather than empirical relationships and with multiples and submultiples of both units based on decimal factors and identified by a common set of prefixes.

Extensibility

The metric system is extensible since the governing body reviews, modifies and extends it needs arise. For example, the katal, a derived unit for catalytic activity equivalent to one mole per second (1 mol/s), was added in 1999.

Realisation

See also: Realisation (metrology)

The base units used in a measurement system must be realisable. To that end, the definition of each SI base unit is accompanied by a mise en pratique (practical realisation) that describes at least one way that the unit can be measured. Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country. In practice, such realisation is done under the auspices of a mutual acceptance arrangement.

The metre was originally defined to be one ten millionth of the distance between the North Pole and the Equator through Paris.

In 1791 the commission originally defined the metre based on the size of the earth, equal to one ten-millionth of the distance from the equator to the North Pole. In the SI, the standard metre is now defined as exactly 1⁄299792458 of the distance that light travels in a second. The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency.

The kilogram was originally defined as the mass of one cubic decimetre of water at 4 °C, standardised as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a new definition was introduced in May 2019. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the Metre Convention serve as de facto standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention. The replicas were subject to periodic validation by comparison to the original, called the IPK. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50 μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of 5×10. The revision of the SI replaced the IPK with an exact definition of the Planck constant as expressed in SI units, which defines the kilogram in terms of fundamental constants.

Base and derived unit structure

Main article: Base unit (measurement) See also: SI derived unit

A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. A base unit is a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has the unit metre and time has the unit second, and speed has the derived unit metre per second. Density, or mass per unit volume, has the unit kilogram per cubic metre.

Decimal ratios

A significant characteristic of the metric system is its use of decimal multiples – powers of 10. For example, a length that is significantly longer or shorter than 1 metre can be represented in units that are a power of 10 or 1000 metres. This differs from many older systems in which the ratio of different units varied. For example, 12 inches is one foot, but the larger unit in the same system, the mile is not a power of 12 feet. It is 5,280 feet – which is hard to remember for many.

In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as kilo- and mega-, and those that were negative powers of ten were given Latin-derived prefixes such as centi- and milli-. However, 1935 extensions to the prefix system did not follow this convention: the prefixes nano- and micro-, for example have Greek roots. During the 19th century the prefix myria-, derived from the Greek word μύριοι (mýrioi), was used as a multiplier for 10000.

When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below.

1 mm (square millimetre) = (1 mm)  = (0.001 m)  = 0.000001 m
1 km (square kilometre)  = (1 km) = (1000 m) = 1000000 m
1 mm (cubic millimetre) = (1 mm) = (0.001 m) = 0.000000001 m
1 km (cubic kilometre) = (1 km) = (1000 m) = 1000000000 m

For the most part, the metric prefixes are used uniformly for SI base, derived and accepted units. A notable exception is that for a large measure of seconds, the non-SI units of minute, hour and day are customary instead. Units of duration longer than a day are problematic since both month and year have varying number of days. Sub-second measures are often indicated via submultiple prefixes. For example, millisecond.

Coherence

Main article: Coherence (units of measurement)
James Clerk Maxwell played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.

Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors. For example, in a coherent system the units of force, energy, and power are chosen so that the equations

force = mass × acceleration
energy = force × distance
energy = power × time

hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, Einstein's mass–energy equation, E = mc, does not require extraneous constants when expressed in coherent units.

The CGS system had two units of energy, the erg that was related to mechanics and the calorie that was related to thermal energy; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the joule.

Rationalisation

Maxwell's equations of electromagnetism contained a factor of 1 / ( 4 π ) {\displaystyle 1/(4\pi )} relating to steradians, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor made equations more awkward than necessary, and so Oliver Heaviside suggested adjusting the system of units to remove it.

Everyday notions

The basic units of the metric system have always represented commonplace quantities or relationships in nature; even with modern refinements of definition and methodology. In cases where laboratory precision may not be required or available, or where approximations are good enough, the commonplace notions may suffice.

Time

The second is readily determined from the Earth's rotation period. Unlike other units, time multiples are not decimal. A second is ⁠1/60⁠ of a minute, which is ⁠1/60⁠ of an hour, which is ⁠1/24⁠ of a day, so a second is ⁠1/86400⁠ of a day.

Length

The length of the equator is close to 40000000 m (more precisely 40075014.2 m). In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre. A dining tabletop is typically about 0.75 metres high. A very tall human is about 2 metres tall.

Mass

A 1-euro coin weighs 7.5 g; a Sacagawea US 1-dollar coin weighs 8.1 g; a UK 50-pence coin weighs 8.0 g.

Temperature

In every day use, Celsius is more commonly used than Kelvin, however a temperature difference of one Kelvin is the same as one degree Celsius and that is defined as ⁠1/100⁠ of the temperature differential between the freezing and boiling points of water at sea level. A temperature in Kelvin is the temperature in Celsius plus about 273. Human body temperature is about 37 °C or 310 K.

Length, mass, volume relationship

The mass of a litre of cold water is 1 kilogram. 1 millilitre of water occupies 1 cubic centimetre and weighs 1 gram.

Candela and Watt relationship

Candela is about the luminous intensity of a moderately bright candle, or 1 candle power. A 60 Watt tungsten-filament incandescent light bulb has a luminous intensity of about 800 lumens which is radiated equally in all directions (i.e. 4π steradians), thus is equal to Iv = ⁠800 lm/4π sr⁠ ≈ 64 cd.

Watt, Volt and Ampere relationship

A 60 W incandescent light bulb consumes 0.5 A at 120 V (US mains voltage). A 60 W bulb rated at 230 V (European mains voltage) consumes 0.26 A at this voltage. This is evident from the formula P = I V.

Mole and mass relationship

A mole of a substance has a mass that is its molecular mass expressed in units of grams. The mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g.

Since all gases have the same volume per mole at a given temperature and pressure far from their points of liquefaction and solidification (see Perfect gas), and air is about ⁠1/5⁠ oxygen (molecular mass 32) and ⁠4/5⁠ nitrogen (molecular mass 28), the density of any near-perfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because ⁠4/5⁠ × 28 + ⁠1/5⁠ × 32 = 28.8 ≈ 29). For example, carbon monoxide (molecular mass 28) has almost the same density as air.

History

Main article: History of the metric system
Pavillon de Breteuil, Saint-Cloud, France, the home of the metric system since 1875

The French Revolution (1789–99) enabled France to reform its many outdated systems of various local weights and measures. In 1790, Charles Maurice de Talleyrand-Périgord proposed a new system based on natural units to the French National Assembly, aiming for global adoption. With the United Kingdom not responding to a request to collaborate in the development of the system, the French Academy of Sciences established a commission to implement this new standard alone, and in 1799, the new system was launched in France.

A number of different metric system have been developed, all using the Mètre des Archives and Kilogramme des Archives (or their descendants) as their base units, but differing in the definitions of the various derived units.

Variants of the metric system
Measure SI/MKS CGSTooltip Centimetre–gram–second system of units MTSTooltip Metre–tonne–second system of units
distance metre
(m) 		centimetre
(cm) 		metre
(m)
mass kilogram
(kg) 		gram
(g) 		tonne
(t)
time second
(s) 		second
(s) 		second
(s)
velocity m/s cm/s m/s
acceleration m/s gal
(Gal) 		m/s
force newton (N) dyne
(dyn) 		sthene
(sn)
pressure pascal (Pa) barye
(Ba) 		pièze
(pz)
energy joule
(J) 		erg
(erg) 		kilojoule
(kJ)
power watt
(W) 		erg/s
(erg/s) 		kilowatt
(kW)
viscosity Pa⋅s poise
(P) 		pz⋅s

19th century

In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the Earth, and together with the milligram and millimetre, this became the first system of mechanical units. He showed that the strength of a magnet could also be quantified in terms of these units, by measuring the oscillations of a magnetised needle and finding the quantity of "magnetic fluid" that produces an acceleration of one unit when applied to a unit mass. The centimetre–gram–second system of units (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874, this system was formally promoted by the British Association for the Advancement of Science (BAAS). The system's characteristics are that density is expressed in g/cm, force expressed in dynes and mechanical energy in ergs. Thermal energy was defined in calories, one calorie being the energy required to raise the temperature of one gram of water from 15.5 °C to 16.5 °C. The meeting also recognised two sets of units for electrical and magnetic properties – the electrostatic set of units and the electromagnetic set of units.

The CGS units of electricity were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the metre, kilogram and second, in the International System of Electrical and Magnetic Units. During the same period in which the CGS system was being extended to include electromagnetism, other systems were developed, distinguished by their choice of coherent base unit, including the Practical System of Electric Units, or QES (quad–eleventhgram–second) system, was being used. Here, the base units are the quad, equal to 10 m (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to 10 g, and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude.

20th century

In 1901, Giovanni Giorgi showed that by adding an electrical unit as a fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre–kilogram–second–coulomb (MKSC) and metre–kilogram–second–ampere (MKSA) systems are examples of such systems.

The metre–tonne–second system of units (MTS) was based on the metre, tonne and second – the unit of force was the sthène and the unit of pressure was the pièze. It was invented in France for industrial use and from 1933 to 1955 was used both in France and in the Soviet Union. Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, Technische Masseneinheit (TME), mug or metric slug. Although the CGPM passed a resolution in 1901 defining the standard value of acceleration due to gravity to be 980.665 cm/s, gravitational units are not part of the International System of Units (SI).

Current

The International System of Units is the modern metric system. It is based on the metre–kilogram–second–ampere (MKSA) system of units from early in the 20th century. It also includes numerous coherent derived units for common quantities like power (watt) and irradience (lumen). Electrical units were taken from the International system then in use. Other units like those for energy (joule) were modelled on those from the older CGS system, but scaled to be coherent with MKSA units. Two additional base units – the kelvin, which is equivalent to degree Celsius for change in thermodynamic temperature but set so that 0 K is absolute zero, and the candela, which is roughly equivalent to the international candle unit of illumination – were introduced. Later, another base unit, the mole, a unit of amount of substance equivalent to the Avogadro number number of specified molecules, was added along with several other derived units.

The system was promulgated by the General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM) in 1960. At that time, the metre was redefined in terms of the wavelength of a spectral line of the krypton-86 atom (krypton-86 being a stable isotope of an inert gas that occurs in undetectable or trace amounts naturally), and the standard metre artefact from 1889 was retired.

Today, the International system of units consists of 7 base units and innumerable coherent derived units including 22 with special names. The last new derived unit, the katal for catalytic activity, was added in 1999. All the base units except the second are now defined in terms of exact and invariant constants of physics or mathematics, barring those parts of their definitions which are dependent on the second itself. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as 1⁄299,792,458 of the distance light travels in a second. The kilogram was defined by a cylinder of platinum-iridium alloy until a new definition in terms of natural physical constants was adopted in 2019. As of 2022, the range of decimal prefixes has been extended to those for 10 (quetta–) and 10 (quecto–).

See also

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