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In power transmission and distribution, alternating current power is distinguished into three different types: real power (P), measured in watts (W); apparent power (S), measured in volt-amperes (VA); and reactive power (Q), measured in volt-amperes reactive (VAr).

The power factor is defined as the ratio:

${\displaystyle {\frac {P}{S}}}$.

In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle such that:

${\displaystyle S^{2}=P^{2}+Q^{2}}$

If φ is the phase angle between the current and voltage, then the power factor is then equal to ${\displaystyle \left|\cos \phi \right|}$, and:

${\displaystyle P=S\left|\cos \phi \right|}$

By definition, the power factor is a dimensionless number between 0 and 1. Power engineers are often interested in the power factor as this determines how efficient a power system is.

The power factor is determined by the type of loads connected to the power system. These can be

• Resistive
• Inductive
• Capacitive

If a purely resistive load is connected to a power supply, the power factor will be unity (1) and only real power will flow. Inductive loads such as transformers and motors (any type of wound coil) absorb reactive power. Capacitive loads such as capacitor banks or buried cable generate reactive power.

A power transmission system is working at its greatest efficiency when the power factor is at unity (i.e. when no reactive power is present, so that the real power is the same as the apparent power). When the power factor is less than unity, the transmission losses increase and the system capacity is reduced. Power companies therefore require customers, especially those with large loads, to maintain, within specified limits, the power factors of their respective loads or be subject to additional charges.

When the load is purely resistive, the power delivered to it is equal to the product of volts and amperes, so the power factor is unity. When the current lags the applied voltage (due to an inductive load) the power factor is said to be lagging. When the current leads the applied voltage (due to a capacitive load) the power factor is said to be leading.

Note that although the value of the power factor reveals the magnitude of the phase angle, it does not reveal whether it is positive or negative. Thus, the power factor is specified as leading or lagging.

For example, to get 1 kW of real power if the power factor is unity, 1 kVA of apparent power needs to be transferred (1 kVA = 1 kW × 1). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor 5 kVA of apparent power needs to be transferred (1 kW = 5 kVA × 0.2).

It is often possible to adjust the power factor of a system to very near unity. This practice is known as power factor correction and is achieved by switching in or out banks of inductors or capacitors. This is of great importance to large power consumers since the electric utility will usually charge customers more if they have a low power factor.

Non-sinusoidal components

In circuits having only sinusoidal currents and voltages,the power factor effect arises only from the difference in phase between the curent and voltage. This is narrowly known as "displacement power factor". The concept can be generalized to a total, distortion, or true power factor where the apparent power includes all harmonic components. This is of importance in practical power systems which contain non-linear loads such as rectifiers, some forms of electric lighting, electric arc furnaces, welding equipment and other devices.

Mnemonics

English-language power engineering students are advised to remember: "ELI the ICE man" - the voltage E leads the current I in an inductor L, the current leads the voltage in a capacitor C

Or even shorter: CIVIL - in a Capacitor the I(current) leads V(Voltage), Voltage leads Current in an inductor L.

• Electronics terms
• Electric power