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The Doomsday algorithm is for calculating the day of the week and makes use of the fact that in each year,

 28/29 February (28/2 or 29/2)
 4 April (4/4)
 6 June  (6/6)
 8 August (8/8)
10 October (10/10) and
12 December (12/12)

are all the same day of the week. This day of the week is called Doomsday and is derived from the last day in February, be it the 28th or 29th. The algorithm also defines 9/5 and 7/11 and their reverses (5/9 and 11/7) to be Doomsday.

Therefore, if you know what day of the week Doomsday - last day in February - is for a given year, you can easily determine the day of the week for any other date in that year.

The Doomsday algorithm was invented by John Horton Conway. It's use is independent of the calendar system used, e.g., Gregorian_Calendar or Julian_Calendar--except for the year in which a given country switched from one system to another.

An example

In the year 2004, 29 February 2004 is Sunday Hence Doomsday for 2004 is Sunday

Hence, we deduce that the following days in even months are sundays

 4 April (4/4)
 6 June  (6/6)
 8 August (8/8)
10 October (10/10) and   
12 December (12/12)

For odd months remember 9/5 7/11. That means that the following are sundays too:

 9 May (9/5)
11 July (11/7)
 5 September (5/9)
 7 November (7/11)

For January and March, its quite different However. The Doomsdays are:

 3 January (3/1)  - for non leap years
 4 January (4/1)  - for leap years

and for March the doomsday is

 7 March (7/3)

As an example to find the day of the week for 17 April:

We know 4 April (4/4) is a Sunday,
So is (4+7) April,
And (4+14) April too,
That is 18 April is a Sunday, and hence
-17 April is a Saturday-

External links

• http://quasar.as.utexas.edu/BillInfo/doomsday.html
• http://rudy.ca/doomsday.html

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