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Day of the week
Calculate the day of the week for any date
mwls.com


Working out the ‘day of the week’ for any date is relatively straight forward. If we ignore leap years for the moment, any year will follow one of seven different patterns of dates — each pattern depending on the 'day of the week' on which 1 January falls.

Once you know this, you can work out the ‘day of the week’ for any date in that year. For example, in 2017 New Year's Day falls on a Sunday, which means that the first Sunday in February will fall on the 5 February, the first Sunday in March will fall on the 5 March, the first Sunday in April will fall on the 2 April...

For convenience we'll give each of the seven patterns a letter ‘A–G’. Table D1 gives the date pattern for the years 2001–2010 and Table D2 gives the first Sunday of the month for each of the date patterns.

2009E
2010F
2011G
2012AB
2013C
2014D
2015E
2016FG
2017A
2018B
Table D1: Date Patterns for years 2009–2018

Notice that leap years have a double date pattern. For example, 2012 has the pattern ‘AB’ which means that pattern ‘A’ should be used for January and February and pattern ‘B’ should be used for the rest of the year.

 JFMAMJJASOND
A155274263853
B744163152742
C633752741631
D522641637527
E411537526416
F377426415375
G266315374264
Table D2: First Sunday of the month for each date pattern

As an example we’ll work out which ‘day of the week’ 17 December 2016 falls on. Now, 2016 is a leap year which means that we use pattern ‘F’ for January and February and pattern ‘G’ for the rest of the year. Using pattern ‘G’, we can see that the first Sunday in December falls on the 4th, so the second Sunday will fall on the 11th and — the 17 December 2008 will fall on a Saturday.

We have produced a dates program that calculates the date of Easter, other moveable holidays, fixed holidays, and the day of the week for any date.

Also see
 2011 Almanac
 2011 International Holidays