How to calculate the Date of Easter

It is actually quite easily done:

see http://aa.usno.navy.mil/faq/docs/easter.php

Computing the Date of Easter

The rule is that Easter is the first Sunday after the first ecclesiastical full moon that occurs on or after March 21. The lunar cycles used by the ecclesiastical system are simple to program. The following algorithm will compute the date of Easter in the Gregorian Calendar system.

The algorithm uses the year, y, to give the month, m, and day, d, of Easter. The symbol * means multiply.

Please note the following: This is an integer calculation. All variables are integers and all remainders from division are dropped. For example, 7 divided by 3 is equal to 2 in integer arithmetic.

    c = y / 100
    n = y - 19 * ( y / 19 )
    k = ( c - 17 ) / 25
    i = c - c / 4 - ( c - k ) / 3 + 19 * n + 15
    i = i - 30 * ( i / 30 )
    i = i - ( i / 28 ) * ( 1 - ( i / 28 ) * ( 29 / ( i + 1 ) )
        * ( ( 21 - n ) / 11 ) )
    j = y + y / 4 + i + 2 - c + c / 4
    j = j - 7 * ( j / 7 )
    l = i - j
    m = 3 + ( l + 40 ) / 44
    d = l + 28 - 31 * ( m / 4 )

For example, using the year 2010,
y=2010,
c=2010/100=20,
n=2010 – 19 x (2010/19) = 2010 – 19 x (105) = 15, [see note above regarding integer calculations]
etc. resulting in Easter on April 4, 2010.

The algorithm is due to J.-M. Oudin (1940) and is reprinted in the Explanatory Supplement to the Astronomical Almanac, ed. P. K. Seidelmann (1992). See Chapter 12, “Calendars”, by L. E. Doggett.

The following are dates of Easter from 1980 to 2024:

1980  April 6        1995  April 16         2010  April 4

1981  April 19       1996  April 7          2011  April 24

1982  April 11       1997  March 30         2012  April 8

1983  April 3        1998  April 12         2013  March 31

1984  April 22       1999  April 4          2014  April 20

1985  April 7        2000  April 23         2015  April 5

1986  March 30       2001  April 15         2016  March 27

1987  April 19       2002  March 31         2017  April 16

1988  April 3        2003  April 20         2018  April 1

1989  March 26       2004  April 11         2019  April 21

1990  April 15       2005  March 27         2020  April 12

1991  March 31       2006  April 16         2021  April 4

1992  April 19       2007  April 8          2022  April 17

1993  April 11       2008  March 23         2023  April 9

1994  April 3        2009  April 12         2024  March 31

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1 Comment

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One response to “How to calculate the Date of Easter

  1. Claire

    Thanks a lot! This was very helpful. But can you please tell me what the letters (apart from y,m,d which are specified) stand for? Thanks!

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