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Calculating the Date of Easter

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The most important holiday of the Christian year is the festival of Easter. It celebrates the resurrection of Jesus Christ after his torture and death. Unlike Christmas, which occurs on the same day every year, Easter is a movable feast, falling some time in late March or in April, but according to a mysterious pattern.

The general rule is that Easter Sunday is the first Sunday after the first Full Moon on or after the Spring Equinox.

This means that Easter can be as early as 22 March or as late as 25 April. Unfortunately, the Moon's phases are not an exact even number of days, so an algorithm is needed to calculate the exact date of the full moon. In addition, the Christian Church decided to use the date of 21 March as the Spring Equinox, even though the actual date of the Equinox varies slightly from year to year.

The detailed algorithm which is used by the Western Church (Roman Catholic and Protestant) is as follows:

' Given the Year as a four digit number in the range 1700 - 2299 ' Calculate Day and Month of Easter Sunday ' Note 1: the algorithm has not been tested outside this range. ' Note 2: the \ operator performs integer division without remainder. ' Note 3: the date returned is the Gregorian Calendar date ' (the one we use now), even for dates in the 18th Century. a = Year mod 19; b = Year \ 100; c = Year mod 100; d = b \ 4; e = b mod 4; f = c \ 4; g = c mod 4; h = (b + 8)\25; i = (b - h + 1)\3; j = (19*a + b - d - i + 15) mod 30; k = (32 + 2*e + 2*f - j - g) mod 7; m = (a + 11*j + 22*k) \ 451; n = j + k - 7*m + 114; Month = n\31; Day = (n mod 31) + 1;

The exact method of calculation of the date of Easter was a hot topic for the early Christian church. It was felt that to celebrate Christ's resurrection on the wrong day would be blasphemous, so it was very important to get the day right. The general rule was agreed at the Council of Nicaea in 325 AD. It was many hundreds of years after this that a working algorithm was devised. This was perfected in the 16th Century by Aloysius Lilius at the same time that he devised the Gregorian Calendar, which is still used today.

Due to a rift between the Eastern and Western churches, the Eastern Church (Greek Orthodox and Russian Orthodox) uses a different algorithm for the calculation of Easter.

For More Information

The Astronomical Society of South Australia's Website gives a more detailed algorithm, which will work up to the year 4099. It also gives the algorithm for Orthodox Easter.

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