  Easter date algorithms (c) Henk Reints

 Gregorian algorithm by Carl Friedrich Gauss (1777-1855). Valid for any year since 1583. Source: Any encyclopedia (at least in The Netherlands).
 NOTE: Many references suggest this algorithm by Gauss is the official Easter dating method and that he was the first to find a method for calculating the date of Easter. However, this is absolutely definitely not true! Lilius & Clavius devised their algorithm in the 1570's, two centuries before Gauss was born in 1777. Only the Lilius/Clavius method and nothing else has been used and will be used by the Roman Catholic Church since the Gregorian calendar reform in 1582, as it was announced and prescribed in Pope Gregory XIII's Bull "Inter Gravissimas". Gauss knew he was born in 1777, on a Wednesday, a bit more than a week before Ascension Day. That's what his parents could remember, not the precise date. However, he was eager to know his exact birth date. Apparently he was unaware of the official Easter dating method used by the Roman Catholic Church (or maybe he simply didn't want to use it or search for it), so, being a very intelligent mathematician, he simply made his own Easter dating formula, and then determined Ascension day was the 8th of May, so he was born on the 30th of April. But please keep in mind that Lilius/Clavius is the ONLY REAL THING as far as the official Easter date of the Roman Catholic Church is concerned! See also my Dutch translations website with historical texts about this Gregorian Calendar reform.

 In most cases where you find Gauss' algorithm in an encyclopedia or so, the values of M and N ar just given as: For the 20st and 21st century M = 24 and N = 5. Below, you will find a method to compute the values of M and N, which I devised myself, since I've never ever been able to find anything originating from Gauss about how to calculate them. I did this around 1998 or so, but on 16-Feb-2009 I found this WikiPedia page describing Gauss' original including calculation of M and N. Not identical, but I think I made a pretty good look-alike! I consider my version even simpler! In the algorithm below, all steps in darkblue are my own work, the steps in black are what I could find in other sources (especially Dutch encyclopedias). The values of M and N vary per century, the core of the Gauss algorithm is what varies per year.

A L G O R I T H M :

 HR: P = year DIV 100
 HR: Q = (3 x P + 3) DIV 4   (or: Q = P - P DIV 4)
 HR: R = (8 x P + 13) DIV 25
 HR: M = (15 + Q - R) MOD 30
 HR: N = (4  +  Q) MOD 7
Most sources simply state: for the 20st and 21st century M = 24 and N = 5.
 Gauss: A = year MOD 19
 Gauss: B = year MOD 4
 Gauss: C = year MOD 7
 Gauss: D = (19 x A + M) MOD 30
 Gauss: E = (2 x B + 4 x C + 6 x D + N) MOD 7
 Gauss: F = 22 + D + E
 HR: if F = 57 or (F = 56 and E = 6 and A > 10) then F = F - 7
 result = F  Use this algorithm | Gebruik deze algoritme  