# The date of Easter

### The date of Easter

#### Dates of Easter: Table

According to tradition, Easter is celebrated on the first Sunday after the first full moon in spring (northern hemisphere). The determination of the date of Easter is based on the cyclic nature of the motion of moon and earth (76 years = 940 moon-months = 27759 days, the so-called Callippic Cycle named after Callippus of Cyzicus, about 330 B.C.). The Easter date is not based on present observations of the ephemerides of moon and earth. An extra adjustment of the Callippic Cycle is made at century borders in order to obtain better agreement between the outcome of the algorithm and the mean duration of the moon-month and the year. Carl Friedrich Gauß (1777 - 1855) of Braunschweig transformed the lengthy 16<small>th</small> century texts of Clavius to a mathematical algorithm. Here we present it in a modified version which was prepared by Dr. Heiner Lichtenberg, Bonn (H. Lichtenberg, Zur Interpretation der Gaußschen Osterformel und ihrer Ausnahmeregeln, Historia Mathematica 24 (1997), p. 441 - 444). It is rather easy to write a program for calculating the Easter date of interest. The results for the years 1980 to 2030 are listed in the table.

In the following equations INT(a/b) is the integer part of the quotient a/b and MOD(a, b) the non-negative remainder of (a/b). Let X be the year of interest and take the following steps:

(1)  K = INT (X/100);

(2)  M = 15 + INT ((3K+3)/4) - INT ((8K+13)/25);

(3)  S = 2 - INT ((3K+3)/4);

(4)  A = MOD (X, 19);

(5)  D = MOD (19A+M, 30);

(6)  R = INT (D/29) + (INT (D/28) - INT (D/ 29)) · INT (A/11);

(7)  OG = 21 + D - R;

(8)  SZ = 7 - MOD (X+INT (X/4)+S, 7);

(9)  OE = 7 - MOD (OG-SZ, 7);

OG  is the date of full moon in March, corresponding to the 14th day of the first month of the Lunar Calendar. SZ is the date of the first sunday in March.

OS = OG + OE is the date of Easter sunday, expressed as a date in March (For example, OS = 32 would mean April 1).

With the calculation of OS, several other Christian holiday dates are calculated as follows:

OS - 46: Ash Wednesday,
OS + 39: Ascension of Christ,
OS + 49: Whitsunday,
OS + 60: Corpus Christi Day.

### Dates of Easter: Table

The date of Easter Sunday for the years 1980  to 2031, calculated according to the formulae given above. Although the Calculations have been performed with great care we can not guarantee the correctness of the dates.

 1980:   April, 6 1981:   April,19 1982:   April,11 1983:   April, 3 1984:   April, 22 1985:   April, 7 1986:   March, 30 1987:   April, 19 1988:   April, 3 1989:   March, 26 1990:   April, 15 1991:   March, 31 1992:   April, 19 1993:   April, 11 1994:   April, 3 1995:   April, 16 1996:   April, 7 1997:   March, 30 1998:   April, 12 1999:   April, 4 2000:   April, 23 2001:   April, 15 2002:   March, 31 2003:   April, 20 2004:   April, 11 2005:   March, 27 2006:   April, 16 2007:   April, 8 2008:   March, 23 2009:   April, 12 2010:   April, 4 2011:   April, 24 2012:   April, 8 2013:   March, 31 2014:   April, 20 2015:   April, 5 2016:   March, 27 2017:   April, 16 2018:   April, 1 2019:   April, 21 2020:   April, 12 2021:   April, 4 2022:   April, 17 2023:   April, 9 2024:   March, 31 2025:   April, 20 2026:   April, 5 2027:   March, 28 2028:   April, 16 2029:   April, 1 2030:   April, 21 2031:   April, 13