Algorithm to calculate Western/Catholic Easter date.

Original report by promes

I saw your request for a Easter calculation function.
I rewrote it several times into new programming languages and at last into PHP.
On top you can see the distance in days from Easter to several Catholic holidays.
The function only needs the year as a parameter.

Additional information by klonos

...this seems to be a php version of the Nature (1876) Algorithm for Calculating the Date of Easter in the Gregorian Calendar. For future reference (in case that site/article goes down for some reason):

Nature (1876) Algorithm for Calculating the Date of Easter in the Gregorian Calendar

Originally published 1996 December by M.J. Montes.
This page was last updated 2001 July 31 by Marcos J. Montes.

The actual origin of this algorithm appears to be by an anonymous correspondent from New York to Nature in 1876 (Thanks Denis!). Samuel Butcher, Bishop of Meath, showed that this algorithm followed from Delambre's analytical solutions, and produces the date of Easter for all years. You can see the algorithm, as well as version for Orthodox Easter at another Easter Date site.

This algorithm appears in Practical Astronomy With Your Calculator, 2nd Edition by Peter Duffett-Smith, and he obtained this algorithm from Butcher's Ecclesiastical Calendar, published in 1876. This algorithm has also been published in the 1922 book General Astronomy by Spencer Jones; in The Journal of the British Astronomical Association (Vol.88, page 91, December 1977); and in Astronomical Algorithms (1991) by Jean Meeus.

This algorithm holds for any year in the Gregorian Calendar, which (of course) means years including and after 1583.

In the text below, / represents an integer division neglecting the remainder, while % is division keeping only the remainder. So 30/7=4 , and 30%7=2 .

a=year%19
b=year/100
c=year%100
d=b/4
e=b%4
f=(b+8)/25
g=(b-f+1)/3
h=(19*a+b-d-g+15)%30
i=c/4
k=c%4
l=(32+2*e+2*i-h-k)%7
m=(a+11*h+22*l)/451
Easter Month =(h+l-7*m+114)/31  [3=March, 4=April]
p=(h+l-7*m+114)%31
Easter Date=p+1     (date in Easter Month)

References

• Nature, 1876 April 20, vol. 13, p. 487.
• Dennis Roegel

Links

Oudin's Algorithm for the calculation of the date of Easter.
Carter's Algorithm for the calculation of the date of Easter.
Gauss' Algorithm for the calculation of the date of the Orthodox Easter.
Calculation of the Ecclesiastical Calendar

Last updated 2001 July 31.
Marcos J. Montes
mmontes@no.spam.smart.net