E404 → Easter
Computation of Date of Easter
Short Answer: Easter is the Sunday after the full moon1 on or after the vernal (or spring) equinox2. Easter occurs as early as March 22 and as late as April 25.
Extended Answer: The observant will notice two footnotes, because it just can't be that simple.
1. It's not exactly the familiar full moon, which most calendars mark when the astronomical full moon occurs (using Greenwich mean time, the universal time zone of Greenwich, England). Easter uses the Paschal Full Moon, which is computed rather than observing the moon. Originally, tables were used. For 2009, the PFM is April 10, and the AFM is April 9 14:56 GMT (10:56 EDT). The PFM and AFM occasionally differ by one or two days.
2. It's not exactly the familiar vernal equinox, which most calendars mark when the Sun crosses directly over the equator (again, using Greenwich mean time), varying from March 19–21. Easter uses the fixed date of March 21. The astronomical vernal equinox for 2009 is March 20 11:44 GMT (07:58 EDT).
A formula to compute the date of Easter is provided below. <formula>
The following feasts and observances are related to Easter:
| Holy Day | Relationship to Easter | Date for 2010 |
| Septuagesima | 63 days before | January 31, 2010 |
| Quinquagesima | 49 days before | February 14, 2010 |
| Ash Wednesday (Beginning of Lent) | 46 days before (often stated as 40 days, but that excludes Sundays) | February 17, 2010 |
| Palm Sunday | 7 days before | March 28, 2010 |
| Holy Thursday (Triduum begins with Mass of the Lord's Supper) | 3 days before | April 1, 2010 |
| Good Friday | 2 days before | April 2, 2010 |
| Easter | this is the day! | April 4, 2010 |
| Ascension Thursday (moved to next Sunday in some locations) | 39 days after | May 13, 2010 |
| Pentecost | 49 days after | May 23, 2010 |
| Monday after Pentecost (Ordinary Time resumes) | 50 days after | May 24, 2010 |
| Trinity Sunday | 56 days after | May 30, 2010 |
| Corpus Christi (moved to previous Thursday in some locations) | 63 days after | June 6, 2010 |
| Sacred Heart | 68 days after | June 11, 2010 |
Algorithm by Jean Baptiste Joseph Delambre (1749-1822) to compute date of Easter
works for the Gregorian calendar (the one we use every day) since 1583
| Computation | Example | |
| / means integer division without a remainder | 13 / 4 = 3 8 / 2 = 4 |
|
| % means modulo division or remainder | 13 % 4 = 1 8 % 2 = 0 |
|
| y is 4-digit year | ||
|
a = y % 19 |
15 | |
|
b = y / 100 |
20 | |
| c = y % 100 | 10 | |
|
d = b / 4 |
5 | |
| e = b % 4 | 0 | |
|
f = (b + 8) / 25 |
1 | |
| g = (b – f + 1) / 3 | 6 | |
|
h = (19 × a + b – d – g + 15) % 30 |
9 | |
| i = c / 4 | 2 | |
|
k = c % 4 |
2 | |
| l = (32 + 2 × e + 2 × i – h × k) % 7 | 4 | |
|
m = (a + 11 × h + 22 × l) / 451 |
0 | |
| r = 22 + h + l – 7 × m | 35 | |
| If r < 32, then r is day of March otherwise (r – 31) is day of April |
April 4, 2010 |