Earliest Easter for 100 years

According to National Review, Easter will not be this early again until 2160. It can in theory be one day earlier than it is this year, but will not be until 2285, and last was in 1818.

Incidentially Easter is observed on the Sunday after the first full moon on or after the day of the vernal equinox which is normally 21 March.

National Review says the formula to work out the date for Easter is:

((19*t+u-w-(u-(u+8)\25)+1)\3)+15)mod30)+(32+2*x+2*y-(19*t+u-w- (u-(u+8)\25)+1)\3)+15)mod30)-z)mod7)-7*(t+11*(19*t+u-w(u- (u+8)\25)+1)\3)+15)mod30)+22*(32+2*x+2*y-(19*t+u-w-(u- (u+8)\25)+1)\3)+15)mod30)-g)mod7)+114)\31

Looks Greek to me. I prefer the Meeus/Jones/Butcher Gregorian algorithm:

1. a = Y mod 19
2. b = Y/100
3. c = Y mod 100
4. d = b/4
5. e = b mod 4
6. f = (b + 8) / 25
7. g = (b – f + 1) / 3
8. h = (19 × a + b – d – g + 15) mod 30
9. i = c / 4
10. k = c mod 4
11. l = (32 + 2 × e + 2 × i – h – k) mod 7
12. m = (a + 11 × h + 22 × L) / 451
13. month = (h + L – 7 × m + 114) / 31
14. day = ((h + L – 7 × m + 114) mod 31) + 1

Simple really. So let us try it for 2008 (you use integers only by truncating)

1. a = 2008 mod 19 = 13
2. b = 2008/100 = 20
3. c = 2008 mod 100 = 8
4. d = 20/4 = 5
5. e = 20 mod 4 = 0
6. f = (20 + 8 )/ 25 = 28/25 = 1
7. g = (20 – 1 + 1) / 3 = 20/3 = 6
8. h = (19 × 13 + 20 – 5 – 6 + 15) mod 30 = 271 mod 30 = 1
9. i = 8 /4 = 2
10. k = 8 mod 4 = 0
11. l = (32 + 2 × 0 + 2 × 2 – 1 – 0) mod 7 = 35 mod 7 = 0
12. m = (13 + 11 × 1 + 22 × 0) / 451 = 46/451 = 0
13. month = (1 + 0 – 7 × 0 + 114) /31 = 115/31 = 3
14. day = ((1 + 0 – 7 × 0 + 114) mod 31) + 1 = 22 +1 = 23

So in 2008 Easter Sunday is the 23rd day of the third month.

I’ve even been bored enough that I have set up a spreadsheet in Excel with the formula so I can now instantly calculate Easter for any year!