The computus
How is Easter calculated? Step by step.
Easter is the first Sunday after a full moon that is reckoned, not observed. Finding it takes the year, a 19-year cycle, and whole-number arithmetic. The worked example below is computed for the current year; type another to follow it through.
The rule
Easter is celebrated on the first Sunday after the Paschal full moon, the first full moon on or after March 21 (Wikipedia, “Date of Easter”). Both the date of the equinox and the moon are fixed by convention: the official equinox is always March 21, and the official full moon may differ from the real one by a day or two (The Calendar FAQ). Working the date out is called the computus.
The golden number
The moon’s phases return to nearly the same days of the year every 19 years, so each year is given a number from 1 to 19, its golden number: (year mod 19) + 1. Years with the same golden number have their new moons on about the same dates. In the Julian reckoning the golden number alone fixes the Paschal full moon (The Calendar FAQ).
The epact
The epact is the age of the reckoned moon on a fixed day: in the Gregorian calendar, at the start of the year. The Gregorian reform kept the 19-year cycle but corrects it by century. The solar equation, 3(c + 1) ÷ 4, takes off a day for each century year that is not a leap year; the lunar equation, (8c + 13) ÷ 25, adds a day eight times in 2,500 years, where c is the year divided by 100 and every division keeps the whole part only. The Gregorian epact is the Julian epact, 11 × (golden number − 1) mod 30, minus the solar equation, plus the lunar equation, plus 8, brought into the range 1 to 30 (The Calendar FAQ).
The epact names the full moon. Epact 23 puts it on March 21 and each step down moves it a day later, to April 12 for epact 1; epacts 24 to 30 give April 18 down to April 13. The Paschal full moon must fall no later than April 18, which keeps Easter from passing April 25 (Wikipedia, “Date of Easter”). So epact 24 takes April 18, and epact 25 takes April 17 instead of April 18 when the golden number is above 11 (The Calendar FAQ). Easter is the Sunday after that date, and the next Sunday if the full moon is itself a Sunday.
Worked example: Easter 2026
Worked for 2026: Western Easter Sunday, April 5, Orthodox Easter Sunday, April 12.
Western Easter: the Anonymous Gregorian algorithm
| Step | Formula | Value | What it is |
|---|---|---|---|
a | year mod 19 | 12 | The year’s place in the 19-year cycle of the moon; the golden number is a + 1. |
b | year ÷ 100, whole part | 20 | The century. |
c | year mod 100 | 26 | The year within the century. |
d | b ÷ 4, whole part | 5 | Century leap years so far. |
e | b mod 4 | 0 | |
f | (b + 8) ÷ 25, whole part | 1 | Part of the correction to the moon’s cycle. |
g | (b − f + 1) ÷ 3, whole part | 6 | The correction to the moon’s cycle. |
h | (19a + b − d − g + 15) mod 30 | 12 | Days from March 21 to the full moon, before the two exceptions; 23 minus the epact, mod 30. |
i | c ÷ 4, whole part | 6 | Leap years within the century. |
k | c mod 4 | 2 | |
l | (32 + 2e + 2i − h − k) mod 7 | 2 | Days from the full moon to the Sunday. |
m | (a + 11h + 22l) ÷ 451, whole part | 0 | The two exceptions: 1 when the date must come back a week. |
n | (h + l − 7m + 114) ÷ 31, whole part | 4 | The month: 3 is March, 4 is April. |
o | (h + l − 7m + 114) mod 31 | 4 | The day of the month, less one. |
| Easter | month n, day o + 1 | April 5 | Sunday, April 5, 2026 |
This is the algorithm this site runs. “A New York correspondent” sent it to the journal Nature in 1876; it was reprinted by Samuel Butcher in 1877, by H. Spencer Jones in 1922 and by Jean Meeus in 1991, and is also called the Meeus/Jones/Butcher algorithm (Wikipedia, “Date of Easter”). It uses whole numbers only and needs no table.
Orthodox Easter: Meeus’s Julian algorithm
| Step | Formula | Value | What it is |
|---|---|---|---|
a | year mod 4 | 2 | |
b | year mod 7 | 3 | |
c | year mod 19 | 12 | The golden number, less one. |
d | (19c + 15) mod 30 | 3 | Days from March 21 (Julian) to the full moon. |
e | (2a + 4b − d + 34) mod 7 | 5 | Days from the full moon to the Sunday, less one. |
d + e + 114 | | 122 | Divided by 31: the whole part is the month, the remainder plus 1 is the day. |
| Julian date | month, day | March 30 | Easter Sunday in the Julian calendar |
| Shift | year ÷ 100 − year ÷ 400 − 2, whole parts | 13 | Days the Julian calendar runs behind the Gregorian in this year |
| Pascha | Julian date + shift | Sunday, April 12, 2026 |
Jean Meeus gives this algorithm in Astronomical Algorithms (1991) for the Julian Easter in the Julian calendar (Wikipedia, “Date of Easter”). This site then converts the Julian date to a day number and the day number to a Gregorian date; the shift in the table is the difference between the two, and the build checks it against the formula for every year from 1583 to 9999.
Days between the two calendars, by century
| Years | Julian behind Gregorian |
|---|---|
| 1583–1699 | 10 days |
| 1700–1799 | 11 days |
| 1800–1899 | 12 days |
| 1900–2099 | 13 days |
| 2100–2199 | 14 days |
| 2200–2299 | 15 days |
| 2300–2499 | 16 days |
| 2500–2599 | 17 days |
| 2600–2699 | 18 days |
The Julian calendar has a leap year every fourth year; the Gregorian calendar drops three of them every 400 years. Each century year that is a leap year in one and not in the other widens the distance by a day. The spans in the table apply to dates after February, which Easter always is.
This is why Orthodox Easter, which falls from March 22 to April 25 in the Julian calendar just as Western Easter does in the Gregorian, reads as April 4 to May 8 in Gregorian dates for the years 1900 to 2099.
How often the dates repeat
In the Julian reckoning the sequence of Easter dates repeats every 532 years, 19 × 28. In the Gregorian reckoning it repeats every 5,700,000 years (The Calendar FAQ). Counted over one full Gregorian cycle, the commonest date is April 19, the date in 3.867% of years, and the rarest is March 22, in 0.483%. How often each Easter date occurs has the full table.
What this does not do
It does not look at the sky. The reckoned full moon is a convention, and so is the date: the computation rests on agreements, not on the movements of the moon (Wikipedia, “Date of Easter”). Some churches follow other rules, and any church may change its own. Whether a feast tied to Easter is a day off work is a matter of each country’s law.
Sources
- Wikipedia, “Date of Easter” (revision 1366577142). Read September 28, 2026.
- Claus Tøndering, “The Calendar FAQ: Easter”. Read September 28, 2026.