How the date of Easter is found
Easter has no fixed date. It falls on the first Sunday after the first full moon of spring, and spring, by this rule, begins on 21 March — the day the Church assigned to the vernal equinox. The rule goes back to the Council of Nicaea in 325, which decided that all Christians should keep Easter together and on a Sunday; the method of reckoning itself took shape in Alexandria.
The full moon here is not astronomical but tabular — the paschal full moon. It is found from the 19-year lunar cycle: after 19 years the phases of the Moon return almost exactly to the same dates. That is why the computus is a table rather than an observation of the sky, and why the date of Easter can be known for any year ahead.
Why the two dates differ
The Orthodox Church reckons Easter by the Alexandrian computus and the Julian calendar. In 1582, under Pope Gregory XIII, the Western Church adopted a new calendar and a new computus. The Julian year is 11 minutes longer than the solar year, and by the sixteenth century the equinox had drifted 10 days before 21 March, while the tabular full moons had fallen behind the real ones.
Hence two reasons for the difference:
- The calendars. 21 March in the Julian calendar now falls on 3 April in the Gregorian: the gap is 13 days and grows to 14 in 2100. Spring comes later in the Orthodox computus.
- The lunar tables. The Gregorian computus was corrected to keep the tabular full moon close to the real one; the Julian one lags behind it.
Today Orthodox Easter either coincides with Western Easter or comes one, four or five weeks later — never earlier.
Almost all Orthodox churches keep the Julian computus for Easter, even those that moved their fixed feasts to the Revised Julian calendar. The exception is the Orthodox Church of Finland, which celebrates Easter together with Western Christians.
Switching to the Gregorian calendar
Great Britain and its colonies, including the future United States, switched in 1752: Wednesday 2 September was followed by Thursday 14 September. Alaska switched in 1867, when it passed from Russia to the United States.
The Gauss algorithm
In 1800 Carl Friedrich Gauss reduced the computus to a few arithmetic steps; the formulas took their final form in 1816. Below, Y is the year, mod is the remainder of division and div is the whole part of the quotient.
- a = Y mod 19 is the year’s place in the 19-year lunar cycle; b = Y mod 4 and c = Y mod 7 account for leap years and the shift of weekdays.
- d = (19a + M) mod 30 is how many days after 21 March the paschal full moon falls.
- e = (2b + 4c + 6d + N) mod 7 is how many days after the full moon Sunday comes.
- Easter is on March (22 + d + e), or, if d + e is greater than 9, on April (d + e − 9).
In the Julian computus M = 15 and N = 6 always. In the Gregorian one they depend on the century: k = Y div 100, p = (13 + 8k) div 25, q = k div 4, M = (15 − p + k − q) mod 30, N = (4 + k − q) mod 7. The numbers k and q account for the leap years the Gregorian calendar skips, and p for the accumulated error of the lunar cycle.
The Gregorian computus has two exceptions: if d = 29 and e = 6, Easter moves from 26 to 19 April; if d = 28, e = 6 and (11M + 11) mod 30 < 19, from 25 to 18 April. In the Julian computus these conditions never occur.
The Julian computus gives an Old Style date. To convert it to New Style, the gap between the calendars is added — 13 days today.
Below is the same calculation with the numbers of the chosen year.