The Paschalion of the Orthodox Church combines the metonic and solar calendrical cycles to determine the date of Pascha for a given year. A common formula to determine the date of Pascha was created in connection with the First Ecumenical Council, held at Nicea in 325 A.D.
The Nicene Formula
The Gregorian Reform
In October 1582, the Roman Catholic Church adopted a major calendar reform designed to correct for the 10-day drift in the vernal equinox since the First Ecumenical Council. The Julian calendar then in common use was based on an average year of 365.25 days, slightly longer than the actual solar mean year of 365.24219 days.
The new calendar was called the Gregorian after its sponsor, Pope Gregory XIII. The reform also introduced refinements to the calculation of Pascha.
East and West Today
The Roman Catholic and Protestant West eventually adopted the Gregorian Calendar for civil and ecclesiastical purposes, including the determination of Pascha. The Orthodox East, however, was not so quick to change. Even when the traditionally Orthodox countries began to adopt the Gregorian calendar for civil purposes, the Orthodox Church retained the Julian calendar and original Paschalion. For the sake of convenience, the date of Pascha is often transposed to the coincident date on the Gregorian calendar for reference.
Because of the difference in calendars and formulas, Western Easter and Orthodox Pascha do not often coincide. Generally, Orthodox Pascha follows Western Easter by between 1 and 5 weeks.
Many notable mathematicians have developed algorithms for determining the date of Orthodox Pascha over the centuries. This simple and elegant one was devised by the brilliant mathematician Jacques Oudin in the 1940s:
N.B. -- In this formula MOD is the modulus function, in which the first number is divided by the second and only the remainder is returned. Further, all division is integer division, in which remainders are discarded. Thus 22 MOD 7 = 1 but 22 / 7 = 3.
G = year MOD 19 I = ((19 * G) + 15) MOD 30 J = (year + (year/4) + I) MOD 7 L = I - J Easter Month = 3 + ((L + 40)/44) Easter Day = L + 28 - 31 * (Easter Month/4)
Easter Month will be a number corresponding to a calendar month (e.g., 4 = April) and Easter Day will be the day of that month. Note that this returns the date of Pascha on the Julian calendar. To get the corresponding date on the Gregorian calendar, add 13 days (14 days after March 1, 2100).
Online Paschalion Utility
This site allows the user to enter a year and uses Oudin's algorithm to compute the relevant dates. Although the Orthodox (Julian-based) formulas are used, the utility returns the corresponding Gregorian calendar dates. For example, in 2005 Pascha falls on Sunday, April 18, on the Julian calendar. That date corresponds to May 1 on the Gregorian calendar.