The Date of Easter

Easter is an annual festival observed throughout the Christian world. The date for Easter shifts every year within the Christian calendar. The Gregorian Calendar used by most Western Christian churches is the standard international calendar for civil use. It also regulates the ceremonial cycle of the Roman Catholic and Protestant churches. The ecclesiastical rules that determine the date of Easter trace back to 325 CE at the First Council of Nicaea convened by the Roman Emperor Constantine. At that time the Roman world used the Julian Calendar (put in place by Julius Caesar).

The Council decided to keep Easter on the same Sunday throughout the Christian world. To fix incontrovertibly the date for Easter, and to make it determinable indefinitely in advance, the Council constructed tables to compute the date. These tables were revised during the following few centuries resulting, eventually in the tables constructed by the 6th century Abbot of Scythia, Dionysius Exiguus. Nonetheless, different means of calculations continued in use throughout the Christian world.

In 1582, Christopher Clavius and a council working at the direction of Gregory XIII (Pope of the Roman Catholic Church) completed a reconstruction of the Julian Calendar producing new Easter tables. The new calendar was issued in February in the papal bull called "Inter gravissimas". This new calendar is referred to as the Gregorian Calendar . One major difference between the Julian and Gregorian Calendars is the "leap year rule". See the Astronomical Information Center page on Calendars for a description of the difference. Universal adoption of this Gregorian calendar occurred slowly. By the 1700's, though, most of western Europe had adopted the Gregorian Calendar. The Eastern Christian churches still determine the Easter dates using the older Julian Calendar method.

The statement that Easter Day is the first Sunday after the full moon that occurs next after the vernal equinox , is only an approximate statement of the actual ecclesiastical rules. The full moon involved is not the astronomical Full Moon but an ecclesiastical moon (determined from tables) that keeps, more or less, in step with the astronomical full Moon.

The ecclesiastical rules are:

• The vernal equinox occurs on March 21,
• the ecclesiastical full moon is the 14th day of a tabular lunation (new moon), and
• Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after the day of the vernal equinox.

Easter can never occur before March 22 or later than April 25. The Gregorian dates for the ecclesiastical full moon are determined using the tables in the Papal bull Inter Gravissimas. The Western (Roman Catholic and Protestant) Christian churches use the Gregorian tables while many Eastern (Orthodox) Christian churches use older tables based on the Julian Calendar. Thus, the civil date of Easter depends upon which tables - Gregorian or pre-Gregorian - are used.

In a congress held in 1923, the Eastern Churches adopted a modified Gregorian Calendar and decided to set the date of Easter according to the astronomical full moon at the meridian of Jerusalem. However, a variety of practices remain among the Eastern Churches.

There are three major differences between the ecclesiastical and the astronomical systems.

• The times of the ecclesiastical full moon are not necessarily identical to the times of astronomical full moons. The ecclesiastical tables do not account for the full complexity of the lunar motion.
• The astronomical definition of the vernal equinox is the instant when the Sun, as seen from the Earth, has a zero apparent ecliptic longitude . (Yes, the Sun's ecliptic longitude, not its declination, is used for the astronomical definition.) This instant shifts slightly from year to year within the civil calendar. In the ecclesiastical system the vernal equinox does not shift. It is fixed on March 21 regardless of the actual position of the Sun.
• The date of Easter is a specific calendar date. Easter starts when that date starts for your local time zone. The astronomical vernal equinox occurs at same instant everywhere on the Earth.

Inevitably, the date of Easter occasionally differs from a date that depends on the astronomical full moon and astronomical vernal equinox. In some cases the difference may apply to some parts of the world and not to others because two different dates separated by midnight are always simultaneously in progress on the Earth.

For example, in 1962 the astronomical full moon occurred on March 21, UTC=7h 55m - about six hours after astronomical equinox . The ecclesiastical full moon, taken from the tables, however, occurred on March 20, before the ecclesiastical equinox on March 21. In the astronomical case, this full moon occurred after the equinox, but in the ecclesiastical case, it preceded the equinox. Following the ecclesiastical rules, Easter was not until the Sunday that followed the next ecclesiastical full moon (Wednesday, April 18) making Easter Sunday, April 22.

Similarly, in 1954 the first ecclesiastical full moon after March 21 fell on Saturday, April 17. Thus, Easter was Sunday, April 18. The astronomical equinox also occurred on March 21. The next astronomical full moon occurred on April 18 at UTC=5h. So in some places in the world Easter was on the same Sunday as the astronomical Full Moon.

For dates of Easter and other Christian observances, see the Selected Christian Observances service.

Computing the Date of Easter

The lunar cycles used by the ecclesiastical system are simple to program. The following algorithm will compute the date of Easter using the Gregorian Calendar.

The algorithm uses the year, y, to determine the month, m, and day, d, of Easter. The symbol * means multiply.

Please note the following: This is an integer calculation. All variables are integers and all remainders from division are dropped. For example, 7 divided by 3 is equal to 2 in integer arithmetic.

    
        c = y / 100
        n = y - 19 * ( y / 19 )
        k = ( c - 17 ) / 25
        i = c - c / 4 - ( c - k ) / 3 + 19
            * n + 15
        i = i - 30 * ( i / 30 )
        i = i - ( i / 28 ) * ( 1 - ( i / 28 )
            * ( 29 / ( i + 1 ) )
            * ( ( 21 - n ) / 11 ) )
        j = y + y / 4 + i + 2 - c + c / 4
        j = j - 7 * ( j / 7 )
        l = i - j
        m = 3 + ( l + 40 ) / 44
        d = l + 28 - 31 * ( m / 4 )
    
    

For example, using the year 2010,
y=2010,
c=2010/100=20,
n=2010 - 19 x (2010/19) = 2010 - 19 x (105) = 15,   [see note above regarding integer calculations]
etc. resulting in Easter on April 4, 2010.

The algorithm is due to J.-M. Oudin (1940) and is reprinted in Richards, E.G. 2012,   "Calendars," Explanatory Supplement to the Astronomical Almanac, 3rd ed., S.E. Urban and P.K. Seidelmann eds., 600-601.