As a moveable feast, the date of Easter is determined in each year through a calculation known as – often simply Computus – or as paschalion particularly in the Eastern Orthodox Church. Easter is celebrated on the first Sunday after the Paschal full moon (a mathematical approximation of the first astronomical full moon, on or after 21 March itself a fixed approximation of the March equinox). Determining this date in advance requires a correlation between the lunar months and the solar year, while also accounting for the month, date, and weekday of the Julian or Gregorian calendar. The complexity of the algorithm arises because of the desire to associate the date of Easter with the date of the Jewish feast of Passover which, Christians believe, is when Jesus was crucified.
It was originally feasible for the entire Christian Church to receive the date of Easter each year through an annual announcement by the pope. By the early third century, however, communications in the Roman Empire had deteriorated to the point that the church put great value in a system that would allow the clergy to determine the date for themselves, independently yet consistently. Additionally, the church wished to eliminate dependencies on the Hebrew calendar, by deriving the date for Easter directly from the March equinox.
In The Reckoning of Time (725), Bede uses as a general term for any sort of calculation, although he refers to the Easter cycles of Theophilus as a "Paschal ." By the end of the 8th century, came to refer specifically to the calculation of time. The calculations produce different results depending on whether the Julian calendar or the Gregorian calendar is used. For this reason, the Catholic Church and Protestant churches (which follow the Gregorian calendar) celebrate Easter on a different date from that of the Eastern and Oriental Orthodoxy (which follow the Julian calendar). It was the drift of 21 March from the observed equinox that led to the Gregorian reform of the calendar, to bring them back into line.
History
Early Roman tables and the development of the Dionysian tables The earliest known Roman tables were devised in 222 by Hippolytus of Rome based on eight-year cycles. Then 84-year tables were introduced in Rome by Augustalis near the end of the 3rd century. Although a process based on the 19-year Metonic cycle was first proposed by Bishop Anatolius of Laodicea around 277, the concept did not fully take hold until the Alexandrian method became authoritative in the late 4th century.
The Alexandrian was converted from the Alexandrian calendar into the Julian calendar in Alexandria around 440, which resulted in a Paschal table (attributed to Pope Cyril of Alexandria) covering the years 437 to 531. This Paschal table was the source that inspired Dionysius Exiguus, who worked in Rome from about 500 to about 540, to construct a continuation of it in the form of his famous Paschal table covering the years 532 to 616. Dionysius introduced the Christian Era (counting years from the Incarnation of Christ) by publishing this new Easter table in 525.
A modified 84-year cycle was adopted in Rome during the first half of the 4th century. Victorius of Aquitaine tried to adapt the Alexandrian method to Roman rules in 457 in the form of a 532-year table, but he introduced serious errors. These Victorian tables were used in Gaul (now France) and Spain until they were displaced by Dionysian tables at the end of the 8th century.
The tables of Dionysius and Victorius conflicted with those traditionally used in the British Isles. The British tables used an 84-year cycle, but an error made the full moons fall progressively too early. The discrepancy led to a report that Queen Eanflæd, on the Dionysian system fasted on her Palm Sunday while her husband Oswiu, king of Northumbria, feasted on his Easter Sunday.
As a result of the Irish Synod of Magh-Lene in 630, the southern Irish began to use the Dionysian tables, and the northern English followed suit after the Synod of Whitby in 664.
The Dionysian reckoning was fully described by Bede in 725. It may have been adopted by Charlemagne for the Frankish Church as early as 782 from Alcuin, a follower of Bede. The Dionysian/Bedan remained in use in western Europe until the Gregorian calendar reform, and remains in use in most Eastern Churches, including the vast majority of Eastern Orthodox Churches and Non-Chalcedonian Churches. The only Eastern Orthodox church which does not follow the system is the Finnish Orthodox Church, which uses the Gregorian.
Having deviated from the Alexandrians during the 6th century, churches beyond the eastern frontier of the former Byzantine Empire, including the Assyrian Church of the East, now celebrate Easter on different dates from Eastern Orthodox Churches four times every 532 years.
Gregorian Calendar Apart from these churches on the eastern fringes of the Roman empire, by the tenth century all had adopted the Alexandrian Easter, which still placed the vernal equinox on 21 March, although Bede had already noted its drift in 725 it had drifted even further by the 16th century. Worse, the reckoned Moon that was used to compute Easter was fixed to the Julian year by the 19-year cycle. That approximation built up an error of one day every 310 years, so by the 16th century the lunar calendar was out of phase with the real Moon by four days.
The Gregorian Easter has been used since 1583 by the Roman Catholic Church and was adopted by most Protestant churches between 1753 and 1869.
Protestant astronomical Easter In 1700, Denmark and the protestant states of the Holy Roman Empire adopted the solar part of the Gregorian calendar by incorporating its leap day rules to correct the drift of the months. However, rather than adopting the Gregorian Easter tables, they chose to determine the date of Easter using an independent astronomical method, calling this hybrid system the "improved calendar" (Verbesserte Kalender). Easter was calculated from the phases of the moon based on the Rudolphine Tables of Johannes Kepler, which were in turn based on astronomical positions of the Sun and Moon observed by Tycho Brahe at his Uraniborg observatory on the island of Ven. Over the following years, the new calendar was adopted by other Protestant countries as well.
This astronomical Easter was defined as the Sunday after the full moon instant that was after the vernal equinox instant using Uraniborg time . However, it was delayed one week if that Sunday was the Jewish date Nisan15, the first day of Passover week, calculated according to modern Jewish methods. This Nisan15 rule affected the Easters of 1700, 1778 and 1798. Instead of being one week before the Gregorian Easter, they were postponed by one week and fell on the same Sunday as the Gregorian Easter.
The astronomical rule nevertheless sometimes produced a different date than the Gregorian one. During its use in Germany, the astronomical Easter fell one week before the Gregorian Easter in 1724 and 1744. In Sweden, which adopted the astronomical Easter in 1740, it fell one week before the Gregorian Easter in 1744, but one week after it in 1805, 1811, and 1818. In the Grand Duchy of Finland, which was separated from Sweden in 1809, the astronomical Easter was also observed one week after the Gregorian Easter in 1825, 1829 and 1845.
The discrepancies between the Catholic and Protestant Easter proved inconvenient, leading Denmark and the Holy Roman Empire to adopt the standard Gregorian Easter rules in 1776. Sweden adopted the Gregorian Easter in 1844, while Finland continued to calculate its Easter astronomically until 1869.
Modern proposals Two modern astronomical Easters were proposed but never used by any Church. The first was proposed as part of the Revised Julian calendar at a Synod in Constantinople in 1923, and the second was proposed by a 1997 World Council of Churches Consultation in Aleppo in 1997. Both used the same rule as the German and Swedish versions, but used modern astronomical calculations and Jerusalem time without the Nisan15 rule. The 1923 version would have placed the astronomical Easter one month before the Gregorian Easter in 1924, 1943, and 1962, but one week after it in 1927, 1954, and 1967. The 1997 version would have placed the astronomical Easter on the same Sunday as the Gregorian Easter for 2000–2025 except for 2019, when it would have been one month earlier.
At the Second Vatican Council, the Catholic Church stated that it had no objections to the feast of Easter being moved to a fixed Sunday subject to ecumenical agreement on the date, or to the adoption of a fixed date for civil purposes so long as this did not compromise the occurrence of Easter on a Sunday and the maintenance of a seven-day week.
Theory The Easter cycle groups days into lunar months, which are either 29 or 30 days long. There is an exception. The month ending in March normally has 30 days, but if 29 February of a leap year falls within it, it contains 31. As these groups are based on the lunar cycle, over the long term the average month in the lunar calendar is a very good approximation of the synodic month, which is days long.
There are 12 synodic months in a lunar year, totalling either 354 or 355 days. The lunar year is about 11 days shorter than the calendar year, which is either 365 or 366 days long. These days by which the solar year exceeds the lunar year are called epacts ()..
It is necessary to add them to the day of the solar year to obtain the correct day in the lunar year. Whenever the epact reaches or exceeds 30, an extra intercalary month (or embolismic month) of 30 days must be inserted into the lunar calendar; then 30 must be subtracted from the epact. Charles Wheatly provides the detail:
Thus, the lunar month took the name of the Julian month in which it ended. The nineteen-year Metonic cycle assumes that 19 tropical years are as long as 235 synodic months. So after 19 years, the lunations should fall the same way in the solar years, and the epacts should repeat. Over 19 years the epact increases by , not . That is, 209 divided by 30 leaves a remainder of 29 instead of being a multiple of 30. This is a problem if compensation is only done by adding months of 30 days. So after 19 years, the epact must be corrected by one day for the cycle to repeat. This is the so-called ("leap of the moon"). The Julian calendar handles it by reducing the length of the lunar month that begins on 1 July in the last year of the cycle to 29 days. This makes three successive 29-day months.
The and the seven extra 30-day months were largely hidden by being located at the points where the Julian and lunar months begin at about the same time. The extra months commenced on 1 January (year 3), 2 September (year 5), 6 March (year 8), 3 January (year 11), 31 December (year 13), 1 September (year 16), and 5 March (year 19). The sequence number of the year in the 19-year cycle is called the "golden number", and is given by the formula GN = (Y mod 19) + 1 That is, the year number Y in the Christian era is divided by 19, and the remainder plus 1 is the golden number. (Some sources specify that one adds 1 before taking the remainder; in that case, one needs to treat a result of 0 as the golden number 19. In the formula above, the remainder is taken first and then 1 is added, so no such adjustment is necessary.)