View source for Date of Easter

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{{About|how the date of Easter is calculated|actual dates of Easter from {{#expr:{{CURRENTYEAR}}-10}} to {{#expr:{{CURRENTYEAR}}+10}}|List of dates for Easter}}
{{Use dmy dates|date=April 2021}}
[[File:Calendario pasquale.jpg|thumb|A calendar of the dates of Easter, for the 95 years 532{{ndash}}626, marble, in the Museum of [[Ravenna Cathedral]], Italy. Five 19-year cycles are represented as concentric circles. Dates are given using the system of the [[Roman calendar]], as well as the day of the lunar month.]]
As a [[moveable feast]],{{sfn|Ayto|2009|p=123}}{{sfn|Peterson |2015|p=468}} the '''date of Easter''' is determined in each year through a calculation known as {{langnf|la|'''computus paschalis'''|Easter computation}} – often simply ''Computus'' – or as '''paschalion''' particularly in the [[Eastern Orthodox Church]].{{sfn|Bede|1999|p=xviii}} [[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&nbsp;March{{snd}} itself a fixed approximation of the [[March equinox]]). Determining this date in advance requires a correlation between the [[lunar month]]s and the [[tropical year|solar year]], while also accounting for the month, date, and weekday of the [[Julian calendar|Julian]] or [[Gregorian calendar]].{{sfn|Bede|1999|pp=xviii–xx}} 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.<ref>{{Bibleverse|John|19:14}}</ref>

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.{{sfn|Bede|1999|p=xx}}  Additionally, the church wished to eliminate dependencies on the [[Hebrew calendar]], by deriving the date for Easter directly from the March equinox.{{sfn|Bede|1999|p=xxxvi}}

In ''[[The Reckoning of Time]]'' (725), [[Bede]] uses {{lang|la|computus}} as a general term for any sort of calculation, although he refers to the Easter cycles of [[Theophilus I of Alexandria|Theophilus]] as a "Paschal {{lang|la|computus}}."  By the end of the 8th century, {{lang|la|computus}} came to refer specifically to the calculation of time.{{sfn|Bede|1999|pp=425–426|loc=Appendix 4: A Note on the Term Computus }}
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 Orthodoxy|Eastern]] and [[Oriental Orthodoxy]] (which follow the Julian calendar). It was the drift of 21&nbsp;March from the observed equinox that led to the [[Gregorian reform of the calendar]], to bring them back into line.

==History==
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 (bishop)|Augustalis]] near the end of the 3rd&nbsp;century.{{efn|Although this is the dating of Augustalis by [[:de:Bruno Krusch|Bruno Krusch]], see arguments for a 5th&nbsp;century date in {{harvnb|Mosshammer|2008|pp=217, 227–228 }}.}} 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.{{efn|The lunar cycle of Anatolius, according to the tables in ''De ratione paschali'', included only two bissextile (leap) years every 19&nbsp;years, so could not be used by anyone using the Julian calendar, which had four or five leap years per lunar cycle.{{sfn|Turner|1895|pp=699–710}}{{sfn|McCarthy|1996|pp=285–320}} }}

The Alexandrian {{lang|la|computus}} was converted from the [[Coptic calendar|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.{{sfn|Declercq|2000|p=80}} This Paschal table was the source which inspired [[Dionysius Exiguus]], who worked in Rome from about 500 to about 540,{{sfn|Declercq|2000|p=97}} to construct a continuation of it in the form of his famous Paschal table covering the years 532 to 616.{{sfn|Declercq|2000|p=99}} Dionysius introduced the [[Anno Domini|Christian Era]] (counting years from the Incarnation of Christ) by publishing this new Easter table in 525.<ref name=audette />{{efn|For confirmation of Dionysius's role see {{harvnb|Blackburn|Holford-Strevens|1999|p=794}}. }}

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.{{sfn|Blackburn|Holford-Strevens|1999|p=793}} These Victorian tables were used in [[Gaul]] (now France) and Spain until they were displaced by Dionysian tables at the end of the 8th&nbsp;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.{{sfn|McCarthy|1993|pp=204–224}}  The discrepancy led to a report that Queen [[Eanflæd]], on the Dionysian system{{snd}} fasted on her [[Palm Sunday]] while her husband [[Oswiu]], king of Northumbria, feasted on his Easter Sunday.{{sfn|Bede|1907|p=193|loc=Book III, Chapter XXV}}

As a result of the Irish [[Synod of Magh-Lene]] in 630, the southern Irish began to use the Dionysian tables,{{sfn|Bede|1943|p=90|ps =: The letter [of Cummian] is at once a report and an apology or justification to Abbot Seghine at Iona of a synod held at ''Campus Lenis'' (Magh-Lene), where the Easter question was considered. The direct result of the synod was an alteration in the observance among the southern Irish and the adoption of the Alexandrian reckoning.}} and the northern English followed suit after the [[Synod of Whitby]] in 664.{{sfn|Bede|1907|p=xxvii}}

The Dionysian reckoning was fully described by [[Bede]] in 725.{{sfn|Bede|1999|pp=lix–lxiii}} It may have been adopted by [[Charlemagne]] for the Frankish Church as early as 782 from [[Alcuin]], a follower of Bede. The Dionysian/Bedan {{lang|la|computus}} 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 [[Oriental Orthodoxy|Non-Chalcedonian Churches]].<ref name=Kekis /> 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&nbsp;century, churches beyond the eastern frontier of the former Byzantine Empire, including the [[Assyrian Church of the East]],<ref name=revradiotowerofsong /> now celebrate Easter on different dates from [[Eastern Orthodox Church]]es four times every 532&nbsp;years.{{citation needed|date=June 2021}}

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&nbsp;March, although Bede had already noted its drift in 725{{snd}} it had drifted even further by the 16th century.{{efn|For example, in the Julian calendar, at Rome in 1550, the March equinox occurred on 11&nbsp;March at 6:51&nbsp;a.m. [[local mean time]].<ref>{{cite web |url=http://www.timeanddate.com/calendar/seasons.html?year=1550&n=215 |title=Seasons calculator |website=Time and Date AS |year=2014 |access-date=23 March 2019 |archive-date=23 March 2019 |archive-url=https://web.archive.org/web/20190323161000/https://www.timeanddate.com/calendar/seasons.html?year=1550&n=215 |url-status=live }}</ref>}} 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&nbsp;years, so by the 16th&nbsp;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 [[Protestantism|Protestant]] churches between 1753 and 1845.

German Protestant states used an astronomical Easter between 1700 and 1776, 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 (Sweden)|Ven]], while Sweden used it from 1739 to 1844. This astronomical Easter was the Sunday after the full moon instant that was after the vernal equinox instant using Uraniborg time {{nowrap|([[Terrestrial Time|TT]] + 51{{sup|m}})}}. However, it was delayed one week if that Sunday was the Jewish date Nisan{{spaces}}15, the first day of Passover week, calculated according to modern Jewish methods.{{sfn|van Gent|2019}}

This Nisan{{spaces}}15 rule affected two Swedish years, 1778 and 1798, that instead of being one week before the Gregorian Easter, were delayed one week so they were on the same Sunday as the Gregorian Easter. Germany's astronomical Easter was one week before the Gregorian Easter in 1724 and 1744.{{sfn|van Gent|2019}} Sweden's astronomical Easter was one week before the Gregorian Easter in 1744, but one week after it in 1805, 1811, 1818, 1825, and 1829.{{sfn|van Gent|2019}}

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 [[Istanbul|Constantinople]] in 1923 and the [[Aleppo Easter dating method|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 {{nowrap|([[Terrestrial Time|TT]] + 2{{sup|h}} 21{{sup|m}})}} without the Nisan{{spaces}}15 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.{{sfn|Shields|1924|pp=407–411}} 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.<ref name=WCC />

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.<ref>{{cite web |author=Pope Paul VI |author-link=Pope Paul VI |url=https://www.vatican.va/archive/hist_councils/ii_vatican_council/documents/vat-ii_const_19631204_sacrosanctum-concilium_en.html |title= Constitution on the sacred liturgy {{!}} ''Sacrosanctum Concilium'' {{!}} Appendix: DECLARATION OF THE SECOND ECUMENICAL COUNCIL OF THE VATICAN ON REVISION OF THE CALENDAR |date=4 December 1963 |access-date=14 April 2025}}</ref>

==Theory==<!-- This section is linked from [[Lunar calendar]] -->
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 {{val|29.53059}} days long.{{sfn|Richards|2013|p=587|ps=: The day consists of 86,400 [[SI]] seconds, and the same value is given for the years 500, 1000, 1500, and 2000.}}

There are 12 synodic months in a lunar year, totaling 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 [[epact]]s ({{langx|grc|ἐπακταὶ ἡμέραι|épaktai hēmérai|intercalary days}}).<ref>{{LSJ|e)pakto/s|ἐπακτός|ref}}.</ref><ref>{{OEtymD|epact}}</ref>

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:

{{blockquote|"Thus beginning the year with March (for that was the ancient custom) they allowed thirty days for the moon [ending] in March, and twenty-nine for that [ending] in April; and thirty again for May, and twenty-nine for June &c. according to the old verses:

<poem>
{{lang|la|Impar luna pari, par fiet in impare mense;}}
{{lang|la|In quo completur mensi lunatio detur.}}
</poem>

"For the first, third, fifth, seventh, ninth, and eleventh months, which are called {{lang|la|impares menses}}, or unequal months, have their moons according to computation of thirty days each, which are therefore called {{lang|la|pares lunae}}, or equal moons: but the second, fourth, sixth, eighth, tenth, and twelfth months, which are called {{lang|la|pares menses}}, or equal months, have their moons but twenty nine days each, which are called {{lang|la|impares lunae}}, or unequal moons."|source={{harvnb|Wheatly|1871|p=44}} }}

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 {{nowrap|1=19 × 11 = 209 ≡ 29 ([[modulo operation|mod]] 30)}}, not {{nowrap|0 (mod 30)}}. 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.{{efn|Although prior to the replacement of the Julian calendar in 1752 some printers of the ''Book of Common Prayer'' placed the {{lang|la|saltus}} correctly, beginning the next month on 30 July, none of them continued the sequence correctly to the end of the year.}}
So after 19 years, the epact must be corrected by one day for the cycle to repeat. This is the so-called {{lang|la|saltus lunae}} ("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.{{efn|Although prior to the replacement of the Julian calendar in 1752 some printers of the ''Book of Common Prayer'' placed the {{lang|la|saltus}} correctly, beginning the next month on 30 July, none of them continued the sequence correctly to the end of the year.}}

The {{lang|la|saltus}} 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).<ref>{{cite book|url=http://archive.org/details/astronomicalalmanac1961/page/n431/mode/2up |publisher=H M Nautical Almanac Office |title=Explanatory Supplement to the Astronomical Ephemeris |date=1961 |location=London |page=422}}</ref>{{sfn|Bede|1999|pp=xlvi}} The sequence number of the year in the 19-year cycle is called the "[[Golden numbers|golden number]]", and is given by the formula
:''GN'' = (''Y'' mod 19) + 1
That is, the year number ''Y'' in the [[Anno Domini|Christian era]] is divided by 19, and the remainder plus 1 is the golden number. (Some sources specify that you add 1 ''before'' taking the remainder; in that case, you need to treat a result of 0 as golden number 19. In the formula above we take the remainder first and ''then'' add 1, so no such adjustment is necessary.) {{efn|"the [Golden Number] of a year AD is found by adding one, dividing by 19, and taking the remainder (treating 0 as 19)."{{harv|Blackburn|Holford-Strevens|1999|p=810}}.}}

Cycles of 19 years are not all the same length, because they may have either four or five leap years. But a period of four cycles, 76 years (a [[Callippic cycle]]), has a length of {{nowrap|1=76 × 365 + 19 = 27,759}} days (if it does not cross a century division). There are {{nowrap|1=235 × 4 = 940}} lunar months in this period, so the average length is 27759{{nbsp}}/{{nbsp}}940 or about 29.530851 days. There are {{nowrap|1=76 × 6 = 456}} usual nominal 30-day lunar months and the same number of usual nominal 29-day months, but with 19 of these lengthened by a day on leap days, plus 24 intercalated months of 30 days and four intercalated months of 29 days. Since this is longer than the true length of a synodic month, about 29.53059 days, the calculated Paschal full moon gets later and later compared to the astronomical full moon, unless a correction is made as in the Gregorian system (see below).

The paschal or Easter-month is the first one in the year to have its fourteenth day (its formal [[Ecclesiastical full moon|full moon]]) on or after 21 March. Easter is the Sunday after its 14th day (or, saying the same thing, the Sunday within its third week). The paschal lunar month always begins on a date in the 29-day period from 8 March to 5 April inclusive. Its fourteenth day, therefore, always falls on a date between 21 March and 18 April inclusive (in the Gregorian or Julian calendar, for the Western and Eastern system, resp.), and the following Sunday then necessarily falls on a date in the range 22 March to 25 April inclusive. However, in the Western system Easter cannot fall on 22 March during the 300-year period 1900–2199 (see below).
In the solar calendar Easter is called a [[moveable feast]] since its date varies within a 35-day range. But in the lunar calendar, Easter is always the third Sunday in the paschal lunar month, and is no more "moveable" than any holiday that is fixed to a particular day of the week and week within a month, such as [[Thanksgiving]].

==Tabular methods==
===Gregorian reform of the {{lang|la|computus|italic=no}}===
<!--[[Gregorian reform of the {{lang|la|computus}}]] redirects here]]-->
{{Further|Gregorian reform of the calendar}}{{Anchor|Gregorian calendar}}
{{More citations needed|section|date=March 2019}}
As reforming the {{lang|la|computus}} was the primary motivation for the introduction of the [[Gregorian calendar]]{{cn|date=April 2025}} in 1582, a corresponding {{lang|la|computus}} methodology was introduced alongside the new calendar.{{efn|See especially the [http://henk-reints.nl/cal/audette/canon1.html first],
[http://henk-reints.nl/cal/audette/canon2.html second],
[http://henk-reints.nl/cal/audette/canon4.html fourth], and
[http://henk-reints.nl/cal/audette/canon6.html sixth canon], and the
[http://henk-reints.nl/cal/audette/calend.html {{lang|la|calendarium}}]}} The general method of working was given by [[Clavius]] in the Six Canons (1582), and a full explanation followed in his {{lang|la|Explicatio}} (1603).{{sfn|Clavius|1603}}

Easter is the Sunday following the Paschal full moon date. The paschal full moon date is the ecclesiastical full moon date on or after the ecclesiastical equinox on 21 March.
The fourteenth day of the lunar month is ecclesiastically considered the day of the [[full moon]].{{sfn|Dershowitz|Reingold|2008|pp=114–115}} It is the day of the lunar month on which the moment of opposition ("full moon") is most likely to fall.

The Gregorian method derives new moon dates by determining the [[epact]] for each year.{{sfn|Dershowitz|Reingold|2008|pp=113–117}} The epact can have a value from * (0 or 30) to 29 days. It is the age of the moon in days (i.e. the lunar date) on 1 January reduced by one day.
The "new moon" is most likely to become visible (as a slender crescent in the western sky after sunset) on the first day of the lunar month. The conjunction of Sun and Moon ("new moon") is most likely to fall on the preceding day, which is day 29 of a "hollow" (29-day) month and day 30 of a "full" (30-day) month.

Historically, in [[Beda Venerabilis' Easter cycle]], the paschal full moon date for a year was found from its sequence number in the Metonic cycle, called the [[Golden number (time)|golden number]], which cycle repeats the lunar phase on January 1 every 19 years.{{sfn|Dershowitz|Reingold|2008|p=114}} This method was modified in the Gregorian reform because the tabular dates go out of sync with reality after about two centuries. From the epact method, a simplified table can be constructed that has a validity of one to three centuries.{{sfn|Grotefend|1891|p=}}{{sfn|Ginzel|1914}}

{| class="wikitable" style="text-align:center"
|+ Current Metonic cycle
!width=5%|Year
|width=5%|2014||width=5%|2015||width=5%|2016||width=5%|2017||width=5%|2018||width=5%|2019||width=5%|2020||width=5%|2021||width=5%|2022||width=5%|2023||width=5%|2024||width=5%|2025||width=5%|2026||width=5%|2027||width=5%|2028||width=5%|2029||width=5%|2030||width=5%|2031||width=5%|2032
|-
!Golden <br /> number
|1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19
|-
!Epact{{efn|Can be verified by using {{harvnb|Blackburn|Holford-Strevens|1999|p=825|loc=Table 7}}. }}
|29||10||21||2||13||24||5||16||27||8||19||*||11||22||3||14||'''''25'''''||6||17
|-
!Full moon<ref>Weisstein (c. 2006) "Paschal full moon" agrees with this line of table through 2009.</ref>
|14 A.||3 A.||23 M.||11 A.||31 M.||18 A.||8 A.||28 M.||16 A.||5 A.||25 M.||13 A.||2 A.||22 M.||10 A.||30 M.||17 A.||7 A.||27 M.
|}

The date of the paschal full moon in a particular year is usually either 11 days earlier than in the previous year, or 19 days later. In 5 out of 19 years it is one day less: in years 1, 6, and 17 of the cycle the date is only 18 days later, and in years 7 and 18 it is only 10 days earlier than in the previous year.

In the [[#Julian calendar|Eastern system]], the Paschal full moon is usually four days later than in the West. It is 34 days later in 5 of the 19 years, and 5 days later in years 6 and 17, because in those years, the Gregorian system puts the Paschal full moon a day earlier than it would normally be, in order to keep Easter before April 26, as explained below. In the year 2100, the difference will increase by another day.{{efn|because the Julian calendar will have a leap year but the Gregorian will not.}}

==== Calendarium ====

The epacts are used to find the dates of the new moon in the following way: Write down a table of all 365 days of the year (the leap day is ignored). Then label all dates with a [[Roman numeral]] counting downwards, from "*" (0 or 30), "xxix" (29), down to "i" (1), starting from 1 January, and repeat this to the end of the year. However, in every second such period count only 29 days and label the date with xxv (25) also with xxiv (24). Treat the 13th period (last eleven days) as long, therefore, and assign the labels "xxv" and "xxiv" to sequential dates (26 and 27 December respectively).{{sfn|Davison|1980|pp=156–164}}

Add the label "25" to the dates that have "xxv" in the 30-day periods; but in 29-day periods (which have "xxiv" together with "xxv") add the label "25" to the date with "xxvi". The distribution of the lengths of the months and the length of the epact cycles is such that each civil calendar month starts and ends with the same epact label, except for February and, one might say, for August, which starts with the double label "xxv"/"xxiv" but ends with the single label "xxiv". This table is called the {{lang|la|calendarium}}. The ecclesiastical new moons for any year are those dates when the epact for the year is entered.{{sfn|Davison|1980|pp=156–164}}

If the epact for the year is for instance 27, then there is an [[ecclesiastical new moon]] on every date in that year that has the epact label "xxvii" (27). If the epact is 25, then there is a complication, introduced so that the ecclesiastical new moon will not fall on the same date twice during a Metonic cycle. If the epact cycle in force includes epact 24 (as does the cycle in use since 1900 and until 2199), then an epact of 25 puts the ecclesiastical new moon on April 4 (having the label "25"), otherwise it is on April 5 (having label "xxv").{{sfn|Davison|1980|pp=156–164}}

An epact of 25 giving April 4 can only happen if the golden number is greater than 11. In which case it will be 11 years after a year with epact 24. So for example, in 1954 the golden number was 17, the epact was 25, the ecclesiastical new moon was reckoned on April 4, the full moon on April 17. Easter was on April 18 rather than April 25 as it would otherwise have been, such as in 1886 when the golden number was 6. This system automatically intercalates seven months per Metonic cycle.

Label all the dates in the table with letters "A" to "G", starting from 1 January, and repeat to the end of the year. If, for instance, the first Sunday of the year is on 5 January, which has letter "E", then every date with the letter "E" is a Sunday that year. Then "E" is called the [[dominical letter]] (DL) for that year – from {{langnf|la|dies dominica|the Lord's day|links=no}}. The dominical letter cycles backward one position every year. In leap years, after 24 February, the Sundays fall on the previous letter of the cycle, so leap years have two dominical letters: the first for before, the second for after the leap day.

In practice, for the purpose of calculating Easter, this need not be done for all 365 days of the year. For the epacts, March comes out exactly the same as January, because {{nowrap|31 + 28 days}} = {{nowrap|30 + 29 epacts,}} so one need not calculate January or February. To avoid the need to calculate the dominical letters for January and February, start with D for 1 March. You need the epacts only from 8 March to 5 April.

[[File:Påsktavla ur Liljegrens Runlära (ur Sverige Runinskrifter).png|thumb|upright 2.0|A table from Sweden to find the date of Easter 1140–1671 according to the [[Julian calendar]]. Each column corresponds to a period of 28 years. Notice the [[rune]]s used as arbitrary symbols.]]
[[File:DiagrammePaques Flammarion.jpg|thumb|upright 2.0|Chronological diagram of the date of Easter for 600 years, from the [[Gregorian calendar]] reform to the year 2200 (by [[Camille Flammarion]], 1907).]]
{| class="wikitable" style="text-align:center"
|+ Calendarium restricted to March and April<!-- possible ecclesiastical new moon dates before paschal full moon highlighted -->
|-
!Epact <br/>label!!March!!DL!!April!!DL
|-
|*||1||D|| ||
|-
|{{rn|xxix}}||2||E||'''1'''||G
|-
|{{rn|xxviii}}||3||F||'''2'''||A
|-
|{{rn|xxvii}}||4||G||'''3'''||B
|-
|{{rn|xxvi}}||5||A||rowspan=2|'''4'''|| rowspan="2" |C
|-
|''25''|| rowspan="2" |6||rowspan=2|B
|-
|{{rn|xxv}}|| rowspan="2" |'''5'''|| rowspan="2" |D
|-
|{{rn|xxiv}}||7||C
|-
|{{rn|xxiii}}||'''8'''||D||6||E
|-
|{{rn|xxii}}||'''9'''||E||7||F
|-
|{{rn|xxi}}||'''10'''||F||8||G
|-
|{{rn|xx}}||'''11'''||G||9||A
|-
|{{rn|xix}}||'''12'''||A||10||B
|-
|{{rn|xviii}}||'''13'''||B||11||C
|-
|{{rn|xvii}}||'''14'''||C||12||D
|-
|{{rn|xvi}}||'''15'''||D||13||E
|-
|{{rn|xv}}||'''16'''||E||14||F
|-
|{{rn|xiv}}||'''17'''||F||15||G
|-
|{{rn|xiii}}||'''18'''||G||16||A
|-
|{{rn|xii}}||'''19'''||A||17||B
|-
|{{rn|xi}}||'''20'''||B||18||C
|-
|{{rn|x}}||'''21'''||C||19||D
|-
|{{rn|ix}}||'''22'''||D||20||E
|-
|{{rn|viii}}||'''23'''||E||21||F
|-
|{{rn|vii}}||'''24'''||F||22||G
|-
|{{rn|vi}}||'''25'''||G||23||A
|-
|{{rn|v}}||'''26'''||A||24||B
|-
|{{rn|iv}}||'''27'''||B||25||C
|-
|{{rn|iii}}||'''28'''||C||26||D
|-
|{{rn|ii}}||'''29'''||D||27||E
|-
|{{rn|i}}||'''30'''||E||28||F
|-
|*||'''31'''||F||29||G
|-
|{{rn|xxix}}|| || ||30||A
|}

As an example, if the epact is 27, an ecclesiastical new moon falls on every date labeled ''xxvii''. The ecclesiastical full moon falls 13 days later. From the table above, this gives new moons on 4 March and 3 April, and so full moons on 17 March and 16 April.
Then Easter Day is the first Sunday after the first ecclesiastical full moon on or after 21 March. <!--(This definition uses "on or after 21 March" to avoid ambiguity with historic meaning of the word "after". In modern language, this phrase simply means "after 20 March". The definition of "on or after 21 March" is frequently incorrectly abbreviated to "after 21 March" in published and web-based articles, resulting in incorrect Easter dates.)-->
In the example, this paschal full moon is on 16 April. If the dominical letter is E, then Easter day is on 20 April.

==== Corrections ====

The label "'''''25'''''" (as distinct from "xxv") is used as follows: Within a Metonic cycle, years that are 11 years apart have epacts that differ by one day. A month beginning on a date having labels "xxiv" and "xxv" written side by side has either 29 or 30 days. If the epacts 24 and 25 both occur within one Metonic cycle, then the new (and full) moons would fall on the same dates for these two years. This is possible for the real moon{{efn|In 2004 and again in 2015, there were full moons on 2 and 31 July.}} but is inelegant in a schematic lunar calendar; the dates should repeat only after 19 years. To avoid this, in years that have epacts 25 and with a Golden Number larger than 11, the reckoned new moon falls on the date with the label ''25'' rather than ''xxv''. Where the labels ''25'' and ''xxv'' are together, there is no problem since they are the same. This does not move the problem to the pair "25" and "xxvi", because the earliest epact 26 could appear would be in year 23 of the cycle, which lasts only 19 years: there is a {{lang|la|saltus lunae}} in between that makes the new moons fall on separate dates.

The Gregorian calendar has a correction to the tropical year by dropping three leap days in 400 years (always in a century year). This is a correction to the length of the tropical year, but should have no effect on the Metonic relation between years and lunations. Therefore, the epact is compensated for this (partially{{snd}} see [[epact]]) by subtracting one in these century years. This is the so-called '''solar correction''' or "solar equation" ("equation" being used in its medieval sense of "correction").

However, 19 uncorrected [[Julian year (calendar)|Julian year]]s are a little longer than 235 lunations. The difference accumulates to one day in about 308 years, or 0.00324 days per year. In one cycle, the epact decreases due to the solar correction by 19&nbsp;×&nbsp;0.0075&nbsp;=&nbsp;0.1425 on average, so a cycle is equivalent to {{nowrap|235 − 0.1425/30 {{=}} 234.99525}} months, whereas there are actually 19&nbsp;×&nbsp;365.2425&nbsp;/&nbsp;29.5305889&nbsp;≈&nbsp;234.997261 synodic months. The difference of 0.002011 synodic months per 19-year cycle, or 0.003126 days per year, necessitates an occasional lunar correction to the epact. In the Gregorian calendar, this is done by adding 1 eight times in 2,500 (Gregorian) years (slightly more than 2500&nbsp;×&nbsp;0.003126, or about 7.8), always in a century year: this is the so-called '''lunar correction''' (historically called "lunar equation"). The first one was applied in 1800, the next is in 2100, and will be applied every 300 years except for an interval of 400 years between 3900 and 4300, which starts a new cycle. At the time of the reform, the epacts were changed by 7, even though 10 days were skipped, in order to make a three-day correction to the timing of the new moons.{{sfn|Davison|1980|pp=156–164}}

The solar and lunar corrections work in opposite directions, and in some century years (for example, 1800 and 2100) they cancel each other. The result is that the Gregorian lunar calendar uses an epact table that is valid for a period of from 100 to 300 years. The epact table listed above is valid for the 20th, 21st and 22nd century.

As explained below, the dates of Easter repeat after 5.7 million years, and over this period the average length of an ecclesiastical month is 2,081,882,250/70,499,183&nbsp;≈&nbsp;29.5305869&nbsp;days,{{sfn|Dershowitz | Reingold |2008|p=117}} which differs from the current actual mean lunation length (29,5305889 d: see [[Lunar month#Synodic month]]) in the 6th figure after the decimal point.  This corresponds to an error of less than a day in the phase of the moon over 40,000 years, but in fact the length of a day is changing (as is the length of a synodic month), so the system is not accurate over such periods. See the article [[ΔT (timekeeping)]] for information on the cumulative change of day length.

====Details====
This method of computation has several subtleties:

Every other lunar month has only 29&nbsp;days, so one day must have two (of the 30)&nbsp;epact labels assigned to it. The reason for moving around the epact label "xxv/25" rather than any other seems to be the following: According to Dionysius (in his introductory letter to Petronius), the Nicene council, on the authority of [[Eusebius of Caesarea|Eusebius]], established that the first month of the ecclesiastical lunar year (the paschal month) should start between 8&nbsp;March and 5&nbsp;April inclusive, and the 14th&nbsp;day fall between 21&nbsp;March and 18&nbsp;April inclusive, thus spanning a period of (only) 29&nbsp;days. A new moon on 7&nbsp;March, which has epact label "xxiv", has its 14th&nbsp;day (full moon) on 20&nbsp;March, which is too early (not following 20&nbsp;March). So years with an epact of "xxiv", if the lunar month beginning on 7&nbsp;March had 30&nbsp;days, would have their paschal new moon on 6&nbsp;April, which is too late: The full moon would fall on 19&nbsp;April, and Easter could be as late as 26&nbsp;April. In the Julian calendar the latest date of Easter was 25&nbsp;April, and the Gregorian reform maintained that limit. So the paschal full moon must fall no later than 18&nbsp;April and the new moon on 5&nbsp;April, which has epact label "xxv". 5&nbsp;April must therefore have its double epact labels "xxiv" and "xxv". Then epact "xxv" must be treated differently, as explained in the [[#Corrections|previous section]].

[[File:Easter dates, 1900-2199.svg|thumb|upright 1.5|Dates of Easter, 1900 to 2199]]

The frequency distribution for the date of Easter is ill-defined, because every 100 to 300 years the mapping from golden number to epact changes, and the long-term frequency distribution is only valid over a period of millions of years (see below), whereas the system will certainly not be used for that long.
The present mapping, valid from 1900 to 2199, gives Easter dates with highly varying frequencies. March 22 can never occur, whereas March 31 occurs 13 times in this 300-year span.

[[File:Easter dates, full cycle.svg|thumb|upright 1.5|Distribution of the date of Easter for the complete 5,700,000&nbsp;year cycle]]

If one does ask the question of what the distribution would be over the whole 5.7-million-year period after which the dates repeat, this distribution is quite different from the distribution in the period 1900 to 2199, or even the distribution over the period since the reform until now. The date of Easter in a given year depends only on the epact for the year, its golden number, and its [[dominical letter]], which tells us which days are Sundays.{{efn|More precisely, the dominical letter for the part of the year after February, which is different in leap years from the letter for January and February). (The golden number only matters when the epact is 25, as explained earlier.}} If we go forward 3,230,000 years from a particular year, we find a year at the same point in the 400-year Gregorian cycle and with the same golden number, but with the epact augmented by 1. Therefore, in the long term, all thirty epacts are equally likely. On the other hand, the dominical letters do not all have the same frequency – years with the letters A and C (at the end of the year) occur 14% of the time each, E and F occur 14.25% of the time, and B, D, and G occur 14.5% of the time. Taking into consideration the complication having to do with epact 25, this gives the distribution shown in the second graph. April 19 is the most common because when the epact is 25 the ecclesiastical full moon falls on April 17 or 18 (depending on the golden number), and it also falls on these dates when the epact is 26 or 24, respectively. There are seven days on which the full moon can fall, including April 17 and April 18, in order for Easter to be on April 19 (this is also the latest possible Easter date that the ecclesiastical full moon can fall on a Saturday, as April 18 is the latest date for the ecclesiastical full moon, which Easter is next day if the ecclesiastical full moon is on a Saturday).{{sfn|Davison|1980|pp=156–164}} As a consequence, 19&nbsp;April is the date on which Easter falls most frequently in the Gregorian calendar, happening about 1 year in every 26. 22&nbsp;March is the least frequent, occurring in just {{frac|208}} years.<ref>{{cite magazine |first=George W. |last=Walker |url=https://ui.adsabs.harvard.edu/abs/1944PA.....52..139W |title=Rare Dates for Easter |magazine=Popular Astronomy |issue=52 |year=1944 |pages=139–142 |bibcode=1944PA.....52..139W |access-date=17 May 2022 |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409160412/https://ui.adsabs.harvard.edu/abs/1944PA.....52..139W/abstract |url-status=live }}</ref>{{sfn|Davison|1980|pp=156–164}}

The relation between lunar and solar calendar dates is made independent of the leap day scheme for the solar year. Basically the Gregorian calendar still uses the Julian calendar with a leap day every four years, so a Metonic cycle of 19&nbsp;years has 6,940 or 6,939&nbsp;days with five or four leap days. Now the lunar cycle counts only {{nowrap|1=19 × 354 + 19 × 11 = 6,935 days}}. By not labeling and counting the leap day with an epact number, but having the next new moon fall on the same calendar date as without the leap day, the current lunation gets extended by a day,{{efn|Traditionally in the Christian West, this situation was handled by extending the first 29-day lunar month of the year to 30&nbsp;days, and beginning the following lunar month one day later than otherwise if it was due to begin before the leap day.{{harv|Blackburn|Holford-Strevens|1999|p=813}}.}} and the 235&nbsp;lunations cover as many days as the 19&nbsp;years (so long as the 19 years do not include a "solar correction" as in 1900). So the burden of synchronizing the calendar with the moon (intermediate-term accuracy) is shifted to the solar calendar, which may use any suitable intercalation scheme, all under the assumption that 19&nbsp;solar years = 235&nbsp;lunations (creating a long-term inaccuracy if not corrected by a "lunar correction"). A consequence is that the reckoned age of the moon may be off by a day, and also that the lunations that contain the leap day may be 31 days long, which would never happen if the real moon were followed (short-term inaccuracies). This is the price of a regular fit to the solar calendar.

From the perspective of those who might wish to use the Gregorian Easter cycle as a calendar for the entire year, there are some flaws in the Gregorian lunar calendar<ref>{{cite web |url=https://members.loria.fr/Roegel/loc/epact19.pdf |first=Denis |last=Roegel |title=The missing new moon of A.D. 16399 and other anomalies of the Gregorian calendar |date=24 November 2004 |access-date=26 June 2021 |archive-date=25 February 2021 |archive-url=https://web.archive.org/web/20210225043951/https://members.loria.fr/Roegel/loc/epact19.pdf |url-status=live }}</ref> (although they have no effect on the paschal month and the date of Easter):
# Lunations of 31 (and sometimes 28)&nbsp;days occur.
# If a year with Golden Number&nbsp;19 happens to have epact&nbsp;19, then the last ecclesiastical new moon falls on 2&nbsp;December; the next would be due on 1&nbsp;January. However, at the start of the new year, a {{lang|la|saltus lunae}} increases the epact by another unit, and the new moon should have occurred on the previous day. So a new moon is missed. The {{lang|la|calendarium}} of the {{lang|la|[[Roman Missal|Missale Romanum]]}} takes account of this by assigning epact label "19" instead of "xx" to 31&nbsp;December of such a year, making that date the new moon. It happened every 19&nbsp;years when the original Gregorian epact table was in effect (for the last time in 1690), and next happens in 8511.
# If the epact of a year is 20, an ecclesiastical new moon falls on 31&nbsp;December. If that year falls before a century year, then in most cases, a solar correction reduces the epact for the new year by one: The resulting epact "*" means that another ecclesiastical new moon is counted on 1&nbsp;January. So, formally, a lunation of one day has passed. This next happens in 4199–4200.
# Other borderline cases occur (much) later, and if the rules are followed strictly and these cases are not specially treated, they generate successive new moon dates that are 1, 28, 59, or (very rarely) 58&nbsp;days apart.

A careful analysis shows that through the way they are used and corrected in the Gregorian calendar, the epacts are actually {{sfrac|1|30}} of a lunation and not full days. See [[epact]] for a discussion.

The solar and lunar corrections repeat after {{nowrap|1=4 × 25 = 100}} centuries. In that period, the epact for a given golden number changes by a total of {{nowrap|1=&minus;1 × {{sfrac|3|4}} × 100 + 1 × {{sfrac|8|25}} × 100 = &minus;43 ≡ 17 mod 30}}. This is prime to the 30&nbsp;possible epacts, so it takes {{nowrap|1=100 × 30 = 3,000 centuries}} before the epact mappings repeat; and {{nowrap|1=3,000 × 19 = 57,000}} centuries before they repeat at the same golden number.  It is not obvious how many ecclesiastic New Moons are counted in this 5.7 Myr period.  The Metonic cycles add up to {{nowrap|1=(5,700,000/19) × 235}} = 70,500,000 lunations.  But there are net {{nowrap|1=&minus;43 × (5,700,000/10,000)}} corrections to the epacts, which divided by 30 add up to a correction of &minus;817 lunations, for a total of 70,499,183 lunations.  This number appears to have been first derived by [[Magnus Georg Paucker]] in 1837.<ref>{{cite book |last=Paucker |first=Georg |author-link=Magnus Georg Paucker |date=1837 |title="Die Osterrechnung oder Vorschlag zur Einführung eines kirchlichen Kalenders und Osterkanons" |url=https://books.google.com/books?id=repKAAAAcAAJ&pg=PA59 |location=Riga |publisher=Eduard Frantzen's Buchhandlung |page=59 |access-date=6 September 2022 |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409160405/https://books.google.com/books?id=repKAAAAcAAJ&pg=PA59 |url-status=live }}</ref> It is also mentioned in the chapter on calendars (p.&nbsp;744) in the [[American Ephemeris and Nautical Almanac|Nautical Almanac]] of 1931<ref>{{cite book |title="Almanac and Astronomical Ephemeris for the year 1931" |publisher=His Majesty's Stationery Office |date=1929 |location=London |url=https://archive.org/details/in.ernet.dli.2015.165859/page/n760/mode/1up}}</ref> and in the [[Astronomical Almanac#Explanatory Supplement to the Astronomical Almanac|Explanatory Supplement]] of 1992 (p.&nbsp;582).<ref>{{cite book |last=Doggett |first=L.E. |date=1992 |title=Explanatory Supplement to the Astronomical Almanac |page=582 |url=https://archive.org/details/131123ExplanatorySupplementAstronomicalAlmanac/page/n305/mode/1up |editor-last=Seidelmann |editor-first=P.Kenneth |publisher=U.S. Naval Observatory |location=Washington |isbn=0-935702-68-7}}</ref>{{efn|The Expl.Suppl. of 2013 on p.599 instead specifies 70,499,175 lunations, without explanation or reference.  This number appears to be the truncated value of dividing 2,081,882,250 days by 29.53059, which is a rounded value for the lunation length found in the table at the top of p.587 . So the number of 70,499,175 would be an estimate of the actual number of lunations in a 5.7Myr period, and not the number of New Moons actually counted by the Gregorian lunar calendar over its full cycle.}}  So the Gregorian Easter dates repeat in exactly the same order only after 5,700,000&nbsp;years, 70,499,183&nbsp;lunations, or 2,081,882,250&nbsp;days; the mean lunation length is then 2,081,882,250/70,499,183 = 29.53058690&nbsp;days. Of course the calendar would have to be adjusted after a few millennia because of changes in the length of the tropical year, the synodic month, and the day.

[[File:Easter_date_graphs.svg|thumb|upright 1.25|Graphs of the dates of Western and Eastern Orthodox Easter Sunday compared with the March equinox and full moons from 1950 to 2050 on the Gregorian calendar]]
This raises the question why the Gregorian lunar calendar has separate solar and lunar corrections, which sometimes cancel each other. Lilius's original work has not been preserved, but his proposal was described in the {{lang|la|Compendium Novae Rationis Restituendi Kalendarium}} circulated in 1577, in which it is explained that the correction system he devised was to be a perfectly flexible tool in the hands of future calendar reformers, since the solar and lunar calendar could henceforth be corrected without mutual interference.{{sfn|de Kort|1949|pp=109–116}} An example of this flexibility was provided through an alternative intercalation sequence derived from Copernicus's theories, along with its corresponding epact corrections.{{sfn|Swerdlow |1986|pp=109–118}}

The "solar corrections" approximately undo the effect of the Gregorian modifications to the leap days of the solar calendar on the lunar calendar: they (partially) bring the epact cycle back to the original Metonic relation between the Julian year and lunar month. The inherent mismatch between Sun and Moon in this basic 19-year cycle is then corrected every three or four centuries by the "lunar correction" to the epacts. However, the epact corrections occur at the beginning of Gregorian centuries, not Julian centuries, and therefore the original Julian Metonic cycle is not fully restored.

While the net {{nowrap|1=4 × 8 &minus; 3 × 25 = 43 epact}} subtractions could be distributed evenly over 10,000&nbsp;years (as has been proposed for example by {{harvnb|Lichtenberg|2003|pp=45–76}}) if the corrections are combined, then the inaccuracies of the two cycles are also added and cannot be corrected separately.

The ratios of (mean solar) days per year and days per lunation change both because of intrinsic long-term variations in the orbits, and because the rotation of the Earth is slowing down due to [[tidal deceleration]], so the Gregorian parameters become increasingly obsolete.

This does affect the date of the equinox, but it so happens that the interval between northward (northern hemisphere spring) equinoxes has been fairly stable over historical times, especially if measured in mean solar time.<ref>{{cite web |title=The Length of the Seasons |url=http://individual.utoronto.ca/kalendis/seasons.htm |website=U. Toronto |location=Canada |access-date=31 January 2018 |archive-date=20 January 2018 |archive-url=https://web.archive.org/web/20180120235025/http://individual.utoronto.ca/kalendis/seasons.htm |url-status=live }}</ref><ref>{{cite web |title=Mean Northward Equinoctial Year Length |url=http://individual.utoronto.ca/kalendis/solar/EqSolst_Years_vary_DeltaT.pdf |website=U. Toronto |location=Canada |access-date=31 January 2018 |archive-date=5 March 2016 |archive-url=https://web.archive.org/web/20160305203532/http://individual.utoronto.ca/kalendis/solar/EqSolst_Years_vary_DeltaT.pdf |url-status=live }}</ref>

Also the drift in ecclesiastical full moons calculated by the Gregorian method compared to the true full moons is affected less than one would expect, because the increase in the length of the day is almost exactly compensated for by the increase in the length of the month, as tidal braking transfers angular momentum of the rotation of the Earth to orbital angular momentum of the Moon.

The Ptolemaic value of the length of the mean synodic month, established around the 4th&nbsp;century&nbsp;BCE by the Babylonians, is {{nowrap|29 days 12 hr 44 min {{sfrac|3|1|3}} s}} (see [[Kidinnu]]); the current value is 0.46&nbsp;s less (see [[new moon]]). In the same historic stretch of time, the length of the mean tropical year has diminished by about 10&nbsp;s. (All values mean solar time.)

====British Calendar Act and ''Book of Common Prayer'' ====
{{main|Calendar (New Style) Act 1750}}
The portion of the [[#Tabular methods|tabular methods]] section above describes the historical arguments and methods by which the present dates of Easter Sunday were decided in the late 16th century by the Catholic Church. In Britain, where the Julian calendar was then still in use, Easter Sunday was defined, from 1662 to 1752 (in accordance with previous practice), by a simple table of dates in the [[Anglican]] ''[[Book of Common Prayer]]'' (decreed by the [[Act of Uniformity 1662]]). The table was indexed directly by the [[golden numbers|golden number]] and the [[dominical letter|Sunday letter]], which (in the Easter section of the book) were presumed to be already known.

For the British Empire and colonies, the new determination of the date of Easter Sunday was defined by what is now called the Calendar (New Style) Act 1750 in an annexe that declares its effect on the ''[[Book of Common Prayer]]''. The method was chosen to give dates agreeing with the Gregorian rule already in use elsewhere, without recognising any Papal authority. As the [[Church of England]] is the [[established church]], Parliament could (and did) require that the dates in the ''Book of Common Prayer'' be modified accordingly, and therefore it is the general Anglican rule. The original act can be seen in the British ''Statutes at Large 1765''.<ref>[https://archive.org/details/bub_gb_rLsuAAAAIAAJ An act for regulating the commencement of the year; and for correcting the calendar now in use] ''Statutes at Large'' 1765, with [https://archive.org/details/bub_gb_rLsuAAAAIAAJ Easter tables]</ref> The annexe to the act includes the definition: "''Easter-day'' (on which the rest depend) is always the first ''Sunday'' after the ''Full Moon'', which happens upon, or next after the Twenty-first Day of ''March''. And if the ''Full Moon'' happens upon a ''Sunday'', ''Easter-day'' is the ''Sunday'' after." The annexe subsequently uses the terms "Paschal Full Moon" and "Ecclesiastical Full Moon", making it clear that they approximate to the real full moon.

The method is quite distinct from that described above in {{slink||Gregorian reform of the computus}}. For a general year, one first determines the [[golden numbers|golden number]], then one uses three tables to determine the [[dominical letter|Sunday letter]], a "cypher", and the date of the paschal full moon, from which the date of Easter Sunday follows. The epact does not explicitly appear. Simpler tables can be used for limited periods (such as 1900–2199) during which the cypher (which represents the effect of the solar and lunar corrections) does not change. Clavius's details were employed in the construction of the method, but they play no subsequent part in its use.<ref>{{cite book|url=https://archive.org/details/bookcommonpraye00englgoog|title=Book of Common Prayer, and Administration of the Sacraments and Other Rites and Ceremonies of the Church|date=9 August 1765|publisher=Joseph Bentham|access-date=9 August 2017|via=Internet Archive}}</ref><ref>{{cite web|url=http://www.eskimo.com/~lhowell/bcp1662/info/tables/tables.html|last=Book of Common Prayer|title=Tables and Rules|access-date=26 June 2021|archive-date=27 May 2021|archive-url=https://web.archive.org/web/20210527215530/http://www.eskimo.com/~lhowell/bcp1662/info/tables/tables.html|url-status=live}}</ref>

J. R. Stockton shows his derivation of an efficient computer algorithm traceable to the tables in the prayer book and the Calendar Act (assuming that a description of how to use the Tables is at hand), and verifies its processes by computing matching tables.<ref>{{cite web|url=http://www.merlyn.demon.co.uk/estr-bcp.htm|title=The Calculation of Easter Sunday after the Book of Common Prayer|last=Stockton|first=J. R.|access-date=9 August 2017|archive-url=https://web.archive.org/web/20150907215917/http://www.merlyn.demon.co.uk/estr-bcp.htm|archive-date=7 September 2015}}</ref>

=== "Paradoxical" Easter dates ===
Due to the discrepancies between the approximations of Computistical calculations of the time of the [[Mean motion|mean]] (northern hemisphere) [[March equinox|vernal equinox]] and the lunar phases, and the true values computed according to astronomical principles, differences occasionally arise between the date of Easter according to computistical reckoning and the hypothetical date of Easter calculated by astronomical methods using the principles attributed to the Church fathers. These discrepancies are called "paradoxical" Easter dates.{{sfn|Nothaft|2018|pp=275–277}}

In his {{lang|la|Kalendarium}} of 1474, [[Regiomontanus]] computed the exact time of all [[Conjunction (astronomy)|conjunctions]] of the Sun and Moon for the longitude of [[Nuremberg]] according to the [[Alfonsine Tables]] for the period from 1475 to 1531. In his work he tabulated 30 instances where the Easter of the Julian {{lang|la|computus}} disagreed with Easter computed using astronomical [[New Moon]]. In eighteen cases the date differed by a week, in seven cases by 35 days, and in five cases by 28 days.{{sfn|Nothaft|2018|pp=275–277}}

[[Ludwig Lange (physicist)|Ludwig Lange]] investigated and classified different types of paradoxical Easter dates using the Gregorian {{lang|la|computus}}.{{sfn|Lange|1928|p=}} In cases where the first vernal full moon according to astronomical calculation occurs on a Sunday and the {{lang|la|computus}} gives the same Sunday as Easter, the celebrated Easter occurs one week in advance compared to the hypothetical "astronomically" correct Easter. Lange called this case a negative weekly (hebdomadal) paradox (H− paradox). If the astronomical calculation gives a Saturday for the first vernal full moon and Easter is not celebrated on the directly following Sunday but one week later, Easter is celebrated according to the {{lang|la|computus}} one week too late in comparison to the astronomical result. He classified such cases a positive weekly (hebdomadal) paradox (H+ paradox).{{sfn|Lange|1928|p=}}

The discrepancies are even larger if there is a difference according to the vernal equinox with respect to astronomical theory and the approximation of the {{lang|la|computus}}. If the astronomical equinoctial full moon falls before the computistical equinoctial full moon, Easter will be celebrated four or even five weeks too late. Such cases are called a positive equinoctial paradox (A+ paradox) according to Lange. In the reverse case when the Computistical equinoctial full moon falls a month before the astronomical equinoctial full moon, Easter is celebrated four or five weeks too early. Such cases are called a negative equinoctial paradox (A− paradox).{{sfn|Lange|1928|p=}}

Equinoctial paradoxes are always valid globally for the whole Earth, because the sequence of equinox and full moon does not depend on the geographical longitude. In contrast, weekly paradoxes are local in most cases and are valid only for part of the Earth, because the change of day between Saturday and Sunday is dependent on the geographical longitude. The computistical calculations are based on astronomical tables valid for the longitude of Venice, which Lange called the Gregorian longitude.{{sfn|Lange|1928|p=}}

In the 21st and 22nd centuries{{sfn|Lange|1928|p=}}{{sfn|Zeyer|2020|pp=5–10}} negative weekly paradoxical Easter dates occur in 2049, 2076, 2106, 2119 (global), 2133, 2147, 2150, 2170, and 2174. Positive weekly paradoxical dates occur in 2045, 2069, 2089 (global), and 2096. Positive equinoctial paradoxical dates in 2019, 2038, 2057, 2076, 2095, 2114, 2133, 2152, 2171, and 2190.{{sfn|Zeyer|2020|pp=5–10}}

In 2076 and 2133, double paradoxes (positive equinoctial and negative weekly) occur. Negative equinoctial paradoxes are extremely rare. They occur only twice until the year 4000 in 2353, when Easter is five weeks too early and in 2372, when Easter is four weeks too early.{{sfn|Zeyer|2020|pp=5–10}}

==Algorithms==
{{more citations|section|date=April 2025}}
===Note on operations===
When expressing Easter algorithms without using tables, it has been customary to employ only the integer operations [[addition]], [[subtraction]], [[multiplication]], [[Division (mathematics)|division]], [[Modulo operation|modulo]], and [[Assignment (computer science)|assignment]] as it is compatible with the use of simple mechanical or electronic calculators. That restriction is undesirable for computer programming, where conditional operators and statements, as well as look-up tables, are available. One can easily see how conversion from day-of-March (22 to 56) to day-and-month (22 March to 25 April) can be done as {{nowrap|1=<code>if (DoM > 31) {Day=DoM-31, Month=Apr} else {Day=DoM, Month=Mar}</code>}}.{{cn|date=April 2025}} More importantly, using such conditionals also simplifies the core of the Gregorian calculation.{{cn|date=April 2025}}

=== Gauss's Easter algorithm<!--'Gauss's Easter algorithm' redirects here-->===
In 1800, the mathematician [[Carl Friedrich Gauss]] presented this algorithm for calculating the date of the Julian or Gregorian Easter.<ref name=Gauß-CD /><ref name=Gauss1 /> He corrected the expression for calculating the variable ''p'' in 1816.<ref name=Gauss2 /> In 1800, he incorrectly stated {{nowrap|1=''p'' = [[Floor and ceiling functions|floor]] ({{sfrac|''k''|3}}) = {{floor|{{sfrac|''k''|3}}}} }}. In 1807, he replaced the condition {{nowrap|(11''M'' + 11) mod 30 < 19}} with the simpler {{nowrap|''a'' > 10}}. In 1811, he limited his algorithm to the 18th and 19th centuries only, and stated that 26 April is always replaced with 19, and 25 April by 18 April in the circumstances stated. In 1816, he thanked his student Peter Paul Tittel for pointing out that ''p'' was wrong in the original version.{{sfn|Bien|2004|pp=439–452}}

<syntaxhighlight lang="python">
gauss_computus_paschalis:
    input(year, calendar)
    
    a = year % 19
    b = year % 4
    c = year % 7

    if calendar is GREGORIAN:
        k = year // 100
        p = (13 + 8 * k) // 25    # fixed (1816), was: k // 3
        q = k // 4
        M = (15 - p + k - q) % 30
        N = (4 + k - q) % 7
    else if calendar is JULIAN:
        M = 15
        N = 6

    d = (19 * a + M) % 30
    e = (2 * b + 4 * c + 6 * d + N) % 7
    march_easter = d + e + 22
    april_easter = d + e - 9

    if april_easter == 25 and d == 28 and e == 6 and a > 10:   # changed (1807), was: (11 * M + 11) % 30 < 19
        april_easter = 18

    if april_easter == 26 and d == 29 and e == 6:
        april_easter = 19

    if march_easter <= 31:
        output(3, march_easter)
    else:
        output(4, april_easter)
</syntaxhighlight>

'''Gauss's Easter algorithm'''<!--boldface per WP:R#PLA--> can be divided into two parts for analysis. The first part is the approximate tracking of the lunar orbiting and the second part is the exact deterministic offsetting to obtain a Sunday following the full moon.{{cn|date=April 2025}}

The first part consists of determining the variable ''d'', the number of days (counting from 22 March) to the day after the full moon. The formula for ''d'' contains the terms 19''a'' and the constant ''M''. ''a'' is the year's position in the 19-year lunar phase cycle, in which by assumption the moon's movement relative to Earth repeats every 19 calendar years. In older times, 19 calendar years were equated to 235 lunar months (the Metonic cycle), which is a close approximation since 235 lunar months amount to 6939.6813 days and 19 solar years are on average 6939.6075 days.

The expression (19''a'' + ''M'') mod 30 repeats every 19 years within each century as ''M'' is determined per century. The 19-year cycle has nothing to do with the '19' in 19''a''; it is just a coincidence that another '19' appears. The '19' in 19''a'' comes from correcting the mismatch between a calendar year and an integer number of lunar months.

A calendar year (non-leap year) has 365 days and the closest one can come with an integer number of lunar months is {{nowrap|1=12 × 29.5 = 354}} days. The difference is 11 days, which must be corrected for by moving the following year's occurrence of a full moon 11 days back. But in modulo 30 arithmetic, subtracting 11 is the same as adding 19, hence the addition of 19 for each year added, i.e. 19''a''.

The ''M'' in {{nowrap|19''a'' + ''M''}} serves to have a correct starting point at the start of each century. It is determined by a calculation taking the number of leap years up until that century where ''k'' inhibits a leap day every 100 years and ''q'' reinstalls it every 400 years, yielding {{nowrap|(''k'' − ''q'')}} as the total number of inhibitions to the pattern of a leap day every four years. Thus we add {{nowrap|(''k'' − ''q'')}} to correct for leap days that never occurred. ''p'' corrects for the lunar orbit not being fully describable in integer terms.

The range of days considered for the full moon to determine Easter are 21 March (the day of the ecclesiastical equinox of spring) to 18 April—a 29-day range. However, in the mod 30 arithmetic of variable ''d'' and constant ''M'', both of which can have integer values in the range 0 to 29, the range is 30. Therefore, adjustments are made in critical cases. Once ''d'' is determined, this is the number of days to add to 22 March (the day after the earliest possible full moon allowed, which is coincident with the ecclesiastical equinox of spring) to obtain the date of the day after the full moon.

So the first allowable date of Easter is {{nowrap|March 22 + ''d'' + 0}}, as Easter is to celebrate the Sunday after the ecclesiastical full moon; that is, if the full moon falls on Sunday 21 March, Easter is to be celebrated 7 days after, while if the full moon falls on Saturday 21 March, Easter is the following 22 March.

The second part is finding ''e'', the additional offset days that must be added to the date offset ''d'' to make it arrive at a Sunday. Since the week has 7 days, the offset must be in the range 0 to 6 and determined by modulo 7 arithmetic. ''e'' is determined by calculating {{nowrap|2''b'' + 4''c'' + 6''d'' + ''N'' mod 7}}. These constants may seem strange at first, but are quite easily explainable if we remember that we operate under mod 7 arithmetic. To begin with, {{nowrap|2''b'' + 4''c''}} ensures that we take care of the fact that weekdays slide for each year.

A normal year has 365 days, but {{nowrap|1=52 × 7 = 364}}, so 52 full weeks make up one day too little. Hence, each consecutive year, the weekday "slides one day forward", meaning if 6 May was a Wednesday one year, it is a Thursday the following year (disregarding leap years). Both ''b'' and ''c'' increase by one for an advancement of one year (disregarding modulo effects). The expression {{nowrap|2''b'' + 4''c''}} thus increases by 6 – but remember that this is the same as subtracting 1 mod 7.

To subtract by 1 is exactly what is required for a normal year – since the weekday slips one day forward we should compensate one day less to arrive at the correct weekday (i.e. Sunday). For a leap year, ''b'' becomes 0 and 2''b'' thus is 0 instead of 8 – which under mod 7, is another subtraction by 1 – i.e., a total subtraction by 2, as the weekdays after the leap day that year slide forward by two days.

The expression 6''d'' works the same way. Increasing ''d'' by some number ''y'' indicates that the full moon occurs y days later this year, and hence we should compensate y days less. Adding 6''d'' is mod 7 the same as subtracting ''d'', which is the desired operation. Thus, again, we do subtraction by adding under modulo arithmetic. In total, the variable ''e'' contains the step from the day after the day of the full moon to the nearest following Sunday, between 0 and 6 days ahead. The constant ''N'' provides the starting point for the calculations for each century and depends on where 1 January, year 1 was implicitly located when the Gregorian calendar was constructed.

The expression {{nowrap|''d'' + ''e''}} can yield offsets in the range 0 to 35 pointing to possible Easter Sundays on 22 March to 26 April. For reasons of historical compatibility, all offsets of 35 and some of 34 are subtracted by 7, jumping one Sunday back to the day of the full moon (in effect using a negative ''e'' of −1). This means that 26 April is never Easter Sunday and that 19 April is overrepresented. These latter corrections are for historical reasons only and have nothing to do with the mathematical algorithm. The offset of 34 is adjusted if (and only if) ''d'' = 28 and ''d'' = 29 elsewhere in the 19-year cycle.

Using the Gauss's Easter algorithm for years prior to 1583 is historically pointless since the Gregorian calendar was not utilised for determining Easter before that year. Using the algorithm far into the future is questionable, since we know nothing about how different churches will define Easter far ahead. Easter calculations are based on agreements and conventions, not on the actual celestial movements nor on indisputable facts of history.

===Anonymous Gregorian algorithm===
{| class="wikitable" style="text-align: right;"
|+ Original format of 1876 ''Nature'' submission
|-
! Dividend !! Divisor !! Quotient !! Remainder
|-
| {{math|1=''year''}} || 19 || {{n/a}} || {{mvar|a}}
|-
| {{math|1=''year''}} || 100 || {{math|1=''b''}} || {{mvar|c}}
|-
| {{math|1=''b''}} || 4 || {{math|1=''d''}} || {{mvar|e}}
|-
| {{math|1=''b'' + 8}} || 25 || {{math|1=''f''}} || {{n/a}}
|-
| {{math|1=''b'' − ''f'' + 1}} || 3 || {{math|1=''g''}} || {{n/a}}
|-
| {{math|1=19''a'' + ''b'' &minus; ''d'' &minus; ''g'' + 15}} || 30 || {{n/a}} || {{mvar|h}}
|-
| {{math|1=''c''}} || 4 || {{math|1=''i''}} || {{mvar|k}}
|-
| {{math|1=32 + 2''e'' + 2''i'' − ''h'' − ''k''}} || 7 || {{n/a}} || {{mvar|l}}
|-
| {{math|1=''a'' + 11''h'' + 22''l''}} || 451 || {{math|1=''m''}} || {{n/a}}
|-
| {{math|1=''h'' + ''l'' − 7''m'' + 114}} || 31 || {{math|1=''n''}} || {{mvar|o}}
|-
|}

"A New York correspondent" submitted this algorithm for determining the Gregorian Easter to the journal ''[[Nature (journal)|Nature]]'' in 1876.{{sfn|Bien|2004|pp=439–452}}<ref>{{cite journal|author=Anon|url=https://books.google.com/books?id=H4ICAAAAIAAJ&pg=PA487|title=To find Easter|journal=Nature|date=20 April 1876|page=487}}</ref>
It has been reprinted many times, e.g.,
in 1877 by Samuel Butcher in ''The Ecclesiastical Calendar'',{{sfn|Butcher|1877|p=225}}
in 1916 by [[A. M. W. Downing|Arthur Downing]] in ''[[The Observatory (journal)|The Observatory]]'',{{sfn|Downing|1916|pp=215–219}}
in 1922 by [[Harold Spencer Jones|H. Spencer Jones]] in ''General Astronomy'',{{sfn|Spencer Jones|1922|p=73}}
in 1977 by the ''Journal of the British Astronomical Association'',<ref>{{cite journal|journal=Journal of the British Astronomical Association|volume=88|date=December 1977|page=91|bibcode=1977JBAA...88...87.|title=Letters to the Editor|author=}}</ref>
in 1977 by [[Old Farmer's Almanac|''The Old Farmer's Almanac'']],
in 1988 by Peter Duffett-Smith in ''[[Practical Astronomy with your Calculator]]'',
and in 1991 by [[Jean Meeus]] in ''Astronomical Algorithms''.{{sfn|Meeus|1991|pp=67–68}}
Because of the Meeus book citation, it is also called the "Meeus/Jones/Butcher" algorithm:

{| class="wikitable" style="text-align: right;"
|-
! Variable !! Expression || ''Y'' = 1961 || {{CURRENTYEAR}} || {{NEXTYEAR}}
|-
| {{math|1=''a'' =}} || {{math|''Y'' mod 19}}
| 4 || {{#expr: {{CURRENTYEAR}} mod 19}}|| {{#expr: {{NEXTYEAR}} mod 19}}
|-
| {{math|1=''b'' =}} || {{math|{{floor|{{sfrac|''Y'' | 100}}}}}}
| 19 || {{#expr:floor({{CURRENTYEAR}} / 100)}}|| {{#expr:floor({{NEXTYEAR}} / 100)}}
|-
| {{math|1=''c'' =}} || {{math|''Y'' mod 100}}
| 61 || {{#expr:{{CURRENTYEAR}} mod 100}}|| {{#expr:{{NEXTYEAR}} mod 100}}
|-
| {{math|1=''d'' =}} || {{math|{{floor|{{sfrac|''b'' | 4}}}}}}
| 4 || {{#expr:floor( (floor({{CURRENTYEAR}}/100)) /4)}}|| {{#expr:floor( (floor({{NEXTYEAR}}/100)) /4)}}
|-
| {{math|1=''e'' =}} || {{math|''b'' mod 4}}
| 3 || {{#expr:(floor({{CURRENTYEAR}} / 100))mod4}}|| {{#expr:(floor({{NEXTYEAR}} / 100))mod4}}
|-
| {{math|1=''f'' =}} || {{math|{{floor|{{sfrac|''b'' + 8 | 25}}}}}}
| 1 || {{#expr:floor((floor({{CURRENTYEAR}}/100)+8)/25)}}|| {{#expr:floor((floor({{NEXTYEAR}}/100)+8)/25)}}
|-
| {{math|1=''g'' =}} || {{math|{{floor|{{sfrac|''b'' − ''f'' + 1 | 3}}}}}}
| 6 || {{#expr:floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3)}}
|| {{#expr:floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3)}}
|-
| {{math|1=''h'' =}} || {{math|(19''a'' + ''b'' − ''d'' − ''g'' + 15) mod 30}}
| 10 || {{#expr:(19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30}}
|| {{#expr:(19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30}}
|-
| {{math|1=''i'' =}} || {{math|{{floor|{{sfrac|''c'' | 4}}}}}}
| 15 || {{#expr:floor(({{CURRENTYEAR}} mod 100)/4)}}|| {{#expr:floor(({{NEXTYEAR}} mod 100)/4)}}
|-
| {{math|1=''k'' =}} || {{math|''c'' mod 4}}
| 1 || {{#expr:({{CURRENTYEAR}} mod 100)mod4}}|| {{#expr:({{NEXTYEAR}} mod 100)mod4}}
|-
| {{math|1=''l'' =}} || {{math|(32 + 2''e'' + 2''i'' − ''h'' − ''k'') mod 7}}
| 1 || {{#expr: (32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7}}
| {{#expr: (32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7}}
|-
| {{math|1=''m'' =}} || {{math|{{floor|{{sfrac|''a'' + 11''h'' + 22''l'' | 451}}}}}}
| 0 || {{#expr:floor((({{CURRENTYEAR}} mod 19) + 11*((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7))/451)}}
|| {{#expr:floor((({{NEXTYEAR}} mod 19) + 11*((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7))/451)}}
|- style="display:none"|
| || {{math|''h'' + ''l'' − 7''m'' + 114}}
| 125 || {{#expr:(((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{CURRENTYEAR}} mod 19) + 11*((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7))/451)) + 114)}}
|| {{#expr:(((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{NEXTYEAR}} mod 19) + 11*((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7))/451)) + 114)}}
|-
|title="month"| {{math|1=''n'' =}} || {{math|{{floor|{{sfrac|''h'' + ''l'' − 7''m'' + 114 | 31}}}}}}
| 4 || {{#expr:floor((((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{CURRENTYEAR}} mod 19) + 11*((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7))/451)) + 114)/31)}}
|| {{#expr:floor((((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{NEXTYEAR}} mod 19) + 11*((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7))/451)) + 114)/31)}}
|-
|title="day of the month offset by one"| {{math|1=''o'' =}} || {{math|(''h'' + ''l'' − 7''m'' + 114) mod 31}}
| 1 || {{#expr: ((((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ( (32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{CURRENTYEAR}} mod 19) + 11*((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7))/451)) + 114) mod 31)}}
|| {{#expr: ((((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ( (32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{NEXTYEAR}} mod 19) + 11*((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7))/451)) + 114) mod 31)}}
|-
!colspan=2| Gregorian Easter
| 2 April 1961 || {{#expr: ((((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ( (32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{CURRENTYEAR}} mod 19) + 11*((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7))/451)) + 114) mod 31) + 1}} {{MONTHNAME|{{#expr:floor((((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{CURRENTYEAR}} mod 19) + 11*((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{CURRENTYEAR}} / 100))mod4) + 2*(floor(({{CURRENTYEAR}} mod 100)/4)) − ((19*({{CURRENTYEAR}} mod 19)+(floor({{CURRENTYEAR}} / 100))-(floor( (floor({{CURRENTYEAR}}/100)) /4))-(floor(((floor({{CURRENTYEAR}} / 100))-(floor((floor({{CURRENTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{CURRENTYEAR}} mod 100)mod4)) mod 7))/451)) + 114)/31)}} }} {{CURRENTYEAR}}
|| {{#expr: ((((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ( (32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{NEXTYEAR}} mod 19) + 11*((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7))/451)) + 114) mod 31) + 1}} {{MONTHNAME|{{#expr:floor((((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) + ((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7) − 7*(floor((({{NEXTYEAR}} mod 19) + 11*((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30)+22*((32 + 2*((floor({{NEXTYEAR}} / 100))mod4) + 2*(floor(({{NEXTYEAR}} mod 100)/4)) − ((19*({{NEXTYEAR}} mod 19)+(floor({{NEXTYEAR}} / 100))-(floor( (floor({{NEXTYEAR}}/100)) /4))-(floor(((floor({{NEXTYEAR}} / 100))-(floor((floor({{NEXTYEAR}}/100)+8)/25))+1)/3))+15)mod30) − (({{NEXTYEAR}} mod 100)mod4)) mod 7))/451)) + 114)/31)}} }} {{NEXTYEAR}}
|}

In this algorithm, the variable ''n'' indicates the month of the year (either March for ''n'' = 3, or April for ''n'' = 4), while the day of the month is obtained as (''o'' + 1). In 1961 the ''New Scientist'' published a version of the ''Nature'' algorithm incorporating a few changes.{{sfn|O'Beirne|1961|p=828}} The variable ''g'' was calculated using Gauss's 1816 correction, resulting in the elimination of variable ''f''. Some tidying results in the replacement of variable ''o'' (to which one must be added to obtain the date of Easter) with variable ''p'', which gives the date directly.

{| class="wikitable" style="text-align: right;"
|-
! Variable !! Expression || {{math|1=''Y'' = 1961}} || {{CURRENTYEAR}}|| {{NEXTYEAR}}
|-
| {{math|1=''f''}} || {{n/a}}
| {{n/a}} || {{n/a}} || {{n/a}}
|-
| {{math|1=''g'' =}} || {{math|{{floor|{{sfrac|8''b'' + 13 | 25}}}}}}
| 6 || {{#expr:floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 )}}|| {{#expr:floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 )}}
|-
| {{math|1=''m'' =}} || {{math|{{floor|{{sfrac|''a'' + 11''h'' + 19''l'' | 433}}}}}}
| 0 || {{#expr:floor((( {{CURRENTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433)}}
|| {{#expr:floor((( {{NEXTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433)}}
|-
|title="month"| {{math|1=''n'' =}} || {{math|{{floor|{{sfrac|''h'' + ''l'' − 7''m'' + 90 | 25}}}}}}
| 4 || {{#expr:floor((( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{CURRENTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25)}}
|| {{#expr:floor((( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{NEXTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25)}}
|-
| {{math|1=''o''}} || {{n/a}}
| {{n/a}} || {{n/a}}|| {{n/a}}
|-
|title="day of the month"| {{math|1=''p'' =}} || {{math|(''h'' + ''l'' − 7''m'' + 33''n'' + 19) mod 32}}
| 2 || {{#expr:( ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{CURRENTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + (33 * ( floor((( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{CURRENTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25) )) + 19) mod 32}}
|| {{#expr:( ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{NEXTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + (33 * ( floor((( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{NEXTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25) )) + 19) mod 32}}
|-
!colspan=2| Gregorian Easter
| 2 April 1961 || {{#expr:( ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{CURRENTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + (33 * ( floor((( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{CURRENTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25) )) + 19) mod 32}} {{MONTHNAME|{{#expr:floor((( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{CURRENTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{CURRENTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{CURRENTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{CURRENTYEAR}} mod 19 ) ) + ( floor({{CURRENTYEAR}} / 100) ) - ( floor( (floor({{CURRENTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{CURRENTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{CURRENTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25)}} }} {{CURRENTYEAR}}
|| {{#expr:( ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{NEXTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + (33 * ( floor((( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{NEXTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25) )) + 19) mod 32}} {{MONTHNAME|{{#expr:floor((( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) + ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ) - (7 * ( floor((( {{NEXTYEAR}} mod 19 ) + (11 * ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 )) + (19 * ( (32 + (2 * ( (floor({{NEXTYEAR}} / 100) ) mod 4 )) + (2 * ( floor( ( {{NEXTYEAR}} mod 100 ) / 4) )) - ( ( ( 19 * ( {{NEXTYEAR}} mod 19 ) ) + ( floor({{NEXTYEAR}} / 100) ) - ( floor( (floor({{NEXTYEAR}} / 100) ) / 4) ) - ( floor( ( (8 * floor({{NEXTYEAR}} / 100) ) + 13 ) / 25 ) ) + 15 ) mod 30 ) - ( ( {{NEXTYEAR}} mod 100 ) mod 4 )) mod 7 ))) / 433) )) + 90) / 25)}} }} {{NEXTYEAR}}
|}

===Meeus's Julian algorithm===
Jean Meeus, in his book ''Astronomical Algorithms'' (1991, p.&nbsp;69), presents the following algorithm for calculating the Julian Easter on the Julian Calendar. To obtain the date of Eastern Orthodox Easter according to the Gregorian Calendar (used as the [[civil calendar]] throughout most of the contemporary world), 13 days must be added to the Julian dates shown. 

{| class="wikitable" style="text-align: right"
|+ Orthodox (Eastern) Easter date
|-
! Variable !! Expression || ''Y'' = 2008 || 2009 || 2010 || 2011 || 2016 || {{CURRENTYEAR}} || {{NEXTYEAR}}
|-
| ''a'' = || ''Y'' mod 4
| 0 || 1 || 2 || 3 || 0 || {{#expr:{{CURRENTYEAR}} mod 4}} || {{#expr:{{NEXTYEAR}} mod 4}}
|-
| ''b'' = || ''Y'' mod 7
| 6 || 0 || 1 || 2 || 0 || {{#expr:{{CURRENTYEAR}} mod 7}}|| {{#expr:{{NEXTYEAR}} mod 7}}
|-
| ''c'' = || ''Y'' mod 19
| 13 || 14 || 15 || 16 || 2 || {{#expr:{{CURRENTYEAR}} mod 19}}|| {{#expr:{{NEXTYEAR}} mod 19}}
|-
| ''d'' = || (19''c'' + 15) mod 30
| 22 || 11 || 0 || 19 || 23 || {{#expr:(19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30}}|| {{#expr:(19 * ({{NEXTYEAR}} mod 19) + 15) mod 30}}
|-
| ''e'' = || (2''a'' + 4''b'' − ''d'' + 34) mod 7
| 1 || 4 || 0 || 1 || 4 || {{#expr:(2*({{CURRENTYEAR}} mod 4) + 4*({{CURRENTYEAR}} mod 7) − ((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + 34) mod 7}}|| {{#expr:(2*({{NEXTYEAR}} mod 4) + 4*({{NEXTYEAR}} mod 7) − ((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + 34) mod 7}}
|-
| || ''d'' + ''e'' + 114
| 137 || 129 || 114 || 134 || 141 || {{#expr:((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + ((2*({{CURRENTYEAR}} mod 4) + 4*({{CURRENTYEAR}} mod 7) − ((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114}}|| {{#expr:((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + ((2*({{NEXTYEAR}} mod 4) + 4*({{NEXTYEAR}} mod 7) − ((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114}}
|-
| ''month''&nbsp;= || {{floor|{{sfrac|''d'' + ''e'' + 114 | 31}}}}
| 4 || 4 || 3 || 4 || 4 || {{#expr:floor((((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + ((2*({{CURRENTYEAR}} mod 4) + 4*({{CURRENTYEAR}} mod 7) − ((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) / 31)}} || {{#expr:floor((((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + ((2*({{NEXTYEAR}} mod 4) + 4*({{NEXTYEAR}} mod 7) − ((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) / 31)}}
|-
| ''day'' = || {{nowrap|((''d'' + ''e'' + 114) mod 31) + 1}}
| 14 || 6 || 22 || 11 || 18 || {{#expr:((((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + ((2*({{CURRENTYEAR}} mod 4) + 4*({{CURRENTYEAR}} mod 7) − ((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) mod 31) + 1}} || {{#expr:((((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + ((2*({{NEXTYEAR}} mod 4) + 4*({{NEXTYEAR}} mod 7) − ((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) mod 31) + 1}}
|-
! colspan=2| Easter Day (Julian calendar)
| 14 April 2008 || 6 April 2009 || 22 March 2010 || 11 April 2011 || 18 April 2016 || {{#expr:((((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + ((2*({{CURRENTYEAR}} mod 4) + 4*({{CURRENTYEAR}} mod 7) − ((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) mod 31) + 1}} {{MONTHNAME|{{#expr:floor((((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + ((2*({{CURRENTYEAR}} mod 4) + 4*({{CURRENTYEAR}} mod 7) − ((19 * ({{CURRENTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) / 31)}}}} {{CURRENTYEAR}} || {{#expr:((((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + ((2*({{NEXTYEAR}} mod 4) + 4*({{NEXTYEAR}} mod 7) − ((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) mod 31) + 1}} {{MONTHNAME|{{#expr:floor((((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + ((2*({{NEXTYEAR}} mod 4) + 4*({{NEXTYEAR}} mod 7) − ((19 * ({{NEXTYEAR}} mod 19) + 15) mod 30) + 34) mod 7) + 114) / 31)}}}} {{NEXTYEAR}}
|- 
! colspan=2| Gregorian calendar equivalent 
| 27 April 2008 || 19 April 2009 || 4 April 2010 || 24 April 2011 || 1 May 2016 || 20 April 2025 || 12 April 2026
|}

==See also==
{{Portal|Christianity}}

* {{Annotated link |Christian Zeller}}
* {{Annotated link |Crucifixion darkness}}
* {{Annotated link |Reform of the date of Easter}}

==References==
===Notes===
{{Notelist}}

=== Citations ===
{{Reflist|refs=

<ref name=audette>{{cite web |url=http://henk-reints.nl/cal/audette/denys.html |title=Dionysius Exiguus – Liber de Paschate |first=Rodolphe |last=Audette |date=9 December 2007 |access-date=26 June 2021 |archive-date=15 April 2021 |archive-url=https://web.archive.org/web/20210415171302/http://henk-reints.nl/cal/audette/denys.html |url-status=live }}</ref>

<ref name=Kekis>{{cite web |author-first = Theoharis |author-last = Kekis |title = The Orthodox Church Calendar |url=http://cyprusactionnetwork.org/yahoo_site_admin/assets/docs/Orthodox_Church_Calendar.334130901.pdf |publisher = Cyprus Action Network of America |access-date = 11 March 2012 |archive-url = https://web.archive.org/web/20121126175435/http://cyprusactionnetwork.org/yahoo_site_admin/assets/docs/Orthodox_Church_Calendar.334130901.pdf |archive-date = 26 November 2012 }}</ref>

<ref name=WCC>{{citation |title=Towards a Common Date for Easter |url=http://www.oikoumene.org/en/resources/documents/commissions/faith-and-order/i-unity-the-church-and-its-mission/towards-a-common-date-for-easter/index#table|archive-url=https://web.archive.org/web/20180330204645/https://www.oikoumene.org/en/resources/documents/commissions/faith-and-order/i-unity-the-church-and-its-mission/towards-a-common-date-for-easter/index|archive-date=30 March 2018 |publisher=World Council of Churches/Middle East Council of Churches Consultation |date=10 March 1997 |location=Aleppo, Syria}}.</ref>

<ref name=Gauß-CD>{{cite web|url=http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Osterformel/Seite1.htm|title=Gauß-CD|website=webdoc.sub.gwdg.de|access-date=9 August 2017|archive-date=6 December 2016|archive-url=https://web.archive.org/web/20161206041747/http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Osterformel/Seite1.htm|url-status=live}}</ref>

<ref name=Gauss1>{{cite book |chapter=Berechnung des Osterfestes |title=Astronomische Abhandlungen |trans-title=Astronomical Treatises |language=de |chapter-url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=137484 |archive-url=https://archive.today/20120709024808/http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=137484|archive-date=9 July 2012 |first=Carl Friedrich|last=Gauss| access-date=9 August 2017}}</ref>

<ref name=Gauss2>{{cite book |chapter= Berichtigung ze dem aufsatze |title=Astronomische Abhandlungen |trans-title=Astronomical Treatises |language=de |chapter-url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=139587 |archive-url=https://archive.today/20120712061012/http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=139587|archive-date=12 July 2012 |first=Carl Friedrich|last=Gauss|access-date=9 August 2017}}</ref>

<ref name=revradiotowerofsong>{{cite web |url=http://www.revradiotowerofsong.org/Easter_Eostre_2013.htm |last=Re-vision Radio's Tower of Song |title=The Many Easters & Eostres for the Many: A Choice of Hallelujahs |access-date=26 June 2021 |archive-date=16 April 2021 |archive-url=https://web.archive.org/web/20210416095229/http://www.revradiotowerofsong.org/Easter_Eostre_2013.htm |url-status=usurped }}</ref>

}}

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*Dionysius Exiguus (525): ''Liber de Paschate''. On-line: [http://henk-reints.nl/cal/audette/denys.html (full Latin text)] {{Webarchive|url=https://web.archive.org/web/20080603031815/http://www.henk-reints.nl/cal/audette/denys.html |date=3 June 2008 }} and [https://web.archive.org/web/20060109025617/http://hbar.phys.msu.su/gorm/chrono/paschata.htm (table with ''Argumenta'' in Latin, with English translation)]
*{{cite book|author=Domus Quaedam Vetus|title=Carmina Medii Aevi Maximam Partem Inedita|url=https://books.google.com/books?id=2uRBt_zHT6oC&pg=PA151|date=July 2009|publisher=BiblioBazaar|isbn=978-1-110-75828-9}}
*{{cite journal|last= Downing|first= A. M. W.|author-link= A. M. W. Downing|date= May 1916|title= The date of Easter|journal= The Observatory|volume= 39|pages= 215–219|bibcode=1916Obs....39..215D}}
*Eusebius of Caesarea, ''The History of the Church'', Translated by G. A. Williamson. Revised and edited with a new introduction by Andrew Louth. Penguin Books, London, 1989.
*Gregory XIII (Pope) and the calendar reform committee (1581): the Papal Bull ''Inter Gravissimas'' and the Six Canons. On-line under: [http://henk-reints.nl/cal/audette/calgreg.html#index "Les textes fondateurs du calendrier grégorien"] {{Webarchive|url=https://web.archive.org/web/20120429062921/http://henk-reints.nl/cal/audette/calgreg.html#index |date=29 April 2012 }}, with some parts of Clavius's ''Explicatio''.
*{{citation |last=van Gent |first=Robert |title=Anomalous Easter Sunday Dates in the 18th and early 19th Century |url=https://webspace.science.uu.nl/~gent0113/easter/easter_text3b.htm |publisher=Utrecht University |year=2019 |access-date=23 July 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801033523/https://webspace.science.uu.nl/~gent0113/easter/easter_text3b.htm |url-status=live }}.
*{{Cite book|last=Ginzel|first=Friedrich Karl|title=Handbuch der mathematischen und technischen Chronologie, Band III|publisher=Hinrichs|year=1914|location=Leipzig, Germany}}
*{{cite book |last=Grotefend |first=Hermann |title=Zeitrechnung des deutschen Mittelalters und der Neuzeit |url=https://books.google.com/books?id=z-UwAAAAMAAJ&pg=PA2 |year=1891 |publisher=Hahn |access-date=27 November 2020 |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409161231/https://books.google.com/books?id=z-UwAAAAMAAJ&pg=PA2 |url-status=live }}
*{{cite book|first= V. |last= Grumel |title= La chronologie |language= fr |location= Paris |publisher= Presses Universitaires de France |date= 1958|oclc=4260118}}
*{{cite book |last=Lange |first=Ludwig |author-link=Ludwig Lange (physicist) |title="Paradoxe" Osterdaten im Gregorianischen Kalender und ihre Bedeutung für die moderne Kalender reform von Ludwig Lange. Vorgelegt von Eduard Schwartz am 7. Juli 1928 |url=https://books.google.com/books?id=8_gZzQEACAAJ |year=1928 |publisher=Bayer. Akad. d. Wissenschaften |access-date=27 November 2020 |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409160919/https://books.google.com/books?id=8_gZzQEACAAJ |url-status=live }}
*{{cite journal |last=Lichtenberg |first=Heiner |year=2003 |title=Das anpassbar zyklische, solilunare Zeitzählungssystem des gregorianischen Kalenders |journal=Mathematische Semesterberichte |volume=50 |pages=45–76 |doi=10.1007/s00591-003-0063-0|s2cid=120639320 }}
*{{cite journal |last = McCarthy |first = Daniel |title = Easter principles and a fifth-century lunar cycle used in the British Isles |journal = Journal for the History of Astronomy |volume = 24 |issue = 3 |date = August 1993 |pages = 204–224 |bibcode = 1993JHA....24..204M|doi = 10.1177/002182869302400304|s2cid=115765809 }}
*{{cite journal |first=Daniel |last=McCarthy |title=The Lunar and Paschal Tables of ''De ratione paschali'' Attributed to Anatolius of Laodicea |journal=Archive for History of Exact Sciences |volume=49 |issue=4 |year=1996 |pages=285–320 |doi=10.1007/bf00374701|bibcode=1996AHES...49..285M |s2cid=120081352 }}
*{{cite book|first= Jean |last= Meeus |title= Astronomical Algorithms |location= Richmond, Virginia |publisher= Willmann-Bell|date= 1991}}
*{{cite book |last=Mosshammer |first=Alden A. |title=The Easter Computus and the Origins of the Christian Era |url=https://books.google.com/books?id=9gkUDAAAQBAJ |year=2008 |publisher=University Press |location=Oxford |isbn=978-0-19-954312-0 |access-date=9 June 2021 |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409160959/https://books.google.com/books?id=9gkUDAAAQBAJ |url-status=live }}
*{{cite book |last=Nothaft |first=C. Philipp E. |title=Scandalous Error: Calendar Reform and Calendrical Astronomy in Medieval Europe |url=https://books.google.com/books?id=G_BIDwAAQBAJ |year=2018 |publisher=Oxford University Press |isbn=978-0-19-879955-9 |access-date=27 November 2020 |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409161010/https://books.google.com/books?id=G_BIDwAAQBAJ |url-status=live }}
*{{cite journal|url=https://books.google.com/books?id=zfzhCoOHurwC&pg=PA828|last=O'Beirne|first=T H|title=How ten divisions lead to Easter|journal=New Scientist|volume=9|number=228|date=30 March 1961|page=828|access-date=7 June 2021|archive-date=9 April 2023|archive-url=https://web.archive.org/web/20230409160953/https://books.google.com/books?id=zfzhCoOHurwC&pg=PA828|url-status=live}}
*{{cite book |last=Peterson |first=Michael D. |editor-last1=Johnston |editor-first1=William M. |editor-last2=Kleinhenz |editor-first2=Christopher |title=Encyclopaedia of Monasticism |date=2015 |page=468 |chapter=Fasting: Eastern Christian |publisher=Routledge |url=https://books.google.com/books?id=iepJAgAAQBAJ |isbn=978-1-57958-090-2 |access-date=21 March 2023 |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409160917/https://books.google.com/books?id=iepJAgAAQBAJ |url-status=live }}
*{{cite book|last= Richards |first= E. G. |date= 2013 |chapter= Calendars |editor1= S. E. Urban |editor2= P. K. Seidelmann |title= Explanatory Supplement to the Astronomical Almanac |edition= 3rd |location= Mill Valley, CA |publisher= Univ Science Books}}
*{{cite journal |first=Noel M. |last=Swerdlow |title=The Length of the Year in the Original Proposal for the Gregorian Calendar |journal=Journal for the History of Astronomy |volume=17 |issue=49 |date=1986 |pages=109–118 |bibcode=1986JHA....17..109S |doi=10.1177/002182868601700204|s2cid=118491152 }}
*{{cite journal |first=Miriam Nancy |last=Shields |title=The new calendar of the Eastern churches |journal=Popular Astronomy |volume=32 |year=1924 |pages=407–411 |bibcode=1924PA.....32..407S}}
*{{cite book |first= H. |last= Spencer Jones |url= https://archive.org/details/bub_gb_EM4MAAAAYAAJ |title= General Astronomy |location= London |publisher= Longsman, Green |date= 1922 |author-link= Harold Spencer Jones }}
*{{cite journal|first= Gustav |last= Teres |bibcode=1984JHA....15..177T |title= Time computations and Dionysius Exiguus |journal= Journal for the History of Astronomy |volume= 15 |date= 1984 |issue= 3 |pages= 177–188 |doi= 10.1177/002182868401500302|s2cid= 117094612}}
*{{cite journal |first=C.H. |last=Turner |title=The Paschal Canon of Anatolius of Laodicea |journal=The English Historical Review |volume=10 |year=1895 |pages=699–710 |doi=10.1093/ehr/x.xl.699}}
*{{cite book |author-first=Charles |author-last=Wheatly |author-link=Charles Wheatly |title=A Rational Illustration of the Book of Common Prayer of the Church of England |orig-date=1710 |year=1871 |location=London |publisher=Bell and Daldy |url=https://archive.org/details/rationalillustra014115mbp/page/n57 }}
*{{Cite journal|last=Zeyer|first=Klaus Peter|date=2020|title=Häufigkeit von Osterparadoxien: Negative Äquinoktialparadoxien der Jahre 2353 und 2372 als seltenste Variante|journal=Regiomontanusbote|volume=33|pages=5–10}}
{{refend}}

===Further reading===
{{refbegin}}
*Borst, Arno (1993). ''The Ordering of Time: From the Ancient Computus to the Modern Computer'' Trans. by Andrew Winnard. Cambridge: Polity Press; Chicago: Univ. of Chicago Press.
*Coyne, G. V., M. A. Hoskin, M. A., and Pedersen, O. (ed.) ''[http://articles.adsabs.harvard.edu//full/book/grc../1983//0000001,001.html Gregorian reform of the calendar: Proceedings of the Vatican conference to commemorate its 400th anniversary, 1582–1982] {{Webarchive|url=https://web.archive.org/web/20070818190405/http://articles.adsabs.harvard.edu/full/book/grc../1983/0000001,001.html |date=18 August 2007 }}'', (Vatican City: Pontifical Academy of Sciences, Specolo Vaticano, 1983).
*Gibson, Margaret Dunlop, ''The Didascalia Apostolorum in Syriac'', Cambridge University Press, London, 1903.
*Schwartz, E., '' Christliche und jüdische Ostertafeln'', (Abhandlungen der königlichen Gesellschaft der Wissenschaften zu Göttingen. Pilologisch-historische Klasse. Neue Folge, Band viii.) [[Weidmannsche Buchhandlung]], Berlin, 1905.
*[http://www.ccel.org/ccel/schaff/npnf203.i.html Philip Schaff (ed.) Theodoret, Jerome, Gennadius, and Rufinius:  historical writings] {{Webarchive|url=https://web.archive.org/web/20190515021008/http://www.ccel.org/ccel/schaff/npnf203.i.html |date=15 May 2019 }}
*Stern, Sacha, ''Calendar and Community: A History of the Jewish Calendar Second Century BCE – Tenth Century CE'', Oxford University Press, Oxford, 2001.
*Walker, George W, ''[https://ui.adsabs.harvard.edu/abs/1945PA.....53..162W Easter Intervals] {{Webarchive|url=https://web.archive.org/web/20220517082051/https://ui.adsabs.harvard.edu/abs/1945PA.....53..162W |date=17 May 2022 }}'', Popular Astronomy, April 1945, Vol. 53, pp.&nbsp;162–179.
*Walker, George W, ''[https://ui.adsabs.harvard.edu/abs/1945PA.....53..218W Easter Intervals] {{Webarchive|url=https://web.archive.org/web/20220517082051/https://ui.adsabs.harvard.edu/abs/1945PA.....53..218W |date=17 May 2022 }}'' (Continued), Popular Astronomy, May 1945, Vol. 53, pp.&nbsp;218–232.
*Weisstein, Eric. (c. 2006) "[https://web.archive.org/web/20060427113242/https://scienceworld.wolfram.com/astronomy/PaschalFullMoon.html Paschal Full Moon]" in ''World of Astronomy''.
{{refend}}

==External links==
{{Commons category|Computus (Easter)}}
* [https://www.contextures.com/exceleastercalculation.html Excel spreadsheet formulae and functions to calculate Easter]
* [https://books.google.com/books?id=ooNIAAAAMAAJ The Complete Works of Venerable Bede Vol. 6] (Contains ''De Temporibus'' and ''De Temporum Ratione''.)
* [http://www.newadvent.org/cathen/05480b.htm The entry on epacts in the Catholic Encyclopedia of 1911]
* [https://web.archive.org/web/20120429062921/http://henk-reints.nl/cal/audette/calgreg.html The original texts of the Gregorian calendar reform (in Latin), with translations into French by Rodolphe Audette]
* [http://webspace.science.uu.nl/~gent0113/easter/eastercalculator.htm An Easter calculator with an extensive bibliography, and with useful links]
* [https://promenade.imcce.fr/en/pages4/440.html Ephemeris site of the Bureau des Longitudes with an Easter calculator (valid between 325 and 2500)]
* [https://web.archive.org/web/20031010200057/http://www.ortelius.de/kalender/east_en.php A calendar page and calculator by Holger Oertel]
* [http://www.davros.org/misc/easter.html A page from Clive Feather with a brief explanation, some more tables, and another algorithm]
* {{in lang|de}} [http://www.nabkal.de/gregkal.html An extensive calendar site and calendar and Easter calculator by Nikolaus A. Bär] {{Webarchive|url=https://web.archive.org/web/20030906090015/http://www.nabkal.de/gregkal.html |date=6 September 2003 }}
* [http://www.madore.org/~david/misc/calendar.html Explanation of the Gregorian solar and lunar calendar, with improved procedures over the tabular method, by David Madore]
* [https://www.janzuidhoek.net/diony2.htm Dionysius Exiguus' Easter table]
* [http://www.bl.uk/onlinegallery/onlineex/illmanus/egermanucoll/m/011ege000003314u00074v00.html Mnemonic Computus Diagrams of Hands from manuscript in The British Library]
* [http://www.e-codices.unifr.ch/en/csg/0378/28/medium St. Gallen, Stiftsbibliothek, Codex Sangallensis 378 (11th century) p. 28. Contains the poem ''Nonae Aprilis norunt quinos''.]
* [http://www.assa.org.au/edm.html A simplified method for determining the date of Easter for all years 326 to 4099 by Ronald W. Mallen]
* [http://www.statutelaw.gov.uk/content.aspx?activeTextDocId=1516754 Text of the Calendar (New Style) Act 1750, British Act of Parliament introducing the Gregorian Calendar] as amended to date. Contains tables for calculating Easter up until the year 8599. Contrast with the Act as passed.
* [http://www.computus.lat Computuslat] A database of medieval manuscripts containing Latin computistical algorithms, texts, tables, diagrams and calendars.

{{Liturgical year of the Catholic Church}}
{{Easter}}
{{Time in religion and mythology}}

[[Category:Calendar algorithms]]
[[Category:Date of Easter]]
[[Category:Christian terminology]]
[[Category:Autumn equinox]] <!-- southern hemisphere -->
[[Category:Spring equinox]] <!-- northern  hemisphere -->