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Date of Easter

Updated: Wikipedia source

Date of Easter

As a moveable feast, the date of Easter is determined in each year through a calculation known as computus paschalis (Latin for 'Easter computation') – often simply Computus – or as paschalion particularly in the Eastern Orthodox Church. Easter is celebrated on the first Sunday after the Paschal full moon (a mathematical approximation of the first astronomical full moon, on or after 21 March – itself a fixed approximation of the March equinox). Determining this date in advance requires a correlation between the lunar months and the solar year, while also accounting for the month, date, and weekday of the Julian or Gregorian calendar. The complexity of the algorithm arises because of the desire to associate the date of Easter with the date of the Jewish feast of Passover which, Christians believe, is when Jesus was crucified. It was originally feasible for the entire Christian Church to receive the date of Easter each year through an annual announcement by the pope. By the early third century, however, communications in the Roman Empire had deteriorated to the point that the church put great value in a system that would allow the clergy to determine the date for themselves, independently yet consistently. Additionally, the church wished to eliminate dependencies on the Hebrew calendar, by deriving the date for Easter directly from the March equinox. In The Reckoning of Time (725), Bede uses computus as a general term for any sort of calculation, although he refers to the Easter cycles of Theophilus as a "Paschal computus." By the end of the 8th century, computus came to refer specifically to the calculation of time. The calculations produce different results depending on whether the Julian calendar or the Gregorian calendar is used. For this reason, the Catholic Church and Protestant churches (which follow the Gregorian calendar) celebrate Easter on a different date from that of the Eastern and Oriental Orthodoxy (which follow the Julian calendar). It was the drift of 21 March from the observed equinox that led to the Gregorian reform of the calendar, to bring them back into line.

Tables

Current Metonic cycle · Tabular methods › Gregorian reform of the <span><span>computus</span></span>
Golden number
Golden number
Year
Golden number
2014
1
2015
2
2016
3
2017
4
2018
5
2019
6
2020
7
2021
8
2022
9
2023
10
2024
11
2025
12
2026
13
2027
14
2028
15
2029
16
2030
17
2031
18
2032
19
Epact
Epact
Year
Epact
2014
29
2015
10
2016
21
2017
2
2018
13
2019
24
2020
5
2021
16
2022
27
2023
8
2024
19
2026
11
2027
22
2028
3
2029
14
2030
25
2031
6
2032
17
Full moon
Full moon
Year
Full moon
2014
14 A.
2015
3 A.
2016
23 M.
2017
11 A.
2018
31 M.
2019
18 A.
2020
8 A.
2021
28 M.
2022
16 A.
2023
5 A.
2024
25 M.
2025
13 A.
2026
2 A.
2027
22 M.
2028
10 A.
2029
30 M.
2030
17 A.
2031
7 A.
2032
27 M.
Year
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
Golden number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Epact
29
10
21
2
13
24
5
16
27
8
19
11
22
3
14
25
6
17
Full moon
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.
Calendarium restricted to March and April · Tabular methods › Gregorian reform of the <span><span>computus</span></span> › Calendarium
mw- .mw- .mw- .mw- .mw- .mw- xxix
mw- .mw- .mw- .mw- .mw- .mw- xxix
Epact label
mw- .mw- .mw- .mw- .mw- .mw- xxix
March
2
DL
E
April
1
DL
G
xxviii
xxviii
Epact label
xxviii
March
3
DL
F
April
2
DL
A
xxvii
xxvii
Epact label
xxvii
March
4
DL
G
April
3
DL
B
xxvi
xxvi
Epact label
xxvi
March
5
DL
A
April
4
DL
C
25
25
Epact label
25
March
6
DL
B
xxv
xxv
Epact label
xxv
March
5
DL
D
xxiv
xxiv
Epact label
xxiv
March
7
DL
C
xxiii
xxiii
Epact label
xxiii
March
8
DL
D
April
6
DL
E
xxii
xxii
Epact label
xxii
March
9
DL
E
April
7
DL
F
xxi
xxi
Epact label
xxi
March
10
DL
F
April
8
DL
G
xx
xx
Epact label
xx
March
11
DL
G
April
9
DL
A
xix
xix
Epact label
xix
March
12
DL
A
April
10
DL
B
xviii
xviii
Epact label
xviii
March
13
DL
B
April
11
DL
C
xvii
xvii
Epact label
xvii
March
14
DL
C
April
12
DL
D
xvi
xvi
Epact label
xvi
March
15
DL
D
April
13
DL
E
xv
xv
Epact label
xv
March
16
DL
E
April
14
DL
F
xiv
xiv
Epact label
xiv
March
17
DL
F
April
15
DL
G
xiii
xiii
Epact label
xiii
March
18
DL
G
April
16
DL
A
xii
xii
Epact label
xii
March
19
DL
A
April
17
DL
B
xi
xi
Epact label
xi
March
20
DL
B
April
18
DL
C
x
x
Epact label
x
March
21
DL
C
April
19
DL
D
ix
ix
Epact label
ix
March
22
DL
D
April
20
DL
E
viii
viii
Epact label
viii
March
23
DL
E
April
21
DL
F
vii
vii
Epact label
vii
March
24
DL
F
April
22
DL
G
vi
vi
Epact label
vi
March
25
DL
G
April
23
DL
A
v
v
Epact label
v
March
26
DL
A
April
24
DL
B
iv
iv
Epact label
iv
March
27
DL
B
April
25
DL
C
iii
iii
Epact label
iii
March
28
DL
C
April
26
DL
D
ii
ii
Epact label
ii
March
29
DL
D
April
27
DL
E
i
i
Epact label
i
March
30
DL
E
April
28
DL
F
xxix
xxix
Epact label
xxix
April
30
DL
A
Epact label
March
DL
April
DL
1
D
mw- xxix
2
E
1
G
xxviii
3
F
2
A
xxvii
4
G
3
B
xxvi
5
A
4
C
25
6
B
xxv
5
D
xxiv
7
C
xxiii
8
D
6
E
xxii
9
E
7
F
xxi
10
F
8
G
xx
11
G
9
A
xix
12
A
10
B
xviii
13
B
11
C
xvii
14
C
12
D
xvi
15
D
13
E
xv
16
E
14
F
xiv
17
F
15
G
xiii
18
G
16
A
xii
19
A
17
B
xi
20
B
18
C
x
21
C
19
D
ix
22
D
20
E
viii
23
E
21
F
vii
24
F
22
G
vi
25
G
23
A
v
26
A
24
B
iv
27
B
25
C
iii
28
C
26
D
ii
29
D
27
E
i
30
E
28
F
31
F
29
G
xxix
30
A
Original format of 1876 Nature submission · Algorithms › Anonymous Gregorian algorithm
year
year
Dividend
year
Divisor
19
Quotient
Remainder
a
year
year
Dividend
year
Divisor
100
Quotient
b
Remainder
c
b
b
Dividend
b
Divisor
4
Quotient
d
Remainder
e
b + 8
b + 8
Dividend
b + 8
Divisor
25
Quotient
f
Remainder
b − f + 1
b − f + 1
Dividend
b − f + 1
Divisor
3
Quotient
g
Remainder
19a + b − d − g + 15
19a + b − d − g + 15
Dividend
19a + b − d − g + 15
Divisor
30
Quotient
Remainder
h
c
c
Dividend
c
Divisor
4
Quotient
i
Remainder
k
32 + 2e + 2i − h − k
32 + 2e + 2i − h − k
Dividend
32 + 2e + 2i − h − k
Divisor
7
Quotient
Remainder
l
a + 11h + 22l
a + 11h + 22l
Dividend
a + 11h + 22l
Divisor
451
Quotient
m
Remainder
h + l − 7m + 114
h + l − 7m + 114
Dividend
h + l − 7m + 114
Divisor
31
Quotient
n
Remainder
o
Dividend
Divisor
Quotient
Remainder
year
19
a
year
100
b
c
b
4
d
e
b + 8
25
f
b − f + 1
3
g
19a + b − d − g + 15
30
h
c
4
i
k
32 + 2e + 2i − h − k
7
l
a + 11h + 22l
451
m
h + l − 7m + 114
31
n
o
· Algorithms › Anonymous Gregorian algorithm
a =
a =
Variable
a =
Expression
Y mod 19
Y = 1961
4
2025
11
2026
12
b =
b =
Variable
b =
Expression
⌊⁠Y/ 100⁠⌋
Y = 1961
19
2025
20
2026
20
c =
c =
Variable
c =
Expression
Y mod 100
Y = 1961
61
2025
25
2026
26
d =
d =
Variable
d =
Expression
⌊⁠b/ 4⁠⌋
Y = 1961
4
2025
5
2026
5
e =
e =
Variable
e =
Expression
b mod 4
Y = 1961
3
2025
0
2026
0
f =
f =
Variable
f =
Expression
⌊⁠b + 8/ 25⁠⌋
Y = 1961
1
2025
1
2026
1
g =
g =
Variable
g =
Expression
⌊⁠b − f + 1/ 3⁠⌋
Y = 1961
6
2025
6
2026
6
h =
h =
Variable
h =
Expression
(19a + b − d − g + 15) mod 30
Y = 1961
10
2025
23
2026
12
i =
i =
Variable
i =
Expression
⌊⁠c/ 4⁠⌋
Y = 1961
15
2025
6
2026
6
k =
k =
Variable
k =
Expression
c mod 4
Y = 1961
1
2025
1
2026
2
l =
l =
Variable
l =
Expression
(32 + 2e + 2i − h − k) mod 7
Y = 1961
1
2025
6
2026
2
m =
m =
Variable
m =
Expression
⌊⁠a + 11h + 22l/ 451⁠⌋
Y = 1961
0
2025
0
2026
0
n =
n =
Variable
n =
Expression
⌊⁠h + l − 7m + 114/ 31⁠⌋
Y = 1961
4
2025
4
2026
4
o =
o =
Variable
o =
Expression
(h + l − 7m + 114) mod 31
Y = 1961
1
2025
19
2026
4
Gregorian Easter
Gregorian Easter
Variable
Gregorian Easter
Expression
2 April 1961
Y = 1961
20 April 2025
2025
5 April 2026
Variable
Expression
Y = 1961
2025
2026
a =
Y mod 19
4
11
12
b =
⌊⁠Y/ 100⁠⌋
19
20
20
c =
Y mod 100
61
25
26
d =
⌊⁠b/ 4⁠⌋
4
5
5
e =
b mod 4
3
0
0
f =
⌊⁠b + 8/ 25⁠⌋
1
1
1
g =
⌊⁠b − f + 1/ 3⁠⌋
6
6
6
h =
(19a + b − d − g + 15) mod 30
10
23
12
i =
⌊⁠c/ 4⁠⌋
15
6
6
k =
c mod 4
1
1
2
l =
(32 + 2e + 2i − h − k) mod 7
1
6
2
m =
⌊⁠a + 11h + 22l/ 451⁠⌋
0
0
0
h + l − 7m + 114
125
143
128
n =
⌊⁠h + l − 7m + 114/ 31⁠⌋
4
4
4
o =
(h + l − 7m + 114) mod 31
1
19
4
Gregorian Easter
2 April 1961
20 April 2025
5 April 2026
· Algorithms › Anonymous Gregorian algorithm
f
f
Variable
f
Expression
Y = 1961
2025
2026
g =
g =
Variable
g =
Expression
⌊⁠8b + 13/ 25⁠⌋
Y = 1961
6
2025
6
2026
6
m =
m =
Variable
m =
Expression
⌊⁠a + 11h + 19l/ 433⁠⌋
Y = 1961
0
2025
0
2026
0
n =
n =
Variable
n =
Expression
⌊⁠h + l − 7m + 90/ 25⁠⌋
Y = 1961
4
2025
4
2026
4
o
o
Variable
o
Expression
Y = 1961
2025
2026
p =
p =
Variable
p =
Expression
(h + l − 7m + 33n + 19) mod 32
Y = 1961
2
2025
20
2026
5
Gregorian Easter
Gregorian Easter
Variable
Gregorian Easter
Expression
2 April 1961
Y = 1961
20 April 2025
2025
5 April 2026
Variable
Expression
Y = 1961
2025
2026
f
g =
⌊⁠8b + 13/ 25⁠⌋
6
6
6
m =
⌊⁠a + 11h + 19l/ 433⁠⌋
0
0
0
n =
⌊⁠h + l − 7m + 90/ 25⁠⌋
4
4
4
o
p =
(h + l − 7m + 33n + 19) mod 32
2
20
5
Gregorian Easter
2 April 1961
20 April 2025
5 April 2026
Orthodox (Eastern) Easter date · Algorithms › Meeus's Julian algorithm
a =
a =
Variable
a =
Expression
Y mod 4
Y = 2008
0
2009
1
2010
2
2011
3
2016
0
2025
1
2026
2
b =
b =
Variable
b =
Expression
Y mod 7
Y = 2008
6
2009
0
2010
1
2011
2
2016
0
2025
2
2026
3
c =
c =
Variable
c =
Expression
Y mod 19
Y = 2008
13
2009
14
2010
15
2011
16
2016
2
2025
11
2026
12
d =
d =
Variable
d =
Expression
(19c + 15) mod 30
Y = 2008
22
2009
11
2010
0
2011
19
2016
23
2025
14
2026
3
e =
e =
Variable
e =
Expression
(2a + 4b − d + 34) mod 7
Y = 2008
1
2009
4
2010
0
2011
1
2016
4
2025
2
2026
5
month =
month =
Variable
month =
Expression
⌊⁠d + e + 114/ 31⁠⌋
Y = 2008
4
2009
4
2010
3
2011
4
2016
4
2025
4
2026
3
day =
day =
Variable
day =
Expression
((d + e + 114) mod 31) + 1
Y = 2008
14
2009
6
2010
22
2011
11
2016
18
2025
7
2026
30
Easter Day (Julian calendar)
Easter Day (Julian calendar)
Variable
Easter Day (Julian calendar)
Expression
14 April 2008
Y = 2008
6 April 2009
2009
22 March 2010
2010
11 April 2011
2011
18 April 2016
2016
7 April 2025
2025
30 March 2026
Gregorian calendar equivalent
Gregorian calendar equivalent
Variable
Gregorian calendar equivalent
Expression
27 April 2008
Y = 2008
19 April 2009
2009
4 April 2010
2010
24 April 2011
2011
1 May 2016
2016
20 April 2025
2025
12 April 2026
Variable
Expression
Y = 2008
2009
2010
2011
2016
2025
2026
a =
Y mod 4
0
1
2
3
0
1
2
b =
Y mod 7
6
0
1
2
0
2
3
c =
Y mod 19
13
14
15
16
2
11
12
d =
(19c + 15) mod 30
22
11
0
19
23
14
3
e =
(2a + 4b − d + 34) mod 7
1
4
0
1
4
2
5
d + e + 114
137
129
114
134
141
130
122
month =
⌊⁠d + e + 114/ 31⁠⌋
4
4
3
4
4
4
3
day =
((d + e + 114) mod 31) + 1
14
6
22
11
18
7
30
Easter Day (Julian calendar)
14 April 2008
6 April 2009
22 March 2010
11 April 2011
18 April 2016
7 April 2025
30 March 2026
Gregorian calendar equivalent
27 April 2008
19 April 2009
4 April 2010
24 April 2011
1 May 2016
20 April 2025
12 April 2026

References

  1. Although this is the dating of Augustalis by Bruno Krusch, see arguments for a 5th century date in Mosshammer 2008, pp.
    https://de.wikipedia.org/wiki/Bruno_Krusch
  2. The lunar cycle of Anatolius, according to the tables in De ratione paschali, included only two bissextile (leap) years
  3. For confirmation of Dionysius's role see Blackburn & Holford-Strevens 1999, p. 794.
  4. For example, in the Julian calendar, at Rome in 1550, the March equinox occurred on 11 March at 6:51 a.m. local mean tim
  5. Although prior to the replacement of the Julian calendar in 1752 some printers of the Book of Common Prayer placed the s
  6. "the [Golden Number] of a year AD is found by adding one, dividing by 19, and taking the remainder (treating 0 as 19)."(
  7. See especially the first, second, fourth, and sixth canon, and the calendarium
    http://henk-reints.nl/cal/audette/canon1.html
  8. Can be verified by using Blackburn & Holford-Strevens 1999, p. 825, Table 7.
  9. because the Julian calendar will have a leap year but the Gregorian will not.
  10. In 2004 and again in 2015, there were full moons on 2 and 31 July.
  11. More precisely, the dominical letter for the part of the year after February, which is different in leap years from the
  12. Traditionally in the Christian West, this situation was handled by extending the first 29-day lunar month of the year to
  13. The Expl.Suppl. of 2013 on p.599 instead specifies 70,499,175 lunations, without explanation or reference. This number
  14. Ayto 2009, p. 123.
  15. Peterson 2015, p. 468.
  16. Bede 1999, p. xviii.
  17. Bede 1999, pp. xviii–xx.
  18. John 19:14
    https://bible.oremus.org/?passage=John%2019:14&version=nrsv
  19. Bede 1999, p. xx.
  20. Bede 1999, p. xxxvi.
  21. Bede 1999, pp. 425–426, Appendix 4: A Note on the Term Computus.
  22. Turner 1895, pp. 699–710.
  23. McCarthy 1996, pp. 285–320.
  24. Declercq 2000, p. 80.
  25. Declercq 2000, p. 97.
  26. Declercq 2000, p. 99.
  27. "Dionysius Exiguus – Liber de Paschate"
    http://henk-reints.nl/cal/audette/denys.html
  28. Blackburn & Holford-Strevens 1999, p. 793.
  29. McCarthy 1993, pp. 204–224.
  30. Bede 1907, p. 193, Book III, Chapter XXV.
  31. Bede 1943, p. 90: The letter [of Cummian] is at once a report and an apology or justification to Abbot Seghine at Iona o
  32. Bede 1907, p. xxvii.
  33. Bede 1999, pp. lix–lxiii.
  34. "The Orthodox Church Calendar"
    https://web.archive.org/web/20121126175435/http://cyprusactionnetwork.org/yahoo_site_admin/assets/docs/Orthodox_Church_Calendar.334130901.pdf
  35. "The Many Easters & Eostres for the Many: A Choice of Hallelujahs"
    https://web.archive.org/web/20210416095229/http://www.revradiotowerofsong.org/Easter_Eostre_2013.htm
  36. Time and Date AS
    http://www.timeanddate.com/calendar/seasons.html?year=1550&n=215
  37. van Gent 2019.
  38. Shields 1924, pp. 407–411.
  39. Towards a Common Date for Easter
    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
  40. Sacrosanctum Concilium
    https://www.vatican.va/archive/hist_councils/ii_vatican_council/documents/vat-ii_const_19631204_sacrosanctum-concilium_en.html
  41. Richards 2013, p. 587: The day consists of 86,400 SI seconds, and the same value is given for the years 500, 1000, 1500,
  42. ἐπακτός. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project.
    https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0057:entry=e)pakto/s
  43. Online Etymology Dictionary
    https://www.etymonline.com/word/epact
  44. Explanatory Supplement to the Astronomical Ephemeris
    http://archive.org/details/astronomicalalmanac1961/page/n431/mode/2up
  45. Bede 1999, pp. xlvi.
  46. Clavius 1603.
  47. Dershowitz & Reingold 2008, pp. 114–115.
  48. Dershowitz & Reingold 2008, pp. 113–117.
  49. Dershowitz & Reingold 2008, p. 114.
  50. Grotefend 1891.
  51. Ginzel 1914.
  52. Weisstein (c. 2006) "Paschal full moon" agrees with this line of table through 2009.
  53. Davison 1980, pp. 156–164.
  54. Dershowitz & Reingold 2008, p. 117.
  55. Popular Astronomy
    https://ui.adsabs.harvard.edu/abs/1944PA.....52..139W
  56. "The missing new moon of A.D. 16399 and other anomalies of the Gregorian calendar"
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