Computus

Computus (Latin for "computation") is the method for calculating the date of Easter. In the early 4th century there was confusion about when Christian Easter or the Resurrection should be celebrated.

Dionysius Exiguus invented the Anno Domini era to calculate the Easter date.

History

Background

At the Arles Council, in 314, all of Christianity was obliged to celebrate Easter on the same day. This date was to be assigned by the Pope, who would send epistles to all the churches in the world with the necessary instructions. However, not all the congregations followed those precepts.

Nicaea Council

In the First Council of Nicaea, in 325, this question was resolved.

It was established that the Resurrection Easter had to be celebrated fulfilling some norms:

• Easter had to be celebrated on Sunday.
• It could not coincide with the Jewish festival of Passover, celebrated independently which day of the week it was.
• Christians could not celebrate Easter twice the same year. This was because the new year started in the spring equinox, so the celebration of Easter before the real equinox was prohibited.

However, there still were discussions between the Roman Church and the Alexandrian Church, while the Nicaea Council said that the Alexandria Church was right, they had to calculate the date (in Alexandria), then communicate it to Rome. The Roman Church had to spread the computus to the rest of the Christianity.

Calculation

Dates for Easter
1982–2022
In Gregorian dates

Year	Western	Eastern
1982	April 11	April 18
1983	April 3	May 8
1984	April 22
1985	April 7	April 14
1986	March 30	May 4
1987	April 19
1988	April 3	April 10
1989	March 26	April 30
1990	April 15
1991	March 31	April 7
1992	April 19	April 26
1993	April 11	April 18
1994	April 3	May 1
1995	April 16	April 23
1996	April 7	April 14
1997	March 30	April 27
1998	April 12	April 19
1999	April 4	April 11
2000	April 23	April 30
2001	April 15
2002	March 31	May 5
2003	April 20	April 27
2004	April 11
2005	March 27	May 1
2006	April 16	April 23
2007	April 8
2008	March 23	April 27
2009	April 12	April 19
2010	April 4
2011	April 24
2012	April 8	April 15
2013	March 31	May 5
2014	April 20
2015	April 5	April 12
2016	March 27	May 1
2017	April 16
2018	April 1	April 8
2019	April 21	April 28
2020	April 12	April 19
2021	April 4	May 2
2022	April 17	April 24

Let's define 5 variables, a, b, c, d, and e; and two constants, M and N. For the years between 1900 and 2100, M and N take the values 24 and 5, respectively (see table below). We'll call A the year that we want to calculate the Easter date.

a is the remainder of the division ${\displaystyle {\frac {A}{19}}}$, or technically according to the modular arithmetic we should say ${\displaystyle A\ mod\ 19}$,

b is the remainder of the division ${\displaystyle {\frac {A}{4}}}$,

c is the remainder of the division ${\displaystyle {\frac {A}{7}}}$,

d is the remainder of the division ${\displaystyle {\frac {19a+M}{30}}}$,

e is the remainder of the division ${\displaystyle {\frac {2b+4c+6d+N}{7}}}$.

If d + e < 10, the Easter date will be in March (d + e + 22). If opposed (d + e > 9), will be in April (d + e − 9).

There are 2 exceptions:

• If the obtained date is April 26, the Easter date will be April 19, not April 26.
• If the obtained date is April 25, with d = 28, e = 6 and a > 10, then the Easter date will be April 18.

The values for M and N for years before 1900 or after 2100 can be obtained from the following table:

Years	M	N
1583-1699	22	2
1700-1799	23	3
1800-1899	23	4
1900-2099	24	5
2100-2199	24	6
2200-2299	25	0

Further reading

• Mosshammer, Alden A. The Easter Computus and the Origins of the Christian Era. Oxford: Oxford University Press, 2008. ISBN 0-19-954312-7.