St. John the Evangelist

How do I find Easter?

Use an ancient formula to predict the first full moon of Spring. Easter Day is the next Sunday.

What is the formula?

For 1900 to 2099, take the year, divide by 19, find the remainder in column 1 of the table on the right and read the date of the full moon in column 2.

What if the formula is inaccurate?

Easter still goes according to the formula. The predicted full moon is called the Paschal Full Moon. For comparison, some actual full moon dates as seen from London are in column 3. The Eastern Churches use a slightly different formula so their Easter may be different.

I don't have a calendar for that year. How do I find when the next Sunday is?

1. Take the year without the century.
2. Add one quarter of the year dropping any fraction.
3. Add 6 if the original year is 2000 or later.
4. Add 3 for March or 6 for April.
5. Add the day.
6. Divide by 7. Remainders 0, 1, etc. indicate Sunday, Monday, etc. respectively.
7. Subtract this remainder from 7 to get the number of days to add to get to Easter Day.

Can I have an example please? Say 2006.

1. 19 into 2006 leaves remainder 11.
2. From the table, 11 gives the Paschal Full Moon as April 13.
3. The year without the century is 6.
4. 4 into 6 goes 1. 6+1=7.
5. Add 6 for the twenty-first century. 7+6=13.
6. Add 6 for April. 13+6=19.
7. Add the day. 19+13=32.
8. 7 into 32 leaves remainder 4 = April 13 is a Thursday.
9. 7-4=3. April 13 + 3 days = April 16.

Can we predict the Moon in other centuries?

There is a table like this for any particular century. It is generated in a complex but regular manner. There are 29 dates on which the Full Moon may fall, March 21st. to April 18th. Notionally there is an extra date between April 17th. and 18th. making 30. The extra date counts as April 17th. if a remainder greater than 10 falls on it, as 16 does currently, otherwise as April 18th. Each remainder is 11 days before or 19 days after the previous. Each century the dates may shift forwards or backwards by 1. (April 18th. shifts forwards to March 21st. and March 21st. back to April 18th.) There is a table of the shifts relative to 1600 in the Book of Common Prayer. Otherwise calculate x-z by formulae below. For example the shift will be 5 in the 2700s compared with 2 now so a remainder of 12 would indicate a date of April 5th. instead of the current April 2nd.

Can I extend the days-of-the-week method to other centuries?

Days of the week recur on a 400 year cycle. E.g. 1999 is the same as 2399. For other centuries add 4 (for 17**, 21** etc.) or 2 (for 18**, 22** etc.) instead of 6 in step 3 above.

Can I use this day-of-week formula for dates in other months?

Count January and February as months 13 and 14 of the previous year. To get the number to add in step 4, take the month number (5 for May etc.), add 1, multiply by 2.6 and discard any fractional part. Otherwise it is as above.

Where does the date of Easter come from?

The link to the first full moon of Spring is because Christ was crucified just before the Jewish Passover. That has fixed dates in the Jewish calendar which is Luni-Solar. The formula for the date of the Paschal Full Moon is based on the Metonic Cycle as decided by the Council of Nicæa (325) and has been followed by Western Churches generally since the 8th century. The Metonic Cycle is the observation by Meton that, relative to the Spring Equinox, the phases of the Moon fall on the same days every 19 years.

I'd like to put these in a program. Can I have the formulae as an algorithm?

There are two algorithms below. One is for years 1582 to 100,000. The other is a simpler algorithm for 1900 to 2099. There is also a link to a calculator if you have active elements enabled.

Is it only lack of accuracy in the formula that causes the difference between us and the Eastern Churches? Could we not have an agreed formula based on the latest astronomical knowledge?

It also matters where you calculate for. For example, if the full moon occurs at the end of Saturday in London then it will be in Sunday further East and so Easter will be a week later. At a conference in Aleppo in 1997 a new formula was agreed based on the Moon as seen from Jerusalem. If adopted, it will first affect the date of Easter in the West in 2019.

One final tip: to find the remainder after dividing the year by 19 in your head, subtract 1900 then divide by 20 and add the quotient. E.g. 2006 subtract 1900 = 106. 106 divide by 20 = 5 remainder 6. 5+6=11. If the answer is over 18 then divide again.

In 2008 Easter fell on 23rd. March, the earliest possible in 20th., 21st. and 22nd. centuries when the Paschal moon can not fall on 21st March. Easter on 22nd March last occurred in 1818 and next occurs in 2285. The gap is longer than from the reign of Henry VIII to now.

In 2011 Easter fell on 24th. April, almost the latest possible date. Easter on 25th. April last occurred in 1943 and next occurs in 2038.

The result is day in March or day plus 31 in April. E.g. 26 indicates Easter is March 26th. and 33 indicates Easter is April 2nd. "div" indicates integer division, i.e. rounding downwards. "mod" indicates taking the remainder after integer division (not negative).

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