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Determining The Date Of Easter

The calendar is very important for a society so that it can determine when things
should be done. In the ancient world, knowing the time to plant crops was vital; and in
modern times the calendar enters every aspect of our lives, telling when to celebrate,
when to work, and when to pay our bills.

Our calendar is based on the sun with the fundamental units being the day (determined
by the rotation of the earth with respect to the direction of the sun) and the year
(determined by the rotation of the earth around the sun).

Not all calendars have been determined by the sun. For example the Moslem calendar is
moon-based; whilst the Babylonians based their calendar on a combination of the sun and

In our calendar, a hint of a moon-based system remains with the "month",
although the average month is a few days longer than the rotation of the moon around the

A further remanent of a moon-based system is the determination of the date of Easter.
Many people know the definition of Easter as "Easter Sunday falls on the first Sunday
after the Full Moon on, or after, the March Equinox".

But this definition hides a number of problems and can require quite accurate knowledge
of the orbit of the moon. The first problem is the need to define a longitude on earth for
which Sunday is determined. For example, at the instant of Full Moon it may be Sunday in
Sydney but still Saturday in London giving rise in certain circumstances to a different
date for Easter. A second problem arises from the variabilities in the orbit of the moon
which is perturbed by the sun and the major planets. The exact orbit of the moon was not
known precisely until recent times and it would be difficult if the date of Easter changed
as our knowledge of the moon’s orbit changed.

To obtain consistency in the date of Easter, the Church at the Council of Nicea decided
to define Easter with respect to an imaginary moon – known as the "ecclesiastic
moon". Also, the date of equinox was fixed at March 21 even though it can vary
slightly from this date. With this definition, the date of Easter can be determined in
advance without further astronomical knowledge. But the sequence of dates varies
significantly from year-to-year with Easter Sunday being as early as March 22 and as late
as April 25. In fact, the exact sequence of Easter dates repeats itself approximately
every 5,700,000 years in our Gregorian calendar.

The Eastern Orthodox churches decided not to follow the above definition and they
determine Easter from the real full moon at the longitude of Jerusalem. Hence, there is
sometimes a difference in the date of Easter between churches. 

For those interested, the following table lists the date of Easter Sunday up to the
year 2010.

April 04, 1999 April 23, 2000 April 15, 2001 March 31, 2002 April 20, 2003 April 11,
2004 March 27, 2005 April 16, 2006 April 08, 2007 March 23, 2008 April 12, 2009 April 04,

The following is an algorithm by which the date of Easter may be calculated.

Divide by Quotient Remainder the year x 19 – a the year x 100 b c

b 4 d e

b + 8 25 f –

b – f + 1 3 g –

19*a + b – d – g + 15 30 – h

c 4 i k

32 + 2*e + 2*i – h – k 7 – L

a + 11*h + 22*L 451 m –

h + L – 7*m + 114 31 n p

Then n is the number of the month (3 = March; 4 = April) and p + 1 is the day of that
month upon which Easter Sunday falls.

The symbol * means the product of the two numbers.

Sources: Astronomical Algorithms, Jean Meeus; Man and the Stars, Robert Hanbury Brown.

Copyright © 1995 by Richard Thompson for IPS Radio & Space Services, Sydney,
Australia. All rights reserved. 

Reproduced with permission from IPS Radio and Space

Services, Sydney, Australia.


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