Thursday, April 05, 2007

Why is Easter always on a different day?

Easter is this weekend! Which is cool, but a little inconvenient because of this huge swing dance event that is also taking place this weekend... but that’s another story.

But why did Easter and the Swing Battle fall on the same weekend this year, when they did not last year, and will not next year? (Easter Sunday is the 8th of April this year. Last year it was the 16th of April. Next year it will be the 23rd of March.)

Those dates seem pretty random to me, but apparently, there is a method to that madness. A very, very, old method. That has been updated. In 1582. And 1923.

The date of Easter varies every year within a specific part of the Gregorian calendar (the one the Western world uses). The current ecclesiastical rules that determine what day Easter falls on date back to 325 AD at the First Council of Nicaea arranged by the Roman Emperor Constantine. The council decided that Easter should always be on a Sunday and that it should be the same Sunday throughout the world. To accomplish this, and to ensure that the date of Easter could be determined for any year in the future, they assembled a series of special tables to plot the date. These tables were revise for the next few centuries, but the whole world never really became standardized.

In 1582, Pope Gregory XIII undertook a complete reconstruction of the Julian calendar and produced new Easter tables. This helped fix some of the problems, including Leap Years. By the 1700s these new calendars had been adopted by most of Western Europe, and basically became the world standard, and the date of Easter was finally determined.


The general rule of determining Easter’s date, that ‘Easter Day is the first Sunday after the full moon that occurs next after the vernal equinox’, is not quite exact because of the differences between the actual lunar cycles and the ecclesiastical (church) calendar.

The rules for the church calendar are:

  • Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after the day of the vernal equinox;
  • This particular ecclesiastical full moon is the 14th day of a tabular lunation (new moon); and
  • The vernal equinox is fixed as March 21.

All these caveats can mean that when Easter should be according to the lunar calendar are sometimes overridden by when the church calendar says that it should be.

To really figure it out exactly, you’ve gotta follow the crazy formula below:

The formula uses the year, y, to give the month, m, and day, d, of Easter. The symbol * means multiply.

(Please note the following: This is an integer calculation. All variables are integers and all remainders from division are dropped. For example, 7 divided by 3 is equal to 2 in integer arithmetic.)

c = y / 100

n = y - 19 * ( y / 19 )

k = ( c - 17 ) / 25

i = c - c / 4 - ( c - k ) / 3 + 19 * n + 15

i = i - 30 * ( i / 30 )

i = i - ( i / 28 ) * ( 1 - ( i / 28 ) * ( 29 / ( i + 1 ) ) * ( ( 21 - n ) / 11 ) )

j = y + y / 4 + i + 2 - c + c / 4

j = j - 7 * ( j / 7 )

l = i - j

m = 3 + ( l + 40 ) / 44

d = l + 28 - 31 * ( m / 4 )

For example, using the year 2010:
n=2010 - 19 x (2010/19) = 2010 - 19 x (105) = 15, [see note above regarding integer calculations]
Therefore, in 2010, Easter is on April 4.

That is WAY too much work for me. I think I’ll just keep looking on the calendar. At least the swing battle is always on the first full weekend of April. I think.

(Thanks to the U.S. Naval Observatory Astronomical Applications Department web page for this information and very tough to follow equation.)

1 comment:

Pookie said...

Wow That's a lot more complicated than I though