In what follows, any time you see a number or calculation in square
brackets [], you should take the integer part of that number.
Thus, [4.333]=4. The bracket operation is not defined for negative
numbers.
Also, Remainder(x|y) means the remainder when you divide x by y. It is defined
in terms of the [] operation as follows:
Remainder(x|y) is always a whole number. For example, this year is 1996. So
The following rules, due to John Conway, allow you to calculate the date
of Easter for any year on the Gregorian or Julian calendar.
First, calculate the Golden Number G. This is fundamental to the
calculation of both the date of Easter and the Date of Rosh Hashanah. It
is intimately connected with the Metonic Cycle. For any year Y, the Golden
Number is defined as
For example, in this year, 1996, the Golden Number is 2 because Remainder(1996|19)=1. Next, compute S, where
For example, this year, S=Remainder(22-6|30)=16.
Then, the Paschal Full Moon falls on the date (March 50=April 19)
- S, except that if this formula gives April 19, the Paschal Full Moon falls
on April 18 instead, and if the rule gives April 18, and if G is
greater than or equal to 12, the Paschal Full Moon falls on April 17.
Then Easter is the first Sunday that falls after this date (if the
date you calculated is a Sunday, then Easter is one week later). You can
use Conway's Doomsday Rule for Day of the Week to determine the day of the
week of the Paschal Full Moon.
For example, this year, the Paschal Full Moon falls on April 19-S = April
19-16 = April 3. Conway's Doomsday Rule tells
us that April 3 is a Wednesday this year, so Easter is the next Sunday,
or April 7.
Here's how to determine C:
For Gregorian dates in other centuries, where the year is Y=Hxx, calculate C as follows:
The following rules are also due to John Conway. In the Gregorian year Y of the Common Era, Rosh Hashanah normally falls on September N, where
N + fraction = {[Y/100] - [Y/400] - 2} + 765433/492480*Remainder(12G|19) + Remainder(Y|4)/4 - (313Y+89081)/98496
Here, G is the Golden Number, and * means multiply. However, if certain conditions are satisfied, Rosh Hashanah is postponed by one or even two days, as follows:
For example, in 1996, G=2. So the calculation gives 13.5239... (check
this for yourself using your calculator)! However, since Doomsday is Thursday
this year, September 5 and 12 are Thursdays, so September 13 is Friday.
By Rule 1, we must postpone by one day, so Rosh Hashanah this year falls
on Saturday, September 14. (It actually begins at sundown on the
13th.) Yom Kippur begins at sundown on the22nd of September, 9 days
after the beginning of Rosh Hashanah.
A simplified formula for the date of Rosh Hashanah on the Gregorian calendar
for 1900-2099 is gotten by calculating
N + fraction = 6.057778996 + 1.554241797*Remainder(12G|19) + 0.25*Remainder(y|4) - 0.003177794*y,
where y=Y-1900. Use the same postponement rules (note that 23269/25920=0.898,
and 1367/2160=0.633). This method is easier to calculate using a pocket
calculator.
Julian Calendar
If you are given a date on the Julian calendar, the rules are the same, except that you must ignore the term in curly braces {} in the formula that gives the date of Rosh Hashanah. This term corrects for the difference between the Julian and Gregorian calendars.
Once you have determined the date of Rosh Hashanah, it is easy to calculate
the date of Passover in the same (Gregorian or Julian) year. Let M = the
number of days from September 6 to Rosh Hashanah. In the example for 1996,
M=September 14-September 6 = 8 days.
Count M days from March 27. That is the date of Passover. It actually begins
at sundown on the previous evening. In the example for 1996, 8 days after
March 27 is April 4 (there are 31 days in March), so Passover begins at
sundown on April 3.
If you pay attention to the dates of Easter and Passover from year to
year, you will notice that although they usually fall within a week or so
of each other, on occasion Passover falls about a month after (Gregorian)
Easter. At the present time, this happens in in the 3rd, 11th, and 14th
years of the Metonoic Cycle (i.e., when the Golden Number equals 3, 11,
or 14). The reason for this discrepancy is the fact that although the Metonic
Cycle is very good, it is not perfect (as we've seen in this course). In
particular, it is a little off if you use it to predict the length of the
tropical year. So, over the centuries the date of the vernal equinox, as
predicted by the Metonic Cycle, has been drifting to later and later
dates. So, the rule for Passover, which was originally intended to track
the vernal equinox, has gotten a few days off. In ancient times this was
never a problem since Passover was set by actual observations of the Moon
and of the vernal equinox. However, after Hillel II standardized the Hebrew
calendar in the 4th century, actual observations of celestial events no
longer played a part in the determination of the date of Passover. The Gregorian
calendar reform of 1582 brought the Western Church back into conformity
with astronomical events, hence the discrepancy.
Similarly, you will notice that in many years Gregorian Easter (the one
marked on all calendars) differs from Julian (Orthodox) Easter, sometimes
by a week, sometimes by a month. Again, this is due to the different rules
of calculation. A major difference is that Orthodox Easter uses the old
Julian calendar for calculation, and the date of the Vernal Equinox is slipping
later and later on the Julian calendar relative to the Gregorian calendar
(and to astronomical fact). Also, the date of Paschal Full Moon for the
Julian calculation is about 4 days later than that for the Gregorian calculation.
At present, in 5 out of 19 years in the Metonic Cycle--the years when the
Golden Number equals 3, 8, 11, 14 and 19--Orthodox Easter occurs a month
after Gregorian Easter. In three of these years, Passover also falls a month
after Gregorian Easter (see above).
You can find additional information on these topics by looking at frequently asked questions about
calendars. This site contains a more detailed discussion of the rules
for various calendars and why they are the way they are.
Here is a pointer to a web pages that can calculate
the date of Easter for both Gregorian and Orthodox (Julian) calendars.