A Staff Report from the Straight Dope Science Advisory Board

Why do we have leap years?

Dear Straight Dope:

I was wondering why we have a leap year, and why it is only every four years.

The leap year is a contrivance so that the calendar year (usually 365 days) doesn't get too far away from the solar (astronomical) year. You say: huh? Well, the astronomical year - the time it takes the earth to go exactly once around the sun - is not precisely 365 days. The ancients estimated it as 365.25 days. That wasn't bad as calculations go; it's actually 365 days, 5 hours, 48 minutes, and 46 seconds.

Now, you may think that crummy little fraction (almost 6 hours or 1/4 of a day) doesn't matter much. But every four years, the calendar would lose a full day against the seasonal year. Christmas (Dec. 25) would start to come a little earlier each year. After about 20 years it would come before the winter solstice; after 200 years or so, Christmas would come in the autumn (since the seasons are tied to the astronomical year, because they depend on the earth's slant relative to the sun) . . . and then in summer . . . and . . .

To prevent this drift between the calendar year and the astronomical (seasonal) year, we add one extra day every four years. Thus, over the four year period, we have 1461 days, not 1460, for an average of 365.25 days per year. That pretty much makes it come out right.

This innovation was imposed in the year 709 AUC (ab urbe condita, after the founding of the city), when Julius Caesar regulated the calendar.  Nowadays, we refer to it as 45 BC.  The Nicaean Council in 325 AD adopted that calendar for Christendom.

But it still wasn't precisely right. As noted above, the astronomical year isn't 365 days 6 hours (365.25 days), it's 365 days 5 hours 48 minutes and 46 seconds (365.2422 days). So as the calendar went along with its jolly add-a-day-every-four-years pattern, it gained about 11 minutes 14 seconds every year. After every 128 years, that was a full day.   Note it's going the other direction - Christmas would fall LATER in the season each year.

This anomaly was corrected by Pope Gregory in March 1582. By that time, the calendar year was 10 days off the seasonal year. ( The real concern was not Christmas, but Easter, which had to occur near the vernal equinox and according to the lunar cycle, but that's another story.) They made two corrections. The first was that they just dropped ten days. The day after October 5, 1582 became October 15, 1582. (Some countries adopted this change later, in some cases centuries later.) This restored the equinox to its rightful place. The second change was to reform the calendar to prevent slippage in the future; and we use that same calendar system today, called the Gregorian.

(Footnote: The Russian Orthodox Church still uses the Julian calendar. Christmas comes out about January 7 in their calendar. About every century, the Orthodox Christmas slips one more day against the solar calendar.  Currently there's a 13 day lag that by 2100 will become a 14 day lag.)

How does the Gregorian system work? We still have a leap year every four years, to accommodate the almost 6 hour difference that was known in Julius Caesar's time. The Gregorian correction is that every hundred years, we make it NOT a leap year. Thus, 1700, 1800, and 1900 were not leap years, even though they would have been in the normal four year cycle. Thus, every 100 years, there are 24 leap years, not 25. So that lets the calendar year average 365.24 days each year.

Does that do it? Sadly, no. There are still those extra seconds - the astronomical year is 365.2422 days. So every 400 years, we DON'T NOT add the extra day (double negative intended). So 1700, 1800, 1900 were NOT leap years, but 2000 was.

If you've followed the math, that gets us very close.  Over a 400 year period the calendar will contain an average of 365.2425 days per year.

Every 4,000 years (the first will be the year 4000, then 8000, etc.) we make the century years NOT leap years again. And that gives us an average of 365.24225 days per year over a 4.000 year period. Still not exact, but the calendar year won't vary by more than a day from its current place in the seasonal (astronomical) year in two hundred centuries - close enough for practical purposes.

So the rule is:

Every year divisible by 4 is a leap year (adds an extra day to February),

EXCEPT the last year of each century, such as 1900, which is NOT a leap year . . .

EXCEPT when the number of the century is a multiple of 4, such as 2000, which IS a leap year . . .

EXCEPT the year 4000 and its later multiples (8000, 12000, etc) which are NOT leap years.

Clear? Wait till I drag in the Jewish and Muslim calendars, as is only fair considering our vast multicultural audience.

The Jewish calendar is based on a lunar cycle - that is, each month is based on the interval, about 29 or 30 days, from new moon to new moon - so it's short by about 11 days per solar year. Since the Jewish holidays are supposed to be season-related (they were originally harvest festivals), the calendar adjusts by adding a whole month about every three years - actually, 7 times every 19 years.  The calculations are precise but VERY complicated, and if it took that much space to describe the fairly simple common calendar, I ain't gonna do anything more than what I just said for the Jewish calendar.

The Muslim calendar is also lunar, but it doesn't adjust. Thus, the holidays come about 11 days earlier in the season each year. Some years, Ramadan comes out in the spring, then in winter, then in fall, etc. Since Ramadan involves fasting from sunrise to sunset, it's a heckuva lot easier when Ramadan comes in deepest winter (shorter period from sunrise to sunset) than when it comes in the spring. It takes about 35 years for everything to cycle round again. About as long as it took you to read this article, probably. But at least now you've got the facts.

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