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A leap year every four years — except 1900 wasn't one, 2000 was, and 2100 won't be. The rule has three parts, and the reason why is a quarter of a day that refuses to be a quarter.
A day is Earth spinning round once.
A year is Earth going all the way round the Sun once.
There is no reason on Earth or off it why one of those should divide neatly into the other. They are two completely unrelated motions — a spin and a lap — and nobody arranged for them to match.
They don't match. One lap takes about 365 days, 5 hours, 48 minutes and 45 seconds.
So a calendar of 365 whole days finishes the year with nearly six hours of the lap still to run. Every single year. And that leftover does not go away — it waits.
Imagine we never invented leap day. Every year is exactly 365 days and the leftover is simply ignored. Here is how far the calendar slips behind the actual seasons. Watch the numbers, but watch the jumps between them more.
Your family uses the no-leap-day calendar in that table. Your great-great-grandmother wrote down that the longest day of summer fell on 21 June. A hundred years later, what does the calendar say it falls on now?
The obvious repair is the one you already know. The leftover is close to a quarter of a day, so every fourth year you stuff an extra day into February and the calendar catches up.
Julius Caesar's astronomers did this two thousand years ago and it worked beautifully — for a while.
Here is the trouble. The leftover is not a quarter of a day. It is 5 hours 48 minutes 45 seconds, and a quarter of a day is 6 hours. Adding a whole day every four years therefore adds about 11 minutes too much, every year.
So the calendar stopped falling behind and started running ahead instead. Slowly — about three days every 400 years — but relentlessly. By the 1580s it had crept far enough that Easter was drifting away from spring, and someone finally did the sums.
Every calendar rule is a compromise with a leftover that refuses to be a whole number. There is no rule that makes it come out exactly even, only rules that are wrong more slowly.
The repair we use today has three parts, and you apply them in order:
1. If the year divides by 4, it is a leap year. 2. Unless it also divides by 100 — then it is not. 3. Unless it also divides by 400 — then it is after all.
That middle rule is the one nobody remembers, and it is the whole point. It throws away three leap days every four centuries, which is exactly the amount the every-four-years rule was adding too many of.
The result: 97 leap days in every 400 years instead of 100. That works out at an average year of 365.2425 days — which is out by about half a minute a year. Our calendar will need its next correction in roughly three thousand years. Somebody else's problem.
Work through the three rules in order for the year 2100. Is there a 29 February in it?
Fixing a calendar means throwing days away, and throwing days away upsets people. Put these in the order they happened.
Tap whichever you think happened next
You’re previewing as a parent — nothing here is recorded.
The tropical year — one full cycle of the seasons — is about 365.2422 days, which is 365 days, 5 hours, 48 minutes and 45 seconds (US Naval Observatory; Royal Museums Greenwich). Ignoring the leftover entirely costs 0.2422 days a year: 0.24 after one year, 0.97 after four, 9.69 after forty, 24.22 after a century and 96.88 after four centuries. Half a year of drift takes about 750 years. The Julian calendar's average year of 365.25 days is about 11 minutes 14 seconds too long, which accumulates to roughly three days every 400 years. The Gregorian reform of 1582 dropped ten days: Thursday 4 October 1582 was followed by Friday 15 October 1582 (Pope Gregory XIII, papal bull Inter gravissimas). Sweden's failed gradual transition produced a 30 February in 1712, the only occurrence of that date in any national calendar. Britain and its colonies adopted the Gregorian calendar in September 1752, dropping eleven days: Wednesday 2 September was followed by Thursday 14 September. The Gregorian rule gives 97 leap days per 400 years, an average year of 365.2425 days — about 27 seconds longer than the tropical year, an error of one day in roughly 3,300 years. 1700, 1800, 1900 and 2100 are not leap years; 1600, 2000 and 2400 are.