Why do we have leap years?
A year is not a whole number of days, so the calendar has to be given an extra day now and then or the seasons slowly drift away from the dates.
Simple intuition
The plain reason, in everyday words
One trip around the Sun does not take a whole number of days. It takes about 365 and a quarter, and the calendar can only ever deal in whole days. So if every year were 365 days, each one would end about six hours before the Earth had actually finished its lap. Six hours a year is a day every four years, a month every 120 years, and eventually you would be having midsummer in what the calendar insists is winter. Adding one day every fourth year hands those six hours back. But the leftover is not exactly a quarter of a day — it is slightly less — so adding a full day every four years gives back a little too much. The fix for that is to skip the leap day occasionally, which is why 1900 was not a leap year but 2000 was.
A leap year is simply any year divisible by four.
Century years break the rule unless they are also divisible by 400. 1900 was not a leap year; 2000 was. Software that only checks divisibility by four has caused real failures, including on 29 February 2000 and in date calculations reaching past 2100.
The year is exactly 365.25 days long.
It is closer to 365.2422. That difference of about 11 minutes is small enough to ignore for a lifetime and large enough to move the calendar by ten days over sixteen centuries, which is exactly what happened.
Leap years and leap seconds are the same kind of correction.
Leap years correct the calendar against the Earth's orbit and follow a fixed arithmetic rule. Leap seconds corrected clock time against the Earth's rotation, which is irregular and cannot be predicted years ahead.
The Gregorian calendar is exact.
It drifts by about one day every 3,200 years, and the quantities it approximates are themselves slowly changing. It is a very good approximation with no claim to being a final one.
It is the clearest everyday case of two natural cycles that do not divide into each other being handled by an agreed set of rules rather than a perfect solution. That pattern recurs constantly: time zones, daylight saving, and the sheer difficulty of date arithmetic in software all descend from the same fact. It is also a reminder that a calendar is an institution, and that changing one required deleting days from history and arguing about it for centuries.
Who worked it out
The Roman calendar before reform was badly out of step, with an extra month inserted at the discretion of officials who had political reasons to lengthen or shorten years. Julius Caesar's reform in 46 BC replaced that with the fixed four-year rule, at the cost of one 445-day year to reset the alignment.
What problem forced it
The Julian rule was slightly too generous, and by the sixteenth century the accumulated error had moved the equinox far enough to disturb the calculation of Easter, which is what actually prompted the reform.
How it changed since
The Gregorian reform of 1582 added the century rule and deleted ten days. Adoption took over three centuries and was resisted along religious and political lines, with Britain switching in 1752 and Russia in 1918. Precise timekeeping later raised a separate question about the Earth's rotation, answered by leap seconds from 1972 and by the decision to abandon them by 2035.
Why time zones and daylight saving are so hard in software
Same underlying problem: political rules layered on astronomical facts, with no clean arithmetic anywhere.
How atomic clocks define a second
Once time stopped being defined by the Earth's rotation, the two had to be reconciled — which is what leap seconds were for.
Written for Curio rather than collected from a forum — it is part of the curated corpus that ships with the platform. The references it draws on are listed under Sources.