What is a leap year? The 4 / 100 / 400 rule explained

A year isn’t a clean number of days. Earth takes about 365.2422 days to orbit the Sun (source: Encyclopædia Britannica, “tropical year”), and that extra quarter-ish day is the whole reason leap years exist. Ignore it and the calendar slowly drifts out of season, with Christmas creeping toward summer over centuries. Leap years are the patch.

Want the verdict for a specific year? Here:

The rule, in plain terms

Three steps, checked in order:

1. Divisible by 4? If not, it’s a common year (365 days). Done.
2. Divisible by 100? If yes, it’s not a leap year, unless step 3 saves it.
3. Divisible by 400? If yes, it’s a leap year after all.

So most years that split evenly by 4 are leap years. The exceptions are the “round” century years: 1700, 1800, 1900 are common, but 1600, 2000, 2400 are leap because they’re divisible by 400.

Why the century exception exists

If we added a leap day every 4 years with no exceptions, we’d be overcorrecting. Four years’ worth of quarter-days is one full day. But the real leftover is 0.2422, not 0.25, so “every 4 years” adds slightly too much. Over centuries that overshoot piles up.

The 100-year skip removes three leap days every four centuries to claw most of it back. The 400-year exception then adds one of those back, because the 100-year rule overcorrects in the other direction. The net result is very close to the true orbital period, off by only about one day in 3,000 years.

Here’s the pattern at the century marks:

The Persian calendar’s answer to the same problem

The Persian (Jalali) calendar faces the identical fractional-day problem and solves it differently: no 4/100/400 formula at all. It pins the new year to the spring equinox and distributes leap years across a 33-year cycle, which is actually more accurate over the long run. The extra day there is 30 Esfand, not 29 February. And because the new year tracks an astronomical event, Nowruz drifts between 20 and 21 March instead of sitting still.

If you need to move a date near a leap boundary between the two calendars, the converter handles 29 February and 30 Esfand correctly, including rejecting dates that don’t exist in a given year.