Leap Years Explained: Why 1900 Wasn't One

Every four years we add a day to February and call it a leap year. Except it's not quite every four years — and the exception is why 1900 wasn't a leap year but 2000 was. Here's the rule, and the elegant reason behind it.

Why we need leap years at all

A year — one full orbit of the Earth around the Sun — isn't exactly 365 days. It's about 365.2422 days. That extra quarter-day doesn't sound like much, but ignore it and the calendar drifts against the seasons by about a day every four years. After a century you'd be off by roughly 24 days, and eventually you'd be celebrating midsummer in the snow. Leap years are the correction.

The basic rule

Add one day — 29 February — every four years. That accounts for the roughly quarter-day of drift, since four quarter-days make one whole day. This is the rule most people know, and for most of us it's all we ever need.

Why the simple rule overcorrects

Adding a day every four years assumes the extra is exactly 0.25 of a day. But it's actually 0.2422 — slightly less. Adding a full day every four years overcorrects by a tiny amount, which itself adds up to about three extra days every four centuries. So the calendar refines the rule.

The full rule

A year is a leap year if it's divisible by 4 — except years divisible by 100, which are not leap years, unless they're also divisible by 400, which are. That's why 1900 (divisible by 100 but not 400) was a common year, while 2000 (divisible by 400) was a leap year. This three-part rule brings the calendar's average year to 365.2425 days, astonishingly close to the true 365.2422.

What it means for date math

Any tool that counts days between dates has to know this rule, or it drifts. That's why our Age Calculator and Date Difference Calculator walk the real calendar rather than assuming a flat 365-day year — so a span crossing 29 February in a leap year is always counted correctly.