In this article
Most people learn: a leap year is any year divisible by 4. It works for your whole life, so it feels complete. But 1900 was not a leap year, 2000 was, and 2100 will not be. The shortcut is nearly right, and the gap is the interesting part.
The full rule
- If the year is divisible by 400, it is a leap year. (2000, 2400)
- Otherwise, if it is divisible by 100, it is not a leap year. (1900, 2100, 2200)
- Otherwise, if it is divisible by 4, it is a leap year. (2024, 2028, 2032)
- Anything else is a normal 365-day year.
| Year | Divisible by 4 | By 100 | By 400 | Leap year? |
|---|---|---|---|---|
| 2024 | Yes | No | No | Yes |
| 2026 | No | No | No | No |
| 1900 | Yes | Yes | No | No |
| 2000 | Yes | Yes | Yes | Yes |
| 2100 | Yes | Yes | No | No |
Century years are the only ones where the “every four years” rule is overruled.
Why a leap year exists at all
Earth takes about 365.2422 days to go round the Sun. A calendar with only 365 days falls behind by nearly a quarter of a day each year. After four years it is almost a whole day out, and the seasons slowly drift against the dates. The extra day on 29 February pulls the calendar back.
Adding a day every four years is too much
A leap day every fourth year makes the average year 365.25 days. That is a hair too long, by about 0.0078 days a year. Small, but it builds up: roughly one extra day every 128 years.
The real tropical year is about 365.2422 days. The Gregorian rule is off by only around 0.0003 days a year.
The fix is to skip the leap day in century years, except every fourth century. In 400 years that is 100 years divisible by 4, minus 4 century years, plus 1 for the one divisible by 400: 97 leap years. And 365 + 97/400 = 365.2425.
Start with 100, remove the 4 century years, then add one back for the year divisible by 400. That leaves 97 per cycle.
A bit of history
- 45 BCThe Julian calendarA leap day every four years, no exceptions. Average year of 365.25 days.
- 1582The Gregorian reformTen days were removed: 4 October was followed by 15 October. The century rule began.
- LaterCountries switched at different timesBritain and its colonies changed in 1752. Others waited until the twentieth century.
Because countries changed on different dates, old records from different places can disagree by days.
Useful facts
- Next leap years: 2028, 2032 and 2036. The year 2100 will skip it.
- A 29 February birthday comes up once in 1,461 days, because four years hold 365 × 4 + 1 days.
- Software bugs. Programs that only check “divisible by 4” fail on 2100. Programs that forget the 400 rule fail on 2000, and some did.
- Days in a leap year: 366, so a year has 52 weeks and 2 days, which is why dates shift weekdays by two in a leap year and one in a normal year.
Questions people ask
Is 2100 a leap year?
No. It is divisible by 100 but not by 400, so the century rule removes it.
Was 2000 a leap year?
Yes. It is divisible by 400, which overrides the century exception.
What is the leap year rule?
Divisible by 4 is a leap year, except years divisible by 100, unless they are also divisible by 400.
Why are there leap years?
Earth’s orbit takes about 365.2422 days, so a 365-day calendar drifts. A leap day keeps dates aligned with the seasons.
How many leap years are there in 400 years?
97. That gives an average calendar year of 365.2425 days.