Leap Year Calculator

Background.

This leap year calculator tells you instantly whether any given year is a leap year under the Gregorian calendar rule, plus how many days are in that year and in February specifically, and which leap years come immediately before and after it. The rule is simple to state but has two exceptions that trip up most hand-rolled implementations: a year is a leap year if it is divisible by 4, EXCEPT century years (divisible by 100) are not leap years, UNLESS they are also divisible by 400. That means 2000 was a leap year (divisible by 400) but 1900 was not (divisible by 100 but not 400), and 2100 will not be either. This calculator applies the exact rule — not an approximation — so century-year edge cases always come out correct.

The extra day exists because Earth's orbit around the sun does not divide evenly into whole days: a solar year is closer to 365.2422 days, and simply ignoring that fraction would slowly drag the calendar's seasons out of alignment with the actual astronomical seasons over the span of a few human lifetimes. The 4-year rule alone overcorrects slightly, so the calendar's designers added the 100- and 400-year exceptions to bring the average year length even closer to the true solar year, keeping calendar dates and astronomical seasons in step for many centuries at a stretch without any further manual adjustment.

What is leap year calculator?

A leap year is a calendar year containing one extra day — February 29 — inserted to keep the calendar synchronized with Earth's orbit around the sun, which takes approximately 365.2422 days rather than an even 365. The Gregorian calendar, introduced by Pope Gregory XIII in 1582, handles that fractional day with the divisible-by-4-except-century-years-except-divisible-by-400 rule, producing an average year length of 365.2425 days — within 27 seconds of the true solar year, versus the older Julian calendar's flat 'every 4 years' rule, which drifts by about 3 days every 400 years.

How to use this calculator.

1. 01Enter any calendar year from 5 to 9999.
2. 02Read the primary 'Is it a leap year?' answer.
3. 03Check 'Days in this year' and 'Days in February' for the exact day counts that follow from the answer.
4. 04Use 'Next leap year' and 'Previous leap year' to find the nearest leap years on either side without checking each year by hand.

The formula.

A year y is a leap year if y is divisible by 4 AND (y is not divisible by 100 OR y is divisible by 400). Applying this to the two classic exception cases: 1900 is divisible by 4 (475×4) and by 100, but not by 400 (1900/400 = 4.75), so it is NOT a leap year. 2000 is divisible by 4, by 100, and by 400 (2000/400 = 5 exactly), so it IS a leap year — the 400-year exception overrides the 100-year exception. The next and previous leap year are found by walking forward or backward one year at a time, testing the same rule at each step, until a match is found — the largest possible gap between two consecutive Gregorian leap years is 8 years (for example, 1896 to 1904, because 1900 is skipped), so the search always terminates quickly.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Pope Gregory XIII, Inter gravissimas (24 February 1582). The papal bull introducing the Gregorian calendar and its leap-year rule (every 4 years, except century years not divisible by 400).