How Leap Years Work: The Rule, the Reason and the Exceptions

A year is a leap year if it is divisible by 4, except that years divisible by 100 are not leap years unless they are also divisible by 400. So 2024 and 2028 are leap years, 1900 and 2100 are not, and 2000 was. Leap years add February 29, making the year 366 days. The extra day exists because Earth takes about 365.2422 days to go through one cycle of seasons, and without correction the calendar would slowly drift away from the seasons.

The leap year rule

As a decision list:

1. Is the year divisible by 400? Leap year. (2000, 2400)
2. Otherwise, is it divisible by 100? Common year. (1900, 2100, 2200, 2300)
3. Otherwise, is it divisible by 4? Leap year. (2024, 2028)
4. Otherwise: common year. (2025, 2026, 2027)

The leap year calculator checks any year and lists the leap years in a range.

Leap years from 2000 to 2100

That is 25 leap years between 2000 and 2100 inclusive. The 2100 exception means anyone alive then will see an eight-year gap between leap days, from 2096 to 2104.

Why the calendar needs leap years

The tropical year, the time from one March equinox to the next, is about 365.24219 days. A 365-day calendar falls behind by almost a quarter of a day each year. After a century, the calendar would be off by about 24 days, and spring would arrive in the “wrong” month.

The Julian fix: every fourth year

Julius Caesar’s calendar, introduced in 45 BCE, added a leap day every four years, for an average year of 365.25 days. That overshoots by 0.0078 days, about 11 minutes a year, or one full day every 128 years. By the 1500s, the March equinox had drifted about 10 days earlier on the calendar.

The Gregorian fix: skip three centuries in four

In 1582, Pope Gregory XIII introduced the current rule. Skipping leap years in century years not divisible by 400 removes 3 leap days every 400 years:

That is only about 27 seconds longer than the tropical year, an error of one day in roughly 3,200 years. To remove the drift that had already built up, 10 days were dropped: Thursday, October 4, 1582 was followed by Friday, October 15. Countries adopted the change at different times. Britain and its American colonies switched in 1752, skipping 11 days (September 2 was followed by September 14). Historical dates before then may be given in “Old Style” (Julian) or “New Style” (Gregorian), which matters for genealogy and history. The Julian date converter handles astronomical day numbers, which avoid calendar changes entirely.

A neat consequence: the 400-year cycle

400 Gregorian years contain exactly 146,097 days, which is exactly 20,871 weeks. So the calendar, including the weekday of every date, repeats every 400 years. January 1, 2026 fell on a Thursday, and so will January 1, 2426. This cycle is what makes weekday algorithms work; see how to find the day of the week for any date.

What leap years change in everyday calculations

Weekdays shift by two

A date normally moves one weekday later each year (365 = 52 weeks + 1 day). After a February 29, it moves two. Your birthday on a Monday in 2027 will fall on a Wednesday in 2028 if it is after February 29. The day of the week calculator shows any date’s weekday.

Day counts and ages

Any span that includes February 29 has one more day. That affects age in days, contract periods and countdowns; how to count days between dates covers the method.

Pay and interest

• Salaried employees receive the same annual salary, so a leap year simply spreads it over one more day.
• Hourly employees paid for every weekday may get one extra day of pay if February 29 falls on a weekday, as it does in 2028 (a Tuesday).
• Daily interest on loans and savings that uses an actual/365 convention earns an extra day’s interest in a leap year; some lenders use actual/366 in leap years, which slightly lowers the daily rate.

Leap day birthdays

The chance of being born on February 29 is about 1 in 1,461 (one day in every four-year cycle of 1,461 days). People born on that date usually celebrate on February 28 or March 1 in common years. For legal purposes, such as reaching the age to vote or drive, rules vary; many jurisdictions treat the person as a year older on March 1 in a common year. The age calculator handles leap-day birthdays.

Checking for a leap year in a spreadsheet

With a year in cell A1:

=IF(OR(MOD(A1,400)=0,AND(MOD(A1,4)=0,MOD(A1,100)<>0)),"Leap year","Common year")

An alternative trick checks whether February 29 exists: =DAY(DATE(A1,2,29))=29 returns TRUE for leap years, because in a common year the DATE function rolls February 29 over to March 1.

Leap-year bugs in software

February 29 is a classic source of software errors. Common mistakes include using only the divisible-by-4 test (which will misfire in 2100), adding one year to February 29 and producing an invalid February 29 in a common year, hard-coding 365 days in a year for expiry dates or interest, and creating annual reports that assume February always has 28 days. Payment cards, certificates and subscriptions with a February 29 anniversary need an explicit rule, usually rolling to February 28 or March 1. Using a well-tested date library, rather than hand-written arithmetic, avoids most of these problems.

Leap seconds are a different thing

Leap years correct for Earth’s orbit. Leap seconds corrected for small, irregular variations in Earth’s rotation, keeping atomic time (UTC) within 0.9 seconds of solar time. Since 1972, 27 leap seconds have been added. In 2022, the General Conference on Weights and Measures voted to stop inserting leap seconds by 2035 because they disrupt computer systems. Leap days are unaffected.