When is the next leap year?

The leap year rule

The Gregorian calendar, the civil calendar used almost everywhere, has one rule. A year divisible by 4 is a leap year, except a century year, which is a leap year only if it is also divisible by 400. In the words of the US Naval Observatory, 1700, 1800, 1900 and 2100 are not leap years, but 1600, 2000 and 2400 are. Applied in order, the test has three questions:

In code it is one line. The same test works in any language:

leap = (y % 4 == 0 and y % 100 != 0) or y % 400 == 0      # Python: calendar.isleap(y)
const leap = (y % 4 === 0 && y % 100 !== 0) || y % 400 === 0;  // JavaScript
=IF(OR(MOD(A1,400)=0,AND(MOD(A1,4)=0,MOD(A1,100)<>0)),"Leap","Common")   ' spreadsheet

A common mistake is to stop at “divisible by 4”. That test happens to give the right answer for every year from 1901 to 2099, which is why it hides in old software, but it fails in 1900 and 2100. Another mistake is to forget the 400 exception: code that treated every century year as common got the year 2000 wrong.

Why leap years exist

The seasons repeat every tropical year of about 365.2422 days. A calendar of 365 days would run short by almost a quarter day a year. The US Naval Observatory puts that at about 24 days a century, enough to move the start of northern spring from March 20 to April 13 within a hundred years.

A leap day every fourth year, the Julian rule, overshoots: 365.25 days is too long by about three quarters of a day per century. The Gregorian rule drops three leap days every 400 years, for 97 instead of 100 and an average year of 365.2425 days. The USNO estimates that it will take about 3,300 years for this calendar to drift a full day from the seasons. The Gregorian calendar tells how the switch was made in 1582, and why Britain had to skip eleven days in 1752.

February 29 and its weekdays

Because 400 Gregorian years are exactly 20,871 weeks, the pattern of weekdays repeats every 400 years, and it is not perfectly even. Over one full cycle, February 29 falls on a Monday or a Wednesday 15 times each, and on a Tuesday, a Thursday or a Sunday only 13 times each. Between century years, the weekday of February 29 follows a 28-year cycle: it moves forward five weekdays from one leap year to the next. 2024 was a Thursday, 2028 is a Tuesday and 2032 a Sunday.

People born on February 29 have a true birthday only in leap years. In common years most celebrate on February 28 or March 1. Which of the two counts for legal purposes, such as coming of age, depends on the country’s law, so check locally when it matters.

Century years at a glance

• 1600: leap
• 1700: common
• 1800: common
• 1900: common
• 2000: leap
• 2100: common
• 2200: common
• 2300: common
• 2400: leap

The century exception matters to software more often than people expect. Microsoft documents that Excel treats 1900 as a leap year. The error was copied from Lotus 1-2-3 for compatibility, and Excel keeps it so that existing dates do not shift by a day. As a result, weekdays that Excel computes for dates before March 1, 1900 are wrong. Excel handles 2100 and every other century year correctly.

Leap years in other calendars

Other calendars solve the same problem in their own ways. The Julian calendar, still used by some churches for feast days, adds a day every four years without exception. That is why it now runs 13 days behind the Gregorian, and the gap grows to 14 days after February 2100. The Islamic tabular calendar has 11 leap years, each with one extra day, in every 30-year cycle. The Umm al-Qura calendar used in Saudi Arabia follows the moon, so its year has 354 or 355 days. The Hebrew calendar adds a whole month, Adar I, in 7 of every 19 years. Iran’s Solar Hijri calendar adds a 30th day to its last month, Esfand, when the astronomical rule for the March equinox requires it, usually every four years and sometimes every five.

Leap seconds are something else: 27 single seconds added to UTC between 1972 and 2016 to keep atomic time close to the Earth’s rotation; the CGPM has decided that UTC will have none from 20 May 2027. They never touch the calendar. Leap seconds explains them.