Leap years, and why 2100 will not be one

By Niraj Kumar · Published October 28, 2026

The Earth takes about 365 days, 5 hours, 48 minutes and 45 seconds to go round the sun, measured from one spring equinox to the next. A calendar of 365 days falls behind by almost a quarter of a day each year, and after a century the seasons have moved by three and a half weeks. Leap years exist to put the quarter days back. The leap year checker applies the rule to any year; this guide is about where the rule comes from and why it has the shape it does.

The rule

A year is a leap year if it is divisible by 4, except that a year divisible by 100 is not, except that a year divisible by 400 is. So 2024 was a leap year, 2100 will not be, and 2000 was. The three clauses give an average year of 365.2425 days, within about 26 seconds of the true figure. The error accumulates to a day in roughly 3,200 years, which nobody has felt the need to fix.

Why the exceptions exist

The Julian calendar, introduced in 45 BC, had only the first clause: every fourth year a leap year, giving an average of 365.25 days. That is 11 minutes too long, and over the sixteen centuries it was in use the spring equinox drifted from 21 March, where the Council of Nicaea had fixed it for calculating Easter, back to about 11 March. The reform of 1582 under Pope Gregory XIII did two things: it dropped three leap days every four hundred years by means of the century rule, and it deleted ten days from October 1582 so that the equinox returned to 21 March. Thursday 4 October was followed by Friday 15 October.

A reform adopted over 340 years

Catholic countries changed in 1582. Protestant and Orthodox ones did not, which meant that for centuries crossing a border could change the date by ten or eleven days. Britain and its colonies, including the future United States, switched in September 1752, skipping eleven days, so that Wednesday 2 September was followed by Thursday 14 September; the tax year in the UK still begins on 6 April because the Treasury refused to lose eleven days of revenue. Russia changed after the 1917 revolution, which is why the October Revolution is commemorated in November. Greece was last among European states, in 1923. Dates before a country’s changeover are often recorded in the old style, and a date calculator applied to them will be a number of days out unless it knows which calendar the record used. This site projects the modern rules backwards for all dates, as most software does, and says so.

Why February

February is short because the Roman calendar it descends from began in March, and February was the last month, the one that took whatever days were left over. When the extra day was added it went into the last month, and it stayed there when January became the first. The leap day was originally inserted by doubling 24 February, which is why some older European traditions treat 24 February rather than 29 February as the leap day. Modern civil calendars count 29 February.

Leap day birthdays and anniversaries

A person born on 29 February has a birthday in one year of four, and the question of when they age in the other three has answers that differ by country. The age guide covers them. Contracts, subscriptions and leases that start on a leap day have the same question in a different form: the annual renewal date has to be defined, and 28 February and 1 March are both in use.

Leap seconds are a different thing

Leap seconds are often mentioned alongside leap years, and they are unrelated. A leap year corrects the calendar for the length of the Earth’s orbit. A leap second corrects the clock for the irregularity of the Earth’s rotation, which is slowing unpredictably, and it is decided a few months ahead by observation rather than by rule. Twenty-seven have been inserted since 1972; none is planned, and the practice is to end by 2035. The UTC guide explains them.

How the rule affects date arithmetic

Any calculation that steps through dates has to know which Februaries have 29 days. Adding a year to 29 February 2024 gives 28 February 2025 or 1 March 2025, and the convention has to be chosen; the date calculator clamps to the last day of the month and says so. Counting days between dates has to include the leap days in the range: from 1 January 2000 to 1 January 2100 is 36,525 days, not 36,524, because 2000 was a leap year and the century rule did not remove it. Dividing by 365 to get years is wrong by about a day every four years; the correct method is to count completed years on the calendar. The calendar shows the 29th whenever it exists, which is the quickest check.

Other calendars

Not every calendar leaps the same way. The Islamic calendar is purely lunar, 354 or 355 days, and takes no leap months, so its months move through the seasons on a 33-year cycle, which is why Ramadan arrives eleven days earlier each year. The Hebrew and Chinese calendars add a whole leap month seven times in nineteen years to stay aligned with the sun. The Persian calendar’s leap years follow the actual equinox rather than a formula, and are more accurate than the Gregorian ones. The Ethiopian calendar still uses the Julian rule and is seven to eight years behind. A date in any of these has to be converted, not just relabelled.

The quick checks

Divisible by 4 and not by 100: leap. Divisible by 400: leap. Otherwise: not. 1900 was not, 2000 was, 2100 will not be, 2400 will be. February has 29 days in a leap year and 28 otherwise, every other month is unchanged, and the year is 366 days. A year’s day of the week pattern shifts by one in a common year and two in a leap year, which is why the calendar repeats only every 28 years, and why the date calculator does the arithmetic on a civil calendar rather than counting seconds.