Why Do We Have Leap Years?

How long is a year compared with 365 days?

A normal calendar year has 365 days, but the cycle of the seasons, which the U.S. Naval Observatory calls the tropical year, lasts approximately 365.2422 days.^[2] NASA's Jet Propulsion Laboratory (JPL) gives the same figure as the time Earth takes to go once around the Sun.^[1] The difference from 365 days is about six hours a year.^[1] Over four years those hours add up to about 24, and they are put back into the calendar as one extra day at the end of February.^[1] That day is February 29, known as leap day, and a year that contains it has 366 days.^[1][6]

The aim is to keep the calendar in step with the seasons.^[2] A calendar year has to be a whole number of days, so no single year length can match the tropical year exactly.^[2]

Sources state the figure with slightly different precision: NIST and the Smithsonian's National Air and Space Museum give 365.242190 days, and Royal Museums Greenwich cites both 365.2422 and 365.24237 days.^[3][4][5]

What would happen to the seasons without leap days?

If every year had exactly 365 days, the calendar would run short of the tropical year by about 0.2422 days each year.^[2] After a century the gap would reach about 24 days, and the start of spring in the Northern Hemisphere would move from March 20 to April 13.^[2] JPL describes the same drift using a different season: after a century without leap days, summer would not start until mid-July.^[1] Equinoxes, solstices and other yearly events would keep sliding later in the calendar.^[1]

Over a longer span the months and the weather would trade places: the National Air and Space Museum estimates that after about 700 years, the northern summer now expected in June would fall in December.^[3]

Why did the Julian calendar's four-year rule over-correct?

The Julian calendar, introduced by Julius Caesar, used a simple fix: one leap day every fourth year.^[2][7] That makes the average calendar year 365.25 days long.^[2] The sources disagree on when it was introduced: the Naval Observatory's leap-year page and Royal Museums Greenwich say 46 B.C., while NIST and the Naval Observatory's introduction to calendars say 45 B.C.^[2][4][5][7] Royal Museums Greenwich adds that the leap years were not inserted correctly until 8 AD.^[4]

An average of 365.25 days is slightly too long.^[2] It exceeds the tropical year by about 0.0078 days, which adds up to a little more than three quarters of a day per century.^[2] JPL expresses the same error in minutes: inserting a full 24-hour leap day every four years adds about 45 minutes too many to each four-year cycle, or about three days every 400 years.^[1]

Between Caesar's time and the sixteenth century, this surplus moved the start of spring on the calendar from March 23 to March 11.^[2]

What did the Gregorian reform of 1582 change?

Pope Gregory XIII introduced the Gregorian calendar in 1582.^[2][5] The church's rules for setting the date of Easter defined March 21 as the vernal (spring) equinox, but over the centuries the astronomical equinox had drifted away from that date.^[7] The Naval Observatory says the Gregorian calendar came out of a perceived need to reform the Easter calculation.^[7] The reform shifted the calendar so that spring began on March 21, and it brought in a new leap-day rule.^[2] Moving spring from March 11 back to March 21 is a shift of 10 days by this article's count, which matches NIST's statement that by 1582 the Julian calendar had become 10 days off.^[2][5]

The new rule keeps the leap day in years divisible by 4 but removes it from century years, unless the century year is also divisible by 400.^[2][7] The result is 97 leap days in every 400 years and an average calendar year of 365.2425 days.^[2] NIST sums up the change as three fewer leap years in every 400 years.^[5] The new average is within half a minute of the tropical year, and the Naval Observatory estimates it will take about 3300 years before the Gregorian calendar is one day out of step with the seasons.^[2]

Countries did not all switch at once: in non-Catholic countries the change came later.^[4] Britain and its colonies adopted the new calendar in 1752, when September 2 was followed by September 14 and 11 days were dropped.^[4] Today the Gregorian calendar is the internationally accepted civil calendar.^[7]

Which years are leap years, and when is the next one?

The Gregorian rule can be checked in three steps:

1. A year that is not divisible by 4 is a common year of 365 days.^[3][4]
2. A year that is divisible by 4 but not by 100 is a leap year.^[2][7]
3. A year that is divisible by 100 is a leap year only if it is also divisible by 400.^[2][7]

The year 2000 was a leap year, but 1700, 1800 and 1900 were not.^[2][3] After 2024, the next leap years are 2028, 2032 and 2036.^[3][4] The next leap year to be skipped is 2100, and 2200 and 2300 will be skipped as well.^[1][3] The year 2400 will be a leap year.^[2]