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Why Are There Leap Years?
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Stone relief on Pope Gregory XIII's tomb in Saint Peter's Basilica, showing the pope seated among clergy as a figure presents a document and another gestures to a globe.
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Stone relief on Pope Gregory XIII's tomb in Saint Peter's Basilica, showing the pope seated among clergy as a figure presents a document and another gestures to a globe.
Gregorian calendar The introduction of the Gregorian calendar, depicted in relief on the tomb of Pope Gregory XIII in St. Peter's Basilica, Vatican City.

Why Are There Leap Years?

Written by
Erik Gregersen
Erik Gregersen is a senior editor at Encyclopaedia Britannica, specializing in the physical sciences and technology. Before joining Britannica in 2007, he worked at the University of Chicago Press on the...
Erik Gregersen
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Britannica Editors
Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree....
Britannica Editors
History

There are leap years because the time it takes for Earth to complete one orbit around the Sun is not a whole number of days. Earth goes around the Sun every 365.2422 days.

The remaining 0.2422 day is pretty close to one-quarter of a day (0.25), so an extra day—February 29—is usually added every four years. This was first done with the Julian calendar in 46 bce, giving an average year length of [(3 ⨉ 365) + (1 ⨉ 366)]/4 = 365.25 days.

For centuries adding a leap day every four years seemed pretty effective, but 0.25 − 0.2422 = 0.0078 days, or just a little under 11 minutes and 14 seconds. Those 11 minutes and 14 seconds added up at the rate of 1 day every 128 years and moved the calendar out of phase with the seasons.

In 1582 Pope Gregory XIII instituted what is now called the Gregorian calendar. That year October 4 was followed by October 15, and henceforth, of years that ended in 00, only years divisible by 400 would be leap years. That is, 1600 was a leap year, but 1700, 1800, and 1900 were not.

Out of every 400 years, instead of there being 100 leap years, the Gregorian calendar has 97 leap years. The average year length then becomes [(303 ⨉ 365) + (97 ⨉ 366)]/400 = 365.2425 days, which is 0.0003 days, or about 26 seconds, off from the true year. That difference adds up at the rate of only 1 day every 3,333 years.

Erik Gregersen