A leap year is a year in which an extra day in added to the calendar in order to synchronize it with the seasons.Since the tropical year is 365.242190 days long, a leap year must be added roughly once every four years (four times the fractional day gives ). In a leap year, the extra day (known as a leap day ) is added at the end of February, giving it 29 instead of the usual 28 days.

In the Gregorian calendar currently in use worldwide (except perhaps the Russian and Iranian calendars ), there is a leap year every year divisible by four except for years which are both divisible by 100 and not divisible by 400. Therefore, the year 2000 will be a leap year, but the years 1700, 1800, and 1900 were not. The complete list of leap years in the first half of the 21st century is therefore 2000, 2004, 2008, 2012, 2016, 2020, 2024, 2028, 2032, 2036, 2040, 2044, and 2048.
The extra rule involving centuries is an additional correction to make up for the fact that one extra day every four years is slightly too much correction (). This scheme results in the vernal equinox gradually shifting its date between March 19 and 21, being shifted once every leap year, and then being abruptly shifted in non-leap centuries (see figure above).
In the Gregorian calendar , 97 years out of every 400 are leap years, giving the total number of days in 400 years as

The leap year was introduced in the Julian calendar in 46 BC.However, around 10 BC, it was found that the priests in charge of computing the calendar had been adding leap years every three years instead of the four decreed by Caesar (Vardi 1991, p. 239). As a result of this error, no more leap years were added until 8 AD. Leap years were therefore 45 BC, 42 BC, 39 BC, 36 BC, 33 BC, 30 BC, 27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, 9 BC, 8 AD, 12 AD, and every fourth year thereafter (Tøndering), until the Gregorian calendar was introduced (resulting in skipping three out of every four centuries)). The UNIX command cal incorrectly lists 4 AD as a leap year (Vardi 1991).