A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) compared to a common year. The 366th day (or 13th month) is added to keep the calendar year synchronised with the astronomical year or seasonal year. Since astronomical events and seasons do not repeat in a whole number of days, calendars that have a constant number of days each year will unavoidably drift over time with respect to the seasons. By inserting an additional day—a leap day—or an additional month—a leap month—into some years but not others, the drift between a civilisation's dating system and the physical properties of the Solar System can be avoided. An astronomical year lasts slightly less than 3651⁄4 days. The historic Julian calendar has three common years of 365 days followed by a leap year of 366 days, by extending February to 29 days rather than the common 28. The Gregorian calendar, the world's most widely used civil calendar, makes a further adjustment for the small error in the Julian algorithm; this extra leap day occurs in each year that is a multiple of 4, except for years evenly divisible by 100 but not by 400. Thus 1600, 2000 and 2400 are leap years, but 1700, 1800, 1900, 2100, 2200, and 2300 are not. In the Solar Hijri and Bahá'í calendars, a leap day is added whenever needed to ensure that the following year begins on the March equinox. A lunar year of 12 lunar months is about 11 days shorter than an astronomical year. Lunisolar calendars, such as are traditional in most of Asia, each has its own rule to decide when to add a leap (lunar) month, so as to keep its calendar year from drifting through the seasons. Pure lunar calendars, such as the lunar Hijri calendar used in most of Islam, do not employ any such arrangement and accept the seasonal drift. The term leap year probably comes from the fact that a fixed date in the Gregorian calendar normally advances one day of the week from one year to the next, but the day of the week in the 12 months following the leap day (from 1 March through 28 February of the following year) will advance two days due to the extra day, thus leaping over one day in the week. For example, since 1 March was a Friday in 2024, a Saturday in 2025, and a Sunday in 2026, and will be a Monday in 2027, the date will then "leap" over Tuesday to fall on a Wednesday in 2028. The length of a day is also occasionally corrected by inserting a leap second into Coordinated Universal Time (UTC) because of variations in Earth's rotation period. Unlike leap days, leap seconds are not introduced on a regular schedule because variations in the length of the day are not entirely predictable.
Julian calendar
On 1 January 45 BC, by edict, Julius Caesar reformed the historic Roman calendar to make it a consistent solar calendar (rather than one which was neither strictly lunar nor strictly solar), thus removing the need for frequent intercalary months. His rule for leap years was a simple one: add a leap day every 4 years. This algorithm is close to reality: a Julian year lasts 365.25 days, a mean tropical year about 365.2422 days, a difference of only ≈ 111/4 min. Consequently, even this Julian calendar drifts out of 'true' by about 3 days every 400 years. The Julian calendar continued in use unaltered for about 1600 years until the Catholic Church became concerned about the widening divergence between the March equinox and 21 March, as explained at Gregorian calendar, below. Prior to Caesar's creation of what would be the Julian calendar, February was already the shortest month of the year for Romans. In the Roman calendar (after the reform of Numa Pompilius that added January and February), all months except February had an odd number of days – 29 or 31. This was because of a Roman superstition that even numbers were unlucky. When Caesar changed the calendar to follow the solar year closely, he made all months have 30 or 31 days, leaving February unchanged except in leap years.
Gregorian calendar
In the Gregorian calendar, the standard calendar in most of the world, almost every fourth year is a leap year. Each leap year, the month of February has 29 days instead of 28. Adding one extra day in the calendar every four years compensates for the fact that a period of 365 days is shorter than a tropical year by almost six hours. However, this correction is excessive and the Gregorian reform modified the Julian calendar's scheme of leap years as follows:
Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the years 1600 and 2000 are.
Whereas the Julian calendar year incorrectly summarised Earth's tropical year as 365.25 days, the Gregorian calendar makes these exceptions to follow a calendar year of 365.2425 days. This more closely resembles a mean tropical year of 365.2422 days. Over a period of four centuries, the accumulated error of adding a leap day every four years amounts to about three extra days. The Gregorian calendar therefore omits three leap days every 400 years, which is the length of its leap cycle. This is done by omitting 29 February in the three century years (multiples of 100) that are not multiples of 400. By this rule, an entire leap cycle is 400 years, which totals 146,097 days, and the average number of days per year is 365 + 1⁄4 − 1⁄100 + 1⁄400 = 365 + 97⁄400 = 365.2425. This rule could be applied to years before the Gregorian reform to create a proleptic Gregorian calendar, though the result would not match any historical records.
The Gregorian calendar was designed to keep the March equinox on or close to 21 March, so that the date of Easter (celebrated on the Sunday after the ecclesiastical full moon that falls on or after 21 March) remains close to the March equinox. The "Accuracy" section of the "Gregorian calendar" article discusses how well the Gregorian calendar achieves this objective, and how well it approximates the tropical year.
Leap day in the Julian and Gregorian calendars
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