In the Gregorian calendar, a year of 366 days, with a day added to the month of February. Any year whose date is a number exactly divisible by four is a leap year, except years ending in 00, which must be divisible by 400 to be leap years. The extra day is added every 4 years to allow for the difference between a year of 365 days and the actual time it takes the Earth to circle the Sun (approximately 365¼ days). The system was introduced to the Western Julian calendar in its final form in AD 8, and modified by the Gregorian calendar of 1582.
A leap year (or intercalary year) is a year containing an extra day, week or month in order to keep the calendar year synchronised with the astronomical or seasonal year. Seasons and astronomical events do not repeat at an exact number of days, so a calendar which had the same number of days in each year would over time drift with respect to the event it was supposed to track. A year which is not a leap year is called a common year.
Leap years (which keep the calendar in sync with the year) should not be confused with leap seconds (which keep clock time in sync with the day).
Gregorian calendar
The Gregorian calendar, the current standard calendar in most of the world, adds a 29th day to February in all years evenly divisible by 4, except for centennial years (those ending in -00), which receive the extra day only if they are evenly divisible by 400.
The reasoning behind this rule is as follows:
The Gregorian calendar is designed to keep the vernal equinox on or close to March 21, so that the date of Easter (celebrated on the Sunday after the 14th day of the Moon that falls on or after 21 March) remains correct with respect to the vernal equinox. The Gregorian leap year rule gives an average year length of 365.2425 days.This difference of a little over 0.0001 days means that in around 8,000 years, the calendar will be about one day behind where it should be.
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This graph shows the variation between the seasonal year versus the calendar year due to unequally spaced 'leap days' rules. See Iranian calendar to contrast with a calendar based on 8 leap days every 33 years. |
Rules for determining when to have a leap year
In order to get a closer approximation, it was decided to have a leap day 97 years out of 400 rather than once every 4 years. The years that are divisible by 100 but not 400 are known as "exceptional common years". By this rule, the average number of days per year will be 365 + 1/4 - 1/100 + 1/400 = 365.2425. The Roman calendar originated as a lunar calendar (though from the 5th century BC it no longer followed the real moon) and named its days after three of the phases of the moon: the new moon (calends, hence "calendar"), the first quarter (nones) and the full moon (ides).
Since 45 BC, February in a leap year had two days called "the sixth day before the calends of March".
Where this custom is followed, anniversaries after the inserted day are moved in leap years. For example, the former feast day of Saint Matthias, 24 February in ordinary years, would be 25 February in leap years.
This historical nicety is, however, in the process of being discarded: The European Union declared that, starting in 2000, 29 February rather than 24 February would be leap day, and the Roman Catholic Church also now uses 29 February as leap day.
Julian, Coptic and Ethiopian Calendars
The Julian calendar adds an extra day to February in years divisible by 4.
The Coptic calendar and Ethiopian calendar also add an extra day to the end of the year once every 4 years before a Julian 29-day February.
This rule gives an average year length of 365.25 days. The excess of about 0.0076 days with respect to the vernal equinox year means that the vernal equinox moves a day earlier in the calendar every 130 years or so.
Revised Julian Calendar
The Revised Julian calendar adds an extra day to February in years divisible by 4, except for years divisible by 100 that do not leave a remainder of 200 or 600 when divided by 900. The first year that dates in the Revised Julian calendar will not agree with the those in the Gregorian calendar will be 2800, because it will be a leap year in the Gregorian calendar but not in the Revised Julian calendar.
This rule gives an average year length of 365.242222… days. This is a very good approximation to the mean tropical year, but because the vernal equinox tropical year is slightly longer, the Revised Julian calendar does not do as good a job as the Gregorian calendar of keeping the vernal equinox on or close to 21 March.
Chinese calendar
The Chinese calendar is lunisolar, so a leap year has an extra month, often called an embolismic month after the Greek word for it. According to the Metonic cycle, this is done seven times every nineteen years, specifically, in years, 3, 6, 8, 11, 14, 17, and 19.
In addition, the Hebrew calendar has postponement rules that postpone the start of the year by one or two days. These postponement rules reduce the number of different combinations of year length and starting day of the week from 28 to 14, and regulate the location of certain religious holidays in relation to the Sabbath.
Calendars with Leap Years synchronised with Gregorian
The Indian National Calendar and the Revised Bangla Calendar of Bangladesh organise their leap years so that the leap day is always close to February 29 in the Gregorian calendar.
Hindu Calendar
In the Hindu calendar, which is a lunisolar calendar, the embolismic month is called adhika maas (extra month).
Iranian calendar
The Iranian calendar also has a single intercalated day once in every four years, but every 33 years or so the leap years will be five years apart instead of four years apart.
Long term leap year rules
The accumulated difference between the Gregorian calendar and the vernal equinoctial year amounts to 1 day in about 8,000 years. This suggests that the calendar needs to be improved by another refinement to the leap year rule: perhaps by avoiding leap years in years divisible by 8,000.
(The most common such proposal is to avoid leap years in years divisible by 4,000 . Others claim, erroneously, that the Gregorian calendar itself already contains a refinement of this kind .)
Hypothetical 128 year based leap years has been proposed, and it can be adopted directly without any modification to current leap year calculations until the year 2048.
However, there is little point in planning a calendar so far ahead because over a timescale of tens of thousands of years the number of days in a year will change for a number of reasons, most notably:
Precession of the equinoxes moves the position of the vernal equinox with respect to perihelion and so changes the length of the vernal equinoctial year. We can't predict these changes accurately enough to be able to make a calendar that will be accurate to a day in tens of thousands of years.Marriage proposal
There is a tradition, said to go back to Saint Patrick and Saint Bridget in 5th century Ireland, but apparently not attested before the 19th century, whereby women may make marriage proposals only in leap years:
Saint Patrick, having driven the snakes out of the bogs was walking along the shores of Lough Neagh, when he was accosted by Saint Bridget in tears, and was told that a mutiny had broken out in the nunnery over which she presided, the ladies claiming the right of proposing for marriage. In Taiwan, for example, the legal birthday of a leapling is 28 February in common years, so a Taiwanese leapling born on 29 February 1980 would have legally reached 18 years old on 28 February 1998.| If a period fixed by weeks, months, and years does not commence from the beginning of a week, month, or year, it ends with the ending of the day which proceeds the day of the last week, month, or year which corresponds to that on which it began to commence. |
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