Leap year
A leap year is a calendar year that contains an additional day added to keep the calendar year synchronized with the astronomical year or seasonal year. Because astronomical events and seasons do not repeat in a whole number of days, calendars that have the same number of days in each year drift over time with respect to the event that the year is supposed to track. By inserting an additional day or month into the year, the drift can be corrected. A year that is not a leap year is a common year.
For example, in the Gregorian calendar, each leap year has 366 days instead of 365, by extending February to 29 days rather than the common 28. These extra days occur in each year which is an integer multiple of 4. Similarly, in the lunisolar Hebrew calendar, Adar Aleph, a 13th lunar month, is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons. In the Bahá'í Calendar, a leap day is added when needed to ensure that the following year begins on the March equinox.
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 will advance two days due to the extra day, thus leaping over one day in the week. For example, Christmas Day fell on a Sunday in 2016, Monday in 2017, Tuesday in 2018 and Wednesday in 2019, but then will leap over Thursday to fall on a Friday in 2020.
The length of a day is also occasionally corrected by inserting a leap second into Coordinated Universal Time 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.
Leap years can present a problem in computing, known as the leap year bug, when a year is not correctly identified as a leap year or when February 29 is not handled correctly in logic that accepts or manipulates dates.
Gregorian calendar
In the Gregorian calendar, the standard calendar in most of the world, most years that are multiples of 4 are leap years. In 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 6 hours. Some exceptions to this basic rule are required since the duration of a tropical year is slightly less than 365.25 days. 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.
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 drops three leap days every 400 years, which is the length of its leap cycle. This is done by dropping February 29 in the three century years that cannot be exactly divided by 400. The years 1600, 2000 and 2400 are leap years, while 1700, 1800, 1900, 2100, 2200 and 2300 are not leap years. By this rule, the average number of days per year is 365 + − + = 365.2425. The rule can be applied to years before the Gregorian reform, if astronomical year numbering is used.
The Gregorian calendar was designed to keep the vernal equinox on or close to March 21, so that the date of Easter remains close to the vernal equinox. The "Accuracy" section of the "Gregorian calendar" article discusses how well the Gregorian calendar achieves this design goal, and how well it approximates the tropical year.
Algorithm
The following pseudocode determines whether a year is a leap year or a common year in the Gregorian calendar. The year variable being tested is the integer representing the number of the year in the Gregorian calendar.if then
else if then
else if then
else
The algorithm applies to proleptic Gregorian calendar years before 1, but only if the year is expressed with astronomical year numbering. It is not valid for the BC or BCE notation. The algorithm is not necessarily valid for years in the Julian calendar, such as years before 1752 in the British Empire. The year 1700 was a leap year in the Julian calendar, but not in the Gregorian calendar.
Leap day
February 29 is a date that usually occurs every four years, and is called the leap day. This day is added to the calendar in leap years as a corrective measure, because the Earth does not orbit the sun in precisely 365 days.The Gregorian calendar is a modification of the Julian calendar first used by the Romans. The Roman calendar originated as a lunisolar calendar and named many of its days after the syzygies of the moon: the new moon and the full moon. The Nonae or nones was not the first quarter moon but was exactly one nundina or Roman market week of nine days before the ides, inclusively counting the ides as the first of those nine days. This is what we would call a period of eight days. In 1825, Ideler believed that the lunisolar calendar was abandoned about 450 BC by the decemvirs, who implemented the Roman Republican calendar, used until 46 BC. The days of these calendars were counted down to the next named day, so February 24 was ante diem sextum Kalendas Martias often abbreviated a. d. VI Kal. Mart. The Romans counted days inclusively in their calendars, so this was actually the fifth day before March 1 when counted in the modern exclusive manner.
The Republican calendar's intercalary month was inserted on the first or second day after the Terminalia. The remaining days of Februarius were dropped. This intercalary month, named Intercalaris or Mercedonius, contained 27 days. The religious festivals that were normally celebrated in the last five days of February were moved to the last five days of Intercalaris. Because only 22 or 23 days were effectively added, not a full lunation, the calends and ides of the Roman Republican calendar were no longer associated with the new moon and full moon.
The Julian calendar, which was developed in 46 BC by Julius Caesar, and became effective in 45 BC, distributed an extra ten days among the months of the Roman Republican calendar. Caesar also replaced the intercalary month by a single intercalary day, located where the intercalary month used to be. To create the intercalary day, the existing ante diem sextum Kalendas Martias was doubled, producing ante diem bis sextum Kalendas Martias. Hence, the year containing the doubled day was a bissextile year. For legal purposes, the two days of the bis sextum were considered to be a single day, with the second half being intercalated; but in common practice by 238, when Censorinus wrote, the intercalary day was followed by the last five days of February, a. d. VI, V, IV, III and pridie Kal. Mart., so that the intercalated day was the first half of the doubled day. Thus the intercalated day was effectively inserted between the 23rd and 24th days of February. All later writers, including Macrobius about 430, Bede in 725, and other medieval computists, continued to state that the bissextum occurred before the last five days of February.
, feast days falling on or after February 24 are celebrated one day later in leap year.
Until 1970, the Roman Catholic Church always celebrated the feast of Saint Matthias on a. d. VI Kal. Mart., so if the days were numbered from the beginning of the month, it was named February 24 in common years, but the presence of the bissextum in a bissextile year immediately before a. d. VI Kal. Mart. shifted the latter day to February 25 in leap years, with the Vigil of St. Matthias shifting from February 23 to the leap day of February 24. This shift did not take place in pre-Reformation Norway and Iceland; Pope Alexander III ruled that either practice was lawful. Other feasts normally falling on February 25–28 in common years are also shifted to the following day in a leap year. The practice is still observed by those who use the older calendars.
Synchronized calendars (Bengali, Indian and Thai)
The Revised Bengali Calendar of Bangladesh and the Indian National Calendar organise their leap years so that the every leap day is close to a February 29 in the Gregorian calendar and vice versa. This makes it easy to convert dates to or from Gregorian.The Thai solar calendar uses the Buddhist Era, but has been synchronized with the Gregorian since AD 1941.
Julian, Coptic and Ethiopian calendars
The Julian calendar was instituted in 45 BC at the order of Julius Caesar, and the original intent was to make every fourth year a leap year, but this was not carried out correctly. Augustus ordered some leap years to be omitted to correct the problem, and by AD 8 the leap years were being observed every fourth year, and the observances were consistent up to and including modern times.From AD 8 the Julian calendar received an extra day added to February in years that are multiples of 4.
The Coptic calendar and Ethiopian calendar also add an extra day to the end of the year once every four years before a Julian 29-day February.
This rule gives an average year length of 365.25 days. However, it is 11 minutes longer than a tropical year. This means that the vernal equinox moves a day earlier in the calendar about every 131 years.
Revised Julian calendar
The Revised Julian calendar adds an extra day to February in years that are multiples of four, except for years that are multiples of 100 that do not leave a remainder of 200 or 600 when divided by 900. This rule agrees with the rule for the Gregorian calendar until 2799. The first year that dates in the Revised Julian calendar will not agree with 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 year is slightly longer, the Revised Julian calendar for the time being does not do as good a job as the Gregorian calendar at keeping the vernal equinox on or close to March 21.
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. In the Chinese calendar the leap month is added according to a rule which ensures that month 11 is always the month that contains the northern winter solstice. The intercalary month takes the same number as the preceding month; for example, if it follows the second month then it is simply called "leap second month" i.e..Hebrew calendar
The Hebrew calendar is lunisolar with an embolismic month. This extra month is called Adar Alef and is added before Adar, which then becomes Adar Bet. According to the Metonic cycle, this is done seven times every nineteen years. This is to ensure that Passover is always in the spring as required by the Torah in many verses relating to Passover.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 days of the week from 28 to 14, and regulate the location of certain religious holidays in relation to the Sabbath. In particular, the first day of the Hebrew year can never be Sunday, Wednesday or Friday. This rule is known in Hebrew as "lo adu rosh", i.e., "Rosh is not Sunday, Wednesday or Friday". Accordingly, the first day of Passover is never Monday, Wednesday or Friday. This rule is known in Hebrew as "lo badu Pesah", which has a double meaning — "Passover is not a legend", but also "Passover is not Monday, Wednesday or Friday".
One reason for this rule is that Yom Kippur, the holiest day in the Hebrew calendar and the tenth day of the Hebrew year, now must never be adjacent to the weekly Sabbath, i.e., it must never fall on Friday or Sunday, in order not to have two adjacent Sabbath days. However, Yom Kippur can still be on Saturday. A second reason is that Hoshana Rabbah, the 21st day of the Hebrew year, will never be on Saturday. These rules for the Feasts do not apply to the years from the Creation to the deliverance of the Hebrews from Egypt under Moses. It was at that time that the God of Abraham, Isaac and Jacob gave the Hebrews their "Law" including the days to be kept holy and the feast days and Sabbaths.
Years consisting of 12 months have between 353 and 355 days. In a k'sidra 354-day year, months have alternating 30 and 29 day lengths. In a chaser year, the month of Kislev is reduced to 29 days. In a malei year, the month of Marcheshvan is increased to 30 days. 13-month years follow the same pattern, with the addition of the 30-day Adar Alef, giving them between 383 and 385 days.
Islamic calendar
The observed and calculated versions of the Islamic calendar do not have regular leap days, even though both have lunar months containing 29 or 30 days, generally in alternating order. However, the tabular Islamic calendar used by Islamic astronomers during the Middle Ages and still used by some Muslims does have a regular leap day added to the last month of the lunar year in 11 years of a 30-year cycle. This additional day is found at the end of the last month, Dhu 'l-Hijja, which is also the month of the Hajj.The Hijri-Shamsi calendar, also adopted by the Ahmadiyya Community, is based on solar calculations and is similar to the Gregorian calendar in its structure with the exception that the first year starts with Hijra.
Bahá'í calendar
The Bahá'í calendar is a solar calendar composed of 19 months of 19 days each. Years begin at Naw-Rúz, on the vernal equinox, on or about March 21. A period of "Intercalary Days", called Ayyam-i-Ha, are inserted before the 19th month. This period normally has 4 days, but an extra day is added when needed to ensure that the following year starts on the vernal equinox. This is calculated and known years in advance.Solar Hijri calendar
The Iranian calendar is an observational calendar that starts on the spring equinox and adds a single intercalated day to the last month once every four or five years; the first leap year occurs as the fifth year of the typical 33-year cycle and the remaining leap years occur every four years through the remainder of the 33-year cycle. This system has less periodic deviation or jitter from its mean year than the Gregorian calendar, and operates on the simple rule that the vernal equinox always falls in the 24-hour period ending at noon on New Year's Day. The 33-year period is not completely regular; every so often the 33-year cycle will be broken by a cycle of 29 years. A similar rule has been proposed to simplify the Gregorian calendar. The centennial leap years would be spaced so that in years giving remainder 3 on division by 100 the dynamic mean sun passes through the equinox in the 24-hour period ending at 1 PM GMT on 19 March. The system would be introduced when for the first time the dynamic mean sun is due to pass through the equinox before 1 PM GMT on 18 March in a year giving remainder 3 on division by 400. The immediately preceding centennial leap year will be cancelled. The first cancellation will probably be AD 8400 and the next two centennial leap years thereafter will probably be AD 8800 and AD 9700.Folk traditions
In Ireland and Britain, it is a tradition that women may propose marriage only in leap years. While it has been claimed that the tradition was initiated by Saint Patrick or Brigid of Kildare in 5th century Ireland, this is dubious, as the tradition has not been attested before the 19th century. Supposedly, a 1288 law by Queen Margaret of Scotland, required that fines be levied if a marriage proposal was refused by the man; compensation was deemed to be a pair of leather gloves, a single rose, £1 and a kiss. In some places the tradition was tightened to restricting female proposals to the modern leap day, February 29, or to the medieval leap day, February 24.According to Felten: "A play from the turn of the 17th century, 'The Maydes Metamorphosis,' has it that 'this is leape year/women wear breeches.' A few hundred years later, breeches wouldn't do at all: Women looking to take advantage of their opportunity to pitch woo were expected to wear a scarlet petticoat — fair warning, if you will."
In Finland, the tradition is that if a man refuses a woman's proposal on leap day, he should buy her the fabrics for a skirt.
In France, since 1980, a satirical newspaper entitled La Bougie du Sapeur is published only on leap year, on February 29.
In Greece, marriage in a leap year is considered unlucky. One in five engaged couples in Greece will plan to avoid getting married in a leap year.
In February 1988 the town of Anthony in Texas, declared itself "leap year capital of the world", and an international leapling birthday club was started.
Birthdays
A person born on February 29 may be called a "leapling" or a "leaper". In common years, they usually celebrate their birthdays on February 28. In some situations, March 1 is used as the birthday in a non-leap year, since it is the day following February 28.Technically, a leapling will have fewer birthday anniversaries than their age in years. This phenomenon is exploited when a person claims to be only a quarter of their actual age, by counting their leap-year birthday anniversaries only: for example, in Gilbert and Sullivan's 1879 comic opera The Pirates of Penzance, Frederic the pirate apprentice discovers that he is bound to serve the pirates until his 21st birthday rather than until his 21st year.
For legal purposes, legal birthdays depend on how local laws count time intervals.