Leap year

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For other uses, see Leap year (disambiguation).

A leap year (or intercalary or bissextile year) is a year containing one additional day (or, in the case of lunisolar calendars, a month) in order to keep the calendar year synchronized with the astronomical or seasonal year.[1] Because seasons and astronomical events do not repeat in a whole number of days, calendars that have the same number of days in each year, over time, drift with respect to the event that the year is supposed to track. By inserting (or intercalating) an additional day or month into the year, the drift can be corrected. A year that is not a leap year is called a common year.

For example, in the Gregorian calendar, each leap year lasts 366 days instead of the usual 365, by extending February to 29 days rather than the common 28 days. 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.

The name "leap" year comes from the fact that while a fixed date in the Gregorian calendar normally advances one day of the week from one year to the next, in a leap year the day of the week will advance two days (from March onwards) due to the year's extra day inserted at the end of February (thus "leaping over" one of the days in the week). For example, Christmas Day fell on Tuesday in 2001, Wednesday in 2002 and Thursday in 2003 but then "leapt" over Friday to fall on a Saturday in 2004.[2]

Gregorian calendar[edit]

In the Gregorian calendar, the current standard calendar in most of the world, most years that are integer multiples of 4 are leap years. In each leap year, the month of February has 29 days instead of 28. Adding an extra day to the calendar every four years compensates for the fact that a period of 365 days is shorter than a solar year by almost 6 hours. This calendar was first used in 1582.

Some exceptions to this basic rule are required since the duration of a solar year is slightly less than 365.25 days. Over a period of 4 centuries, the accumulated error of adding a leap day every 4 years amounts to about 3 extra days. The Gregorian Calendar therefore omits 3 leap days every 400 years, which is the length of its leap cycle. This is done by omitting February 29 in the 3 century years (integer multiples of 100) that are not also integer multiples of 400.[3] For example, 1700, 1800, 1900, 2100 and 2200 are common years, but 1600, 2000 and 2400 are leap years. By this rule, the average number of days per year is 365 + 1/4 − 1/100 + 1/400 = 365.2425.[4] The rule can be applied to years before the Gregorian reform (the proleptic Gregorian calendar). The rule is not directly applicable to years numbered with BC notation. Since 0 is divisible by 4, 100, and 400, the "year 0" (1 BC) is a leap year. Thus the rule can be applied to years before AD 1 if astronomical year numbering is used.[5]

Gregoriancalendarleap solstice.svg
This graph shows the variations in date and time of the June Solstice due to unequally spaced "leap day" rules. Contrast this with the Iranian Solar Hijri calendar, which has 8 leap year days every 33 years.


The Gregorian calendar was 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—i.e. a full moon—that falls on or after March 21) remains close to the vernal equinox.[6] The vernal equinox year is about 365.242374 days long, measured in ephemeris time.[7]


The following pseudocode determines whether a year is a leap year or a common year in the Gregorian calendar (and in the proleptic Gregorian calendar before 1582). The year variable being tested is the integer representing the number of the year in the Gregorian calendar, and the tests are arranged to dispatch the most common cases first. Care should be taken in translating mathematical integer divisibility into specific programming languages.

else (it is a leap year)

Leap day[edit]

Main article: February 29
A Swedish pocket calendar from the year 2008 showing February 29
February 1900 calendar showing that 1900 was not a leap year

February 29 is a date that usually occurs every four years, and is called leap day. This day is added to the calendar in leap years as a corrective measure, because the Earth does not orbit around the sun in precisely 365 days.



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 Martii (February 24) was doubled, producing ante diem bis sextum Kalendas Martii. Hence, the year containing the doubled day was a bissextile (bis sextum, "twice sixth") 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. Mar. (the days numbered 24, 25, 26, 27, and 28 from the beginning of February in a common year), 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 (calculators of Easter), continued to state that the bissextum (bissextile day) occurred before the last five days of February.

In the older Roman Missal, 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. Mar., 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. Mar. 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 (Liber Extra, 5. 40. 14. 1). Other feasts normally falling on February 25–28 in common years are also shifted to the following day in a leap year (although they would be on the same day according to the Roman notation). The practice is still observed by those who use the older calendars.

Synchronized calendars (Bangla, Indian, Thai and Bahá'í)[edit]

The Revised Bangla Calendar of Bangladesh and the Indian National Calendar organise their leap years so that the leap day is always close to February 29 in the Gregorian calendar. This makes it easy to convert dates to or from Gregorian.



Julian, Coptic and Ethiopian calendars[edit]

Since AD 8 the Julian calendar added, or will add, an extra day to February in years that are integer multiples of 4.


This rule gives an average year length of 365.25 days. However, it is 11 minutes longer than a vernal equinox year. This means that the vernal equinox moves a day earlier in the calendar about every 131 years.

Revised Julian calendar[edit]

The Revised Julian calendar adds an extra day to February in years that are integer multiples of four, except for years that are integer 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 does not do as good a job as the Gregorian calendar of keeping the vernal equinox on or close to March 21.

Chinese calendar[edit]

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 i.e. February (二月) then it is simply called "leap second month" i.e. "Leap February" (simplified Chinese: 闰二月; traditional Chinese: 閏二月; pinyin: rùn'èryuè).

Hebrew calendar[edit]

The Hebrew calendar is lunisolar with an embolismic month. This extra month is called Adar Alef (first Adar) and is added before Adar, which then becomes Adar Bet (second Adar). According to the Metonic cycle, this is done seven times every nineteen years (specifically, in years 3, 6, 8, 11, 14, 17, and 19). This is to ensure that Pesah (Passover) is always in the spring as required by the Torah (Pentateuch) in many verses[10] relating to Pesah.


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 (which is Saturday), 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. 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 (cf. Exodus 13) 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.


Islamic calendar[edit]

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 each in no apparent 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.[11] This additional day is found at the end of the last month, Dhu 'l-Hijja, which is also the month of the Hajj.[12]

The Hijri-Shamsi calendar, also adopted by the Ahmadiyya Muslim 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.[13]

Hindu calendar[edit]

In the Hindu calendar, which is a lunisolar calendar, the embolismic month is called adhika maasa (extra month). It is the month in which the sun is in the same sign of the stellar zodiac on two consecutive dark moons. Adhika maasa occurs once every two or three years, compensating for the approximately eleven fewer days per year in twelve lunar months than the solar calendar. Thus, Hindu festivals tend to occur within a given span of the Gregorian calendar. For example: the No Moon during Diwali festival tends to occur between October 22 and November 15. Buddhist calendars in several related forms (each a simplified version of the Hindu calendar) are used on mainland Southeast Asia in the countries of Cambodia, Laos, Thailand, Myanmar (formerly Burma) and Sri Lanka.

The Hindu Calendar also known as Vikram Samvat is used in Nepal as National Calendar. All the official work is done based on this calendar.

The calendar followed in some parts of South India (mainly in Tamil Nadu) is solar. It has a leap year every four years.

Solar Hejri calendar[edit]

Main article: 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 (Esfand) 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. The system used is more accurate and more complicated, and is based on the time of the March equinox as observed from Tehran. The 33 year period is not completely regular; every so often the 33-year cycle will be broken by a cycle of 29 or 37 years.[14]


Folk traditions[edit]

A spinster eagerly awaits the upcoming leap day, in this 1903 cartoon by Bob Satterfield.

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.[15] Supposedly, a 1288 law by Queen Margaret of Scotland (then age five and living in Norway), 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.[16] In some places the tradition was tightened to restricting female proposals to the modern leap day, February 29, or to the medieval (bissextile) leap day, February 24.


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.[citation needed]

In Greece, marriage in a leap year is considered unlucky.[18] One in five engaged couples in Greece will plan to avoid getting married in a leap year.[19]

1908 postcards
Woman capturing man with butterfly-net. 
Women anxiously awaiting January 1st 
Histrionically preparing 


A person born on February 29 may be called a "leapling" or a "leaper".[20] 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. 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 (that is, when he turns 84 years old) rather than until his 21st year.


Republic of China[edit]

The Civil Code of the Republic of China since October 10, 1929,[21] implies that the legal birthday of a leapling is February 28 in common years:


Hong Kong[edit]

Since 1990 non-retroactively, Hong Kong considers the legal birthday of a leapling March 1 in common years:[23]

  1. The time at which a person attains a particular age expressed in years shall be the commencement of the anniversary corresponding to the date of his birth.
  2. Where a person has been born on February 29 in a leap year, the relevant anniversary in any year other than a leap year shall be taken to be March 1.
  3. This section shall apply only where the relevant anniversary falls on a date after the date of commencement of this Ordinance.

See also[edit]


  1. ^ Meeus, Jean. (1998.) Astronomical Algorithims. Willmann-Bell. pp. 62.
  2. ^ Douglas Harper, "leap year", Online Etymology Dictionary, 2012.
  3. ^ United States Naval Observatory. (June 14, 2011). Leap Years. Author.
  4. ^ Richards, E. G. (2013). Calendars. in S. E. Urban and P. K. Seidelmann eds. Explanatory Supplement to the Astronomical Almanac 3rd ed. Mill Valley CA: University Science Books. p. 598. ISBN 9781891389856
  5. ^ Dogget, L.E. (1992). "Calendars" in P. K. Seidelmann (ed.). Explanatory Supplement to the Astronomical Almanac, 2nd ed. Sausalito, CA: University Science Books. p. 580–1.
  6. ^ E.G. Richards, E.G. (1998). Mapping time: The calendar and its history. Oxford University Press. p. 240. ISBN 0-19-286205-7.
  7. ^ Meeus, J. & Savoie, D. (1992). The history of the tropical year. Journal of the British Astronomical Association, 102(1), p. 42.
  8. ^ Thomas Hewitt Key, Calendarium (1875)[dead link]
  9. ^ Smith, Peter (2000). "Ayyám-i-Há". A concise encyclopedia of the Bahá'í Faith. Oxford: Oneworld Publications. p. 53. ISBN 1-85168-184-1. 
  10. ^ Exodus 23,15 ; Exodus 34,18 ; Deuteronomy 15,1 ; Deuteronomy 15, 13
  11. ^ "The Islamic leap year". (n.d.). Time and Date AS. Retrieved February 29, 2012.
  12. ^ "Leap year trivia you might want to know". (n.d.) GMA News. Retrieved February 29, 2012.
  13. ^ "Hijri-Shamsi Calendar". Al Islam. Retrieved June 5, 2014. 
  14. ^ M. Heydari-Malayeri, A concise review of the Iranian calendar, Paris Observatory, 2004.[self-published source?]
  15. ^ Mikkelson, B. & Mikkelson, D.P. (2010). The Privilege of Ladies by Barbara Mikkelson. The Urban Legends Reference Pages. snopes.com.
  16. ^ Virtually no laws of Margaret survive. Indeed, none concerning her subjects are recorded in the twelve volume Acts of the Parliaments of Scotland (1814–75) covering the period 1124–1707 (two laws concerning young Margaret herself are recorded on pages 424 & 441–2 of volume I).
  17. ^ Felten, E. (February 23, 2008). The bissextile beverage. Wall Street Journal.
  18. ^ A Greek Wedding Anagnosis Books Retrieved January 12, 2012.
  19. ^ Teaching Tips 63, at Developing Teachers; retrieved January 12, 2012.
  21. ^ [http://law.moj.gov.tw/Eng/LawClass/LawHistory.aspx?PCode=B0000001 Legislative history of the Civil Code of the Republic of China now in effect in Taiwan
  22. ^ Article 121 of the Civil Code Part I General Principles of the Republic of China now in effect in Taiwan
  23. ^ "Age of Majority (Related Provisions) Ordinance" (Ch. 410 Sec. 5) (June 30, 1997). Hong Kong Department of Justice(Enacted in 1990).

External links[edit]