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A leap year (also known as an intercalary year or bissextile year) is a
calendar year A calendar is a system of organizing days. This is done by giving names to periods of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, ...
that contains an additional day (or, in the case of a
lunisolar calendar A lunisolar calendar is a calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single, specific day ...
, a month) 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 a constant number of days in each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting (called '' intercalating'' in technical terminology) an additional day or month into some years, the drift between a civilization's dating system and the physical properties of the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

Solar System
can be corrected. A year that is not a leap year is a
common year A common year is a calendar year A calendar is a system of organizing days. This is done by giving names to periods of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in ...
. For example, in the
Gregorian calendar The Gregorian calendar is the calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single, speci ...
, 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 An integer (from the Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to ...
multiple of 4 (except for years evenly divisible by 100, but not by 400). The leap year of 366 days has 52 weeks and two days, hence the year following a leap year will start later by two days of the week. In the lunisolar
Hebrew calendar The Hebrew calendar ( Hebrew: , ), also called Jewish calendar, is a lunisolar calendar used today for Jewish religious observance, and as an official calendar of the state of Israel Israel (; he, יִשְׂרָאֵל; ar, إِس ...
, 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 March equinox or northward equinox is the equinox An equinox is traditionally defined as the time when the plane In mathematics, a plane is a flatness (mathematics), flat, two-dimensional surface (mathematics), surface that extends ...
. 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 March 1 through February 28 of the following year) will advance two days due to the extra day, thus leaping over one day in the week. For example,
Christmas Day Christmas is an annual festival commemorating Nativity of Jesus, the birth of Jesus Christ, observed primarily on December 25 as a religious and cultural celebration among billions of people Observance of Christmas by country, around the world ...

Christmas Day
(December 25) fell on a Friday in 2020, fell on a Saturday in 2021, falls on a Sunday in 2022 and a Monday in 2023, but then will leap over Tuesday to fall on a Wednesday in 2024. The length of a day is also occasionally corrected by inserting a
leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise solar tim ...

leap second
into
Coordinated Universal Time Coordinated Universal Time or UTC is the primary time standard A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been o ...
(UTC) because of variations in Earth's
rotation period The rotation period of a celestial object (e.g., star, gas giant, planet, moon, asteroid) is as its ''sidereal period, sidereal rotation period'' i.e. the time that the object takes to complete a single revolution around its axis of rotation rela ...
. 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 The leap year problem (also known as the leap year bug or the leap day bug) is a problem for both digital (computer-related) and non-digital documentation and data storage situations which results from the wrong calculation of which years are leap y ...
, 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.


Julian calendar

On , by edict,
Julius Caesar Gaius Julius Caesar (; 12 July 100 BC – 15 March 44 BC) was a Roman Roman or Romans most often refers to: *, the capital city of Italy *, Roman civilization from 8th century BC to 5th century AD *, the people of ancient Rome *', shortened ...

Julius Caesar
reformed the historic
Roman calendar The Roman calendar was the calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single, specific ...
to make it a consistent
solar calendar A solar calendar is a calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single, specific day within ...
(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 four years. This algorithm is close to reality: a Julian year lasts 365.25 days, a
mean tropical year A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position of the Sun, position in the cycle of seasons, as seen from Earth; for example, the time from March equinox, vernal equinox to vernal equino ...
about 365.2422 days. Consequently, the calendar drifts out 'true' by about three 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 The March equinox or northward equinox is the equinox An equinox is traditionally defined as the time when the plane In mathematics, a plane is a flatness (mathematics), flat, two-dimensional surface (mathematics), surface that extends ...
and 21 March, as explained
below Below may refer to: *Earth *Ground (disambiguation) *Soil *Floor *Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Fred Below (1926–1988), American blues drummer *Fritz von Below (1853 ...
. In the modern calendar, leap day falls on 29 February. This was not always the case: when the Julian calendar was introduced, leap day was handled differently in two respects. First, leap day fell ''within'' February and not at the end. Second, the leap day was simply not counted so that a leap year still had 365 days. The Romans treated leap day as a second sixth day before the
KalendsThe calends or kalends ( la, kalendae) is the first day of every month in the Roman calendar. The English word ''calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, mo ...
(first day) of March, in Latin . This was translated as 'bissextile': the 'bissextile day' is the leap day and a 'bissextile year' is a year which includes a leap day. This second instance of the sixth day before the Kalends of March was inserted in calendars between the 'normal' fifth and sixth days. By a legal fiction, the Romans treated both the first "sixth day" and the additional "sixth day" before the Kalends of March as one day. Thus a child born on either of those days in a leap year would have its first birthday on the following sixth day before the Kalends of March. When, many years later, modern consecutive day counts were laid alongside the Roman dates the sixth day before the Kalends of March fell on 24 February. However, in a leap year the sixth day fell on 25 February because the additional sixth day came before the 'normal' sixth day. The medieval Church continued the Roman practice which can be illustrated by, for example, the feast of
Saint Matthias Matthias (Koine Greek: Μαθθίας, ''Maththías'' , from Biblical Hebrew, Hebrew מַתִּתְיָהוּ ''Mattiṯyāhū''; cop, ⲙⲁⲑⲓⲁⲥ; died c. AD 80) was, according to the Acts of the Apostles (written c. AD 80–90), chosen ...
which used to be celebrated on the sixth day before the Kalends of March in both common and leap years. The calendar for February in the Book of Common Prayer of 1549 shows the position in a normal year when the feast of St Matthias is on the sixth day before the Kalends of March which is alongside 24 February. The position in a leap year is not shown in the
Church of England The Church of England (C of E) is a Christian church Christian Church is a Protestant Protestantism is a form of Christianity that originated with the 16th-century Reformation, a movement against what its followers perceived to be Critic ...
's 1549
Book of Common Prayer A book is a medium for recording information Information is processed, organised and structured data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sense, data are a set of v ...

Book of Common Prayer
but the prior insertion of the second sixth day meant the feast of St Matthias fell on 25 February in leap years. This practice ended in England some time after Henry VIII split from Rome, specifically in the 1662 edition of the Book of Common Prayer. Consecutive day counting has entirely replaced the Roman system. The feast of St Matthias is invariably on 24 February and leap day is shown at the end of February. The Church and civil society also continued the Roman practice whereby the leap day was simply not counted so that a leap year was only reckoned as 365 days. Henry III of England's instructed magistrates to ignore the leap day when persons were being ordered to appear before the court within a year. The practical application of the rule is obscure. It was regarded as in force in the time of the famous lawyer Sir
Edward Coke Sir Edward Coke ( "cook", formerly ; 1 February 1552 – 3 September 1634) was an English , judge, and politician who is considered the greatest jurist of the and eras. Born into an upper-class family, Coke was educated at , before leavin ...

Edward Coke
(1552-1634) because he cites it in his ''
Institutes of the Lawes of England The ''Institutes of the Lawes of England'' are a series of legal treatises written by Sir Edward Coke. They were first published, in stages, between 1628 and 1644. Widely recognized as a foundational document of the common law, they have been cite ...
''. However, Coke merely quotes the act with a short translation and does not give practical examples.


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 A tropical year (also known as a solar year or tropical period) is the time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past ...
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#REDIRECT Gregorian Reform : ''Should not be confused with the Gregorian calendar''. The Gregorian Reforms were a series of reforms initiated by Pope Gregory VII and the circle he formed in the Roman Curia, papal curia, c. 1050–80, which dealt w ...
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 omits three leap days every 400 years, which is the length of its ''leap cycle''. This is done by omitting February 29 in the three century years (multiples of 100) that are not multiples of 400. The years 2000 and 2400 are leap years, but not 1700, 1800, 1900, 2100, 2200 and 2300. By this rule, an entire leap cycle is 400 years which total 146,097 days, and the average number of days per year is 365 +  −  +  =  = 365.2425. The rule can be applied to years before the Gregorian reform (the
proleptic Gregorian calendar The proleptic Gregorian calendar is produced by extending the Gregorian calendar The Gregorian calendar is the calendar used in most of the world. It was introduced in October 1582 by Pope Gregory XIII as a minor modification of the Julian ca ...
), and before the year 1 if
astronomical year numbering Astronomical year numbering is based on AD/ CE year numbering, but follows normal decimal The decimal numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually representing ...
is used. The Gregorian calendar was designed to keep the vernal equinox on or close to March 21, so that the date of
Easter Easter,Traditional names for the feast in English are "Easter Day", as in the ''Book of Common Prayer''; "Easter Sunday", used by James Ussher''The Whole Works of the Most Rev. James Ussher, Volume 4'' and Samuel Pepys''The Diary of Samuel Pe ...

Easter
(celebrated on the Sunday after the ecclesiastical
full moon The full moon is the lunar phase s in 2022 as viewed from the Southern Hemisphere The Southern Hemisphere is the half (hemisphere Hemisphere may refer to: * A half of a sphere As half of the Earth * A hemispheres of Earth, hemisphere o ...

full moon
that falls on or after March 21) remains close to the vernal equinox. The "
Accuracy In a set of measurements, accuracy is closeness of the measurements to a specific value, while precision is the closeness of the measurements to each other. ''Accuracy'' has two definitions: # More commonly, it is a description of ''systematic er ...

Accuracy
" section of the "
Gregorian calendar The Gregorian calendar is the calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single, speci ...
" article discusses how well the Gregorian calendar achieves this design goal, and how well it approximates the
tropical year A tropical year (also known as a solar year or tropical period) is the time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past ...
.


Algorithm

The following
pseudocode In computer science, pseudocode is a plain language description of the steps in an algorithm or another system. Pseudocode often uses structural conventions of a normal programming language, but is intended for human reading rather than machine re ...
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. if (''year'' is not
divisible In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

divisible
by 4) then (it is a common year) else if (''year'' is not divisible by 100) then (it is a leap year) else if (''year'' is not divisible by 400) then (it is a common year) else (it is a leap year)
The algorithm applies to proleptic Gregorian calendar years before 1, but only if the year is expressed with
astronomical year numbering Astronomical year numbering is based on AD/ CE year numbering, but follows normal decimal The decimal numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually representing ...
instead of 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: for example, 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 The Julian calendar, proposed by Julius Caesar Gaius Julius Caesar (; 12 July 100 BC – 15 March 44 BC) was a Roman Roman or Romans usually refers to: *Rome, the capital city of Italy *Ancient Rome, Roman civilization from 8th century B ...
first used by the Romans. The
Roman calendar The Roman calendar was the calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single, specific ...
originated as a lunisolar calendar and named many of its days after the syzygies of the moon: the new moon (''Kalendae'' or calends, hence "calendar") and the full moon (''Idus'' or ides). 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, believed that the lunisolar calendar was abandoned about 450 BC by the
decemvirs The decemviri or decemvirs (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the powe ...
, who implemented the Roman Republican calendar, used until 46 BC. The days of these calendars were counted down (inclusively) to the next named day, so February 24 was ''ante diem sextum Kalendas Martias'' ("the sixth day before the calends of March") 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 (not including the starting day). The Republican calendar's intercalary month was inserted on the first or second day after the Terminalia (a. d. VII Kal. Mar., February 23). The remaining days of Februarius were dropped. This intercalary month, named Intercalaris or
MercedoniusMercedonius (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Repub ...
, 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 Gaius Julius Caesar (; 12 July 100 BC – 15 March 44 BC) was a Roman Roman or Romans most often refers to: *, the capital city of Italy *, Roman civilization from 8th century BC to 5th century AD *, the people of ancient Rome *', shortened ...

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'' (February 24) was doubled, producing ''ante diem bis sextum Kalendas Martias''. 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 Censorinus was a Roman Roman or Romans most often refers to: *, the capital city of Italy *, Roman civilization from 8th century BC to 5th century AD *, the people of ancient Rome *', shortened to ''Romans'', a letter in the New Testament of ...

Censorinus
wrote, the intercalary day was followed by the last five days of February, a. d. VI, V, IV, III and pridie Kal. Mart. (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 Macrobius Ambrosius Theodosius, usually referred to as Macrobius (fl. AD 400), was a Roman provincial who lived during the early fifth century, during Late Antiquity Late antiquity is a periodization Periodization is the process or study ...

Macrobius
about 430,
Bede Bede ( ; ang, Bǣda , ; 672/326 May 735), also known as Saint Bede, The Venerable Bede, and Bede the Venerable ( la, Beda Venerabilis), was an English Benedictine The Benedictines, officially the Order of Saint Benedict ( la, Ordo Sa ...

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. Until 1970, the
Roman Catholic Church The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptised Baptism (from the Greek language, Greek noun βάπτισμα ''báptisma'') is a Christians, Christian ...

Roman Catholic Church
always celebrated the feast of
Saint Matthias Matthias (Koine Greek: Μαθθίας, ''Maththías'' , from Biblical Hebrew, Hebrew מַתִּתְיָהוּ ''Mattiṯyāhū''; cop, ⲙⲁⲑⲓⲁⲥ; died c. AD 80) was, according to the Acts of the Apostles (written c. AD 80–90), chosen ...
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 A vigil, from the Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to be in ...

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 Pope Alexander III (c. 1100/1105 – 30 August 1181), born Roland ( it, Rolando), was head of the Catholic Church The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion bap ...

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 (Bengali, Indian and Thai)

The Revised
Bengali Calendar The Bengali Calendar or Bangla Calendar ( bn, বঙ্গাব্দ , , Baṅgābda) is a luni-solar calendar A lunisolar calendar is a calendar in many culture Culture () is an umbrella term which encompasses the social behavior and Nor ...
of Bangladesh and the
Indian National Calendar The Indian national calendar, sometimes called the Saka calendar, is used, alongside the Gregorian calendar, by ''The Gazette of India'', in news broadcasts by All India Radio and in calendars and communications issued by the Government of India. ...

Indian National Calendar
organise their leap years so that every leap day is close to February 29 in the Gregorian calendar and vice versa. This makes it easy to convert dates to or from Gregorian. The
Thai solar calendar The Thai solar calendar ( th, ปฏิทินสุริยคติ, , "solar calendar") was adopted by King Chulalongkorn Chulalongkorn ( th, จุฬาลงกรณ์, 20 September 1853 – 23 October 1910) was the fifth monarc ...
uses the Buddhist Era (BE) but has been synchronized with the Gregorian since 1941.


Julian, Coptic and Ethiopian calendars

The
Julian calendar The Julian calendar, proposed by Julius Caesar Gaius Julius Caesar (; 12 July 100 BC – 15 March 44 BC) was a Roman Roman or Romans usually refers to: *Rome, the capital city of Italy *Ancient Rome, Roman civilization from 8th century B ...
was instituted in 45 BC at the order of
Julius Caesar Gaius Julius Caesar (; 12 July 100 BC – 15 March 44 BC) was a Roman Roman or Romans most often refers to: *, the capital city of Italy *, Roman civilization from 8th century BC to 5th century AD *, the people of ancient Rome *', shortened ...

Julius Caesar
, and the original intent was to make every fourth year a leap year, but this was not carried out correctly.
Augustus Caesar Augustus (23 September 63 BC19 August AD 14) was the first Roman emperor The Roman emperor was the ruler of the Roman Empire during the imperial period (starting in 27 BC). The emperors used a variety of different titles through ...

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 (although the AD year numbering system was not introduced until AD 525). The
Coptic calendar The Coptic calendar, also called the Alexandrian calendar, is a liturgical calendar The liturgical year, also known as the church year or Christian year, as well as the kalendar, consists of the cycle of liturgy, liturgical seasons in Christ ...
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 The Revised Julian calendar, also known as the Milanković calendar, or less formally new calendar, is a calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months an ...
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 The traditional Chinese calendar (officially known as the Agricultural Calendar [], Former Calendar [], Traditional Calendar [] or Yin Calendar []), is a lunisolar calendar which reckons years, months and days according to astronomical pheno ...
is lunisolar calendar, 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 A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere In astronomy and navigation, the celestial sphere is an abstraction, abstr ...

solstice
. The intercalary month takes the same number as the preceding month; for example, if it follows the second month (二月) then it is simply called "leap second month" i.e. .


Hebrew calendar

The Hebrew calendar is lunisolar with an
embolismic month Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendar A lunisolar calendar is a calendar in many culture Cul ...
. This extra month is called ''Adar Alef'' ( first Adar) and is added before ''
Adar Adar ( he, אֲדָר ; from Akkadian language, Akkadian ''adaru'') is the sixth month of the civil year and the twelfth month of the ecclesiastical year on the Hebrew calendar, roughly corresponding to the month of March in the Gregorian calend ...
'', which then becomes ''Adar Bet'' ( second Adar). According to the
Metonic cycle For example, by the 19-year Metonic cycle, the full moon repeats on or near Christmas day between 1711 and 2300. A small horizontal libration is visible comparing their appearances. A red color shows full moons that are also lunar eclipses. 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
Passover Passover, also called Pesach (; he, פֶּסַח '), is a major Jewish holiday Jewish holidays, also known as Jewish festivals or ''Yamim Tovim'' ( he, ימים טובים, , Good Days, or singular , in transliterated Translitera ...
() is always in the spring as required by the
Torah The Torah (; he, תּוֹרָה, "Instruction", "Teaching" or "Law") includes the first five books of the Hebrew Bible The Hebrew Bible or Tanakh (; Hebrew: , or ), is the Biblical canon, canonical collection of Hebrew language, Heb ...

Torah
(Pentateuch) 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 Abrahamic religions The Abrahamic religions, also referred to collectively as the world of Abrahamism and Semitic religions, are a group of -originated s that claim descent from the of the ancient and the worship of the . The Abrahamic ...

Sabbath
. In particular, the first day of the Hebrew year can never be Sunday, Wednesday or Friday. This rule is known in Hebrew as "" (), i.e., "Rosh a-Shanah, first day of the yearis not Sunday, Wednesday or Friday" (as the Hebrew word is written by three
Hebrew letters The Hebrew alphabet ( he, אָלֶף־בֵּית עִבְרִי, ), known variously by scholars as the Ktav Ashuri Ktav Ashuri ( he, כְּתָב אַשּׁוּרִי, ' "Assyrian script"; also Ashurit) is the traditional Hebrew language ...

Hebrew letters
signifying Sunday, Wednesday and Friday). Accordingly, the first day of Passover is never Monday, Wednesday or Friday. This rule is known in Hebrew as "" (), which has a double meaning — "Passover is not a legend", but also "Passover is not Monday, Wednesday or Friday" (as the Hebrew word is written by three Hebrew letters signifying Monday, Wednesday and Friday). One reason for this rule is that
Yom Kippur Yom Kippur (; he, יוֹם כִּיפּוּר, Yōm Kīpūr, , ; plural , ) is the holiest day of the year in Judaism Judaism is an Abrahamic The Abrahamic religions, also referred to collectively as the world of Abrahamism and Semi ...
, 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. A second reason is that
Hoshana Rabbah Hoshana Rabbah ( arc, הוֹשַׁעְנָא רַבָּא, , Great Hoshana/Supplication) is the seventh day of the Jewish holiday of Sukkot, the 21st day of the month of Tishrei. This day is marked by a special synagogue service, the Hoshana R ...
, 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 (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. Years consisting of 12 months have between 353 and 355 days. In a ("in order") 354-day year, months have alternating 30 and 29 day lengths. In a ("lacking") year, the month of
Kislev Kislev or Chislev (: כִּסְלֵו, ''Kīslev'' ''Kīslēw''), also 'Chisleu' in the King James (authorized English) Bible, is the third month of the civil year and the ninth month of the ecclesiastical year on the . In the its name was A ...
is reduced to 29 days. In a ("filled") year, the month of
Marcheshvan Marcheshvan ( he, מַרְחֶשְׁוָן, Hebrew language#Modern Hebrew, Standard , Tiberian vocalization, Tiberian , Yemenite Hebrew, Yemenite ; from Akkadian language, Akkadian , literally, 'eighth month'), sometimes shortened to Cheshvan (, ...
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 The Hijri calendar ( ar, ٱلتَّقْوِيم ٱلْهِجْرِيّ '), also known as the Lunar Hijri calendar and (in English) as the Islamic, Muslim or Arabic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 o ...
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 The Tabular Islamic calendar (an example is the Fatimid or Misri calendar) is a rule-based variation of the Islamic calendar. It has the same numbering of years and months, but the months are determined by arithmetical rules rather than by obser ...
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 al-Hijjah Dhu al-Hijjah ( ar, ذُو ٱلْحِجَّة, ', ), also spelled Zu al-Hijjah, is the twelfth and final month in the Islamic calendar. It is a very sacred month in the Islamic calendar, one in which the ''Hajj, Ḥajj'' (Pilgrimage) takes place ...
, which is also the month of the
Hajj The Hajj (; ar, حَجّ ' "wikt:pilgrimage, ''pilgrimage''"; sometimes also spelled Hadj, Hadji or Haj in English) is an annual Islamic pilgrimage to Mecca, Saudi Arabia, the Holiest sites in Islam, holiest city for Muslims. Hajj is a Far ...
.


Baháʼí calendar

The Baháʼí calendar is a solar calendar composed of 19 months of 19 days each (361 days). Years begin at Naw-Rúz, on the vernal equinox, on or about March 21. A period of "Intercalary Days", called Ayyam-i-Ha, is 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
Solar Hijri calendar The Solar Hijri calendar ( fa, گاه‌شماری هجری خورشیدی, gāhshomāri-ye hejri-ye khorshidi; ps, لمريز لېږدیز کلیز, lamrez legdez kalhandara) is a solar calendar and one of the various ancient Iranian calendars. ...
is the modern Iranian calendar that is also used in Afghanistan. It 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. 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. The Hijri-Shamsi calendar, also adopted by the
Ahmadiyya Ahmadiyya (, ), officially the Ahmadiyya Muslim Community or the Ahmadiyya Muslim Jama'at ( ar, الجماعة الإسلامية الأحمدية, al-Jamāʿah al-Islāmīyah al-Aḥmadīyah; ur, , translit=Jamā'at Aḥmadiyyah Muslimah) ...

Ahmadiyya
Community, is based on solar calculations and is similar to the Gregorian calendar in its structure with the exception that its
epoch In chronology 222px, Joseph Scaliger's ''De emendatione temporum'' (1583) began the modern science of chronology Chronology (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-E ...
is the Hijra.


Folk traditions

In Ireland and Britain, it is a
tradition A tradition is a belief A belief is an attitude Attitude may refer to: Philosophy and psychology * Attitude (psychology) In psychology Psychology is the science of mind and behavior. Psychology includes the study of conscious ...

tradition
that women may only in leap years. While it has been claimed that the tradition was initiated by
Saint Patrick Saint Patrick ( la, Patricius; ga, Pádraig ; cy, Padrig) was a fifth-century Romano-British Christian missionary A missionary is a member of a Religious denomination, religious group sent into an area to promote their faith or provide ...
or
Brigid of Kildare Saint Brigid of Kildare or Brigid of Ireland ( ga, Naomh Bríd; la, Brigida; 525) is one of Ireland's patron saint A patron saint, patroness saint, patron hallow or heavenly protector is a saint who in Catholic Church, Catholicism, Angli ...
in 5th century Ireland, this is dubious, as the tradition has not been attested before the 19th century. Supposedly, a 1288 law by Queen (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. 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. 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 A petticoat or underskirt is an article of clothing Clothing (also known as clothes, apparel, and attire) are items worn on the body. Typically, clothing is made of fabrics or textile A textile is a flexible material made by c ...
— 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 ''La Bougie du Sapeur'' () is a French French (french: français(e), link=no) may refer to: * Something of, from, or related to France France (), officially the French Republic (french: link=no, République française), is a country prima ...
'' 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. File:PostcardLeapYearBeCarefulClara1908.jpg, Woman capturing man with butterfly-net File:PostcardLeapYearMaidensAre1908.jpg, Women anxiously awaiting January 1 File:PostcardTheMaidensVowIn1908.jpg, Histrionically preparing


Birthdays

A person born on February 29 may be called a "leapling" or a "leaper". In common years, they usually celebrate their
birthday A birthday is the anniversary An anniversary is the date on which an event took place or an institution was founded in a previous year, and may also refer to the commemoration or celebration of that event. For example, the first event ...

birthday
s 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 Gilbert and Sullivan refers to the Victorian-era In the history of the United Kingdom The history of the United Kingdom began in the early eighteenth century with the Treaty of Union and Acts of Union. The core of the United Ki ...
's 1879
comic opera Comic opera, sometimes known as light opera, is a sung dramatic work of a light or comic nature, usually with a happy ending and often including spoken dialogue. Forms of comic opera Opera is a form of theatre Theatre or theater i ...
''
The Pirates of Penzance ''The Pirates of Penzance; or, The Slave of Duty'' is a comic opera in two acts, with music by Arthur Sullivan and libretto by W. S. Gilbert, W. S. Gilbert. The opera's official premiere was at the Fifth Avenue Theatre in New York Cit ...
'', Frederic the pirate apprentice discovers that he is bound to serve the pirates until his 21st ''birthday'' (that is, when he turns 88 years old, since 1900 was not a leap year) rather than until his 21st ''year''. For legal purposes, legal birthdays depend on how local laws count time intervals.


Taiwan

The Civil Code of the
Taiwan Taiwan, officially the Republic of China (ROC), is a country in East Asia East Asia is the eastern region of Asia Asia () is Earth's largest and most populous continent, located primarily in the Eastern Hemisphere, Eastern and N ...

Taiwan
since October 10, 1929, implies that the legal birthday of a leapling is February 28 in common years:


Hong Kong

Since 1990 non-retroactively,
Hong Kong Hong Kong (; , ), officially the Hong Kong Special Administrative Region of the People's Republic of China (HKSAR), is a city A city is a large human settlement.Goodall, B. (1987) ''The Penguin Dictionary of Human Geography''. London: Pe ...

Hong Kong
considers the legal birthday of a leapling March 1 in common years: (Enacted in 1990).


See also

*
Century leap year A century leap year is a leap year in the Gregorian calendar that is divisible by 400 without a remainder. Like all leap years, it has an extra day in February for a total of 366 days instead of 365. In the obsolete Julian Calendar, all years that ...
*
Calendar reform Calendar reform or calendrical reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design. Principles The prime objective of a calendar is to unambiguou ...
includes proposals that have not (yet) been adopted. *
Leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise solar tim ...

Leap second
*
Leap week calendar A leap week calendar is a calendar system with a whole number of weeks in a year, and with every year starting on the same weekday. Most leap week calendars are proposed calendar reform, reforms to the civil calendar, in order to achieve a perenni ...
*
Leap year bug The leap year problem (also known as the leap year bug or the leap day bug) is a problem for both digital (computer-related) and non-digital documentation and data storage situations which results from the wrong calculation of which years are leap y ...
*
Sansculottides The Sansculottides (; also Epagomènes; french: Sans-culottides, Sanculottides, jours complémentaires, jours épagomènes) are holidays following the last month of the year on the French Republican Calendar The French Republican calendar (fren ...
*
Zeller's congruenceZeller's congruence is an algorithm of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers ''a'' and ''b'' in locations named A and B. The algorithm proceeds by successive subtractions in two loops ...


Notes


References


External links

*
Famous Leapers

Leap Day Campaign: Galileo Day

History Behind Leap Year
National Geographic Society The National Geographic Society (NGS), headquartered in Washington, D.C., United States, is one of the largest non-profit scientific and educational organizations in the world. Founded in 1888, its interests include geography, archaeology, and ...
{{DEFAULTSORT:Leap Year Calendars Units of time Articles with example pseudocode Types of year