Leap year
Encyclopedia
A leap year is a year containing one extra day (or, in the case of lunisolar calendar
s, a month) in order to keep the calendar year
synchronized with the astronomical or seasonal year
. Because seasons and astronomical events do not repeat in a whole number
of days, a calendar that had the same number of days in each year would, over time, drift with respect to the event it was supposed to track. By occasionally 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
(a common solar calendar), February in a leap year has 29 days instead of the usual 28, so the year lasts 366 days instead of the usual 365. Similarly, in the Hebrew calendar
(a lunisolar calendar), 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 too rapidly.
, the current standard calendar in most of the world, most years that are evenly divisible by 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.
Some exceptions to this rule are required since the duration of a solar year is slightly less than 365.25 days. Years that are evenly divisible by 100 are not leap years, unless they are also evenly divisible by 400, in which case they are leap years. For example, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. Similarly, 2100, 2200, 2300, 2500, 2600, 2700, 2900 and 3000 will not be leap years, but 2400 and 2800 will be. Therefore, in a duration of two millennia, there will be 485 leap years. By this rule, the average number of days per year will be 365 + 1/4 − 1/100 + 1/400 = 365.2425, which is 365 days, 5 hours, 49 minutes, and 12 seconds. 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 correct with respect to the vernal equinox. The vernal equinox year is about 365.242374 days long (and increasing).
The marginal difference of 0.000125 days between the Gregorian calendar average year and the actual year means that, in 8,000 years, the calendar will be about one day behind where it is now. But in 8,000 years, the length of the vernal equinox year will have changed by an amount that cannot be accurately predicted (see below ). Therefore, the current Gregorian calendar suffices for practical purposes, and the correction suggested by John Herschel
of making 4000 a non-leap year will probably not be necessary.
to determine whether a year is a leap year or not in either the Gregorian calendar since 1582 or in the proleptic Gregorian calendar
before 1582:
if year modulo
4 is 0
then
if year modulo 100 is 0
then
if year modulo 400 is 0
then
is_leap_year
else
not_leap_year
else is_leap_year
else not_leap_year
See Microsoft Support for further explanation.
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 (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 nundinae or Roman market week of nine days before the ides, inclusively counting the ides as the first of those nine 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 (inclusively) to the next named day, so February 24 was ante diem sextum Kalendas Martii ("the sixth day before the calends of March") often abbreviated a. d. VI Kal. Mar. 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 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 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 common practice by 238, when Censorinus
wrote, was that the intercalary day was followed by the last five days of February, a. d. VI, V, IV, III and pridie Kal. Mar. (which would be those days numbered 24, 25, 26, 27, and 28 from the beginning of February in a common year), i.e. the intercalated day was the first half of the doubled day. 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.
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.
adds an extra day to February in years evenly divisible by four.
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 vernal equinox year. This means that the vernal equinox moves a day earlier in the calendar about every 131 years.
adds an extra day to February in years divisible by four, except for years divisible by 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.
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 complicated 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 (二月) then it is simply called "leap second month" .
is also 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 relating to Pesah.
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" (לא אד"ו ראש), i.e. "Rosh [ha-Shanah, first day of the year] is not Sunday, Wednesday or Friday" (as the Hebrew word adu is written by three Hebrew letters
signifying Sunday, Wednesday and Friday). Accordingly, the first day of Pesah (Passover) is never Monday, Wednesday or Friday. This rule is known in Hebrew as "lo badu Pesah" (לא בד"ו פסח), which has a double meaning — "Pesah is not a legend", but also "Pesah is not Monday, Wednesday or Friday" (as the Hebrew word badu is written by three Hebrew letters signifying Monday, Wednesday and 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
(which is Saturday), i.e. it must never fall on Friday or Sunday, in order not to have two adjacent Sabbath days. (Ironically, if the belief that man was created on Rosh Hashanah and on Friday are both correct, then the Yom Kippur of that year would have been on a Sunday.) However, Yom Kippur can still be on Saturday.
Years consisting of 12 months have between 353 and 355 days. In a k'sidra ("in order") 354-day year, months have alternating 30 and 29 day lengths. In a chaser ("lacking") year, the month of Kislev
is reduced to 29 days. In a malei ("filled") year, the month of 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.
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.
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
. This makes it easy to convert dates to or from Gregorian.
The Bahá'í calendar
is structured such that the leap day always falls within Ayyám-i-Há
, a period of four or five days corresponding to Gregorian February 26 – March 1. Because of this, Baha'i dates consistently line up with exactly one Gregorian date.
The Thai solar calendar
uses the Buddhist Era (BE), but has been synchronized with the Gregorian since AD 1941.
, 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 calendar
s 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.
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. 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.
that women may propose marriage
only on 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
(then age five and living in Norway), required that fines be levied if a marriage proposal was refused by the man; compensation ranged from a kiss to £1 to a silk gown, in order to soften the blow. Because men felt that put them at too great a risk, the tradition was in some places 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—fair warning, if you will."
In Denmark
, the tradition is that women may propose on the bissextile leap day, February 24, and that refusal must be compensated with 12 pairs of gloves.
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.
s on February 28 or March 1. 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 rather than until his 21st year.
For legal purposes, legal birthdays depend on how local laws count time intervals.
since 10 October 1929 implies that the legal birthday of a leapling is February 28 in common years:
Lunisolar calendar
A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will...
s, a month) in order to keep the calendar year
Calendar year
Generally speaking, a calendar year begins on the New Year's Day of the given calendar system and ends on the day before the following New Year's Day. By convention, a calendar year consists of a natural number of days. To reconcile the calendar year with an astronomical cycle , certain years...
synchronized with the astronomical or seasonal year
Seasonal year
The seasonal year is the time between successive recurrences of a seasonal event such as the flooding of a river, the migration of a species of bird, or the flowering of a species of plant....
. Because seasons and astronomical events do not repeat in a whole number
Whole number
Whole number is a term with inconsistent definitions by different authors. All distinguish whole numbers from fractions and numbers with fractional parts.Whole numbers may refer to:*natural numbers in sense — the positive integers...
of days, a calendar that had the same number of days in each year would, over time, drift with respect to the event it was supposed to track. By occasionally inserting (or intercalating
Intercalation
Intercalation 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 calendars may require intercalations of both days and months.- Solar calendars :...
) 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
Common year
A common year is a common type of calendar year. It has exactly 365 days and so is not a leap year. More generally, it is a calendar year without intercalation....
.
For example, in the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
(a common solar calendar), February in a leap year has 29 days instead of the usual 28, so the year lasts 366 days instead of the usual 365. Similarly, in the Hebrew calendar
Hebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
(a lunisolar calendar), 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 too rapidly.
Gregorian calendar
In the Gregorian calendarGregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
, the current standard calendar in most of the world, most years that are evenly divisible by 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.
Some exceptions to this rule are required since the duration of a solar year is slightly less than 365.25 days. Years that are evenly divisible by 100 are not leap years, unless they are also evenly divisible by 400, in which case they are leap years. For example, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. Similarly, 2100, 2200, 2300, 2500, 2600, 2700, 2900 and 3000 will not be leap years, but 2400 and 2800 will be. Therefore, in a duration of two millennia, there will be 485 leap years. By this rule, the average number of days per year will be 365 + 1/4 − 1/100 + 1/400 = 365.2425, which is 365 days, 5 hours, 49 minutes, and 12 seconds. The Gregorian calendar was designed to keep the vernal equinox on or close to March 21, so that the date of Easter
Easter
Easter is the central feast in the Christian liturgical year. According to the Canonical gospels, Jesus rose from the dead on the third day after his crucifixion. His resurrection is celebrated on Easter Day or Easter Sunday...
(celebrated on the Sunday after the 14th day of the Moon—i.e. a full moon
Full moon
Full moon lunar phase that occurs when the Moon is on the opposite side of the Earth from the Sun. More precisely, a full moon occurs when the geocentric apparent longitudes of the Sun and Moon differ by 180 degrees; the Moon is then in opposition with the Sun.Lunar eclipses can only occur at...
—that falls on or after March 21) remains correct with respect to the vernal equinox. The vernal equinox year is about 365.242374 days long (and increasing).
The marginal difference of 0.000125 days between the Gregorian calendar average year and the actual year means that, in 8,000 years, the calendar will be about one day behind where it is now. But in 8,000 years, the length of the vernal equinox year will have changed by an amount that cannot be accurately predicted (see below ). Therefore, the current Gregorian calendar suffices for practical purposes, and the correction suggested by John Herschel
John Herschel
Sir John Frederick William Herschel, 1st Baronet KH, FRS ,was an English mathematician, astronomer, chemist, and experimental photographer/inventor, who in some years also did valuable botanical work...
of making 4000 a non-leap year will probably not be necessary.
 This graph shows the variations in date and time of the June Solstice Solstice A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes... due to unequally spaced 'leap day' rules. See Iranian calendar to contrast with a calendar based on 8 leap days every 33 years. |
Algorithm
PseudocodePseudocode
In computer science and numerical computation, pseudocode is a compact and informal high-level description of the operating principle of a computer program or other algorithm. It uses the structural conventions of a programming language, but is intended for human reading rather than machine reading...
to determine whether a year is a leap year or not in either the Gregorian calendar since 1582 or in the proleptic Gregorian calendar
Proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582.-Usage:...
before 1582:
if year modulo
Modulo operation
In computing, the modulo operation finds the remainder of division of one number by another.Given two positive numbers, and , a modulo n can be thought of as the remainder, on division of a by n...
4 is 0
then
if year modulo 100 is 0
then
if year modulo 400 is 0
then
is_leap_year
else
not_leap_year
else is_leap_year
else not_leap_year
See Microsoft Support for further explanation.
Leap day
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 Gregorian calendar is a modification of the Julian calendar
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
first used by the Romans. The Roman calendar
Roman calendar
The Roman calendar changed its form several times in the time between the founding of Rome and the fall of the Roman Empire. This article generally discusses the early Roman or pre-Julian calendars...
originated as a lunisolar calendar
Lunisolar calendar
A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will...
and named many of its days after the syzygies
Syzygy (astronomy)
In astronomy, a syzygy is a straight line configuration of three celestial bodies in a gravitational system. The word is usually used in reference to the Sun, the Earth and either the Moon or a planet, where the latter is in conjunction or opposition. Solar and lunar eclipses occur at times of...
of the moon: the new moon (Kalendae or calends, hence "calendar") and the full moon
Full moon
Full moon lunar phase that occurs when the Moon is on the opposite side of the Earth from the Sun. More precisely, a full moon occurs when the geocentric apparent longitudes of the Sun and Moon differ by 180 degrees; the Moon is then in opposition with the Sun.Lunar eclipses can only occur at...
(Idus or ides). The Nonae or nones was not the first quarter moon
Lunar phase
A lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon, and Sun...
but was exactly one nundinae or Roman market week of nine days before the ides, inclusively counting the ides as the first of those nine days. In 1825, Ideler
Christian Ludwig Ideler
Christian Ludwig Ideler , German chronologist and astronomer, was born near Perleberg on the 21st of September 1766.-Life:...
believed that the lunisolar calendar was abandoned about 450 BC by the decemvirs, who implemented the Roman Republican calendar
Roman calendar
The Roman calendar changed its form several times in the time between the founding of Rome and the fall of the Roman Empire. This article generally discusses the early Roman or pre-Julian calendars...
, 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 Martii ("the sixth day before the calends of March") often abbreviated a. d. VI Kal. Mar. The Romans
Ancient Rome
Ancient Rome was a thriving civilization that grew on the Italian Peninsula as early as the 8th century BC. Located along the Mediterranean Sea and centered on the city of Rome, it expanded to one of the largest empires in the ancient world....
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
Terminus (mythology)
In Roman religion, Terminus was the god who protected boundary markers; his name was the Latin word for such a marker. Sacrifices were performed to sanctify each boundary stone, and landowners celebrated a festival called the "Terminalia" in Terminus' honor each year on February 23...
(a. d. VII Kal. Mar., February 23). The remaining days of Februarius were dropped. This intercalary month, named Intercalaris or Mercedonius
Mercedonius
Mercedonius, also known as Intercalaris, was the intercalary month added in leap years of the Roman calendar. The resulting year was either 377 or 378 days long. The exact mechanism by which this was done is not clearly specified in ancient sources. Modern scholarship holds that Februarius was...
, 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
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
, which was developed in 46 BC by Julius Caesar
Julius Caesar
Gaius Julius Caesar was a Roman general and statesman and a distinguished writer of Latin prose. He played a critical role in the gradual transformation of the Roman Republic into the Roman Empire....
, 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 common practice by 238, when Censorinus
Censorinus
Censorinus, Roman grammarian and miscellaneous writer, flourished during the 3rd century AD.He was the author of a lost work De Accentibus and of an extant treatise De Die Natali, written in 238, and dedicated to his patron Quintus Caerellius as a birthday gift...
wrote, was that the intercalary day was followed by the last five days of February, a. d. VI, V, IV, III and pridie Kal. Mar. (which would be those days numbered 24, 25, 26, 27, and 28 from the beginning of February in a common year), i.e. the intercalated day was the first half of the doubled day. All later writers, including Macrobius about 430, Bede
Bede
Bede , also referred to as Saint Bede or the Venerable Bede , was a monk at the Northumbrian monastery of Saint Peter at Monkwearmouth, today part of Sunderland, England, and of its companion monastery, Saint Paul's, in modern Jarrow , both in the Kingdom of Northumbria...
in 725, and other medieval computists
Computus
Computus is the calculation of the date of Easter in the Christian calendar. The name has been used for this procedure since the early Middle Ages, as it was one of the most important computations of the age....
(calculators of Easter
Easter
Easter is the central feast in the Christian liturgical year. According to the Canonical gospels, Jesus rose from the dead on the third day after his crucifixion. His resurrection is celebrated on Easter Day or Easter Sunday...
), continued to state that the bissextum (bissextile day) occurred before the last five days of February.
Until 1970, the Roman Catholic Church
Roman Catholic Church
The Catholic Church, also known as the Roman Catholic Church, is the world's largest Christian church, with over a billion members. Led by the Pope, it defines its mission as spreading the gospel of Jesus Christ, administering the sacraments and exercising charity...
always celebrated the feast of Saint Matthias
Saint Matthias
Matthias , according to the Acts of the Apostles, was the apostle chosen by the remaining eleven apostles to replace Judas Iscariot following Judas' betrayal of Jesus and his suicide.-Biography:...
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
Vigil
A vigil is a period of purposeful sleeplessness, an occasion for devotional watching, or an observance...
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.
Julian, Coptic and Ethiopian calendars
The Julian calendarJulian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
adds an extra day to February in years evenly divisible by four.
The Coptic calendar
Coptic calendar
The Coptic calendar, also called the Alexandrian calendar, is used by the Coptic Orthodox Church and still used in Egypt. This calendar is based on the ancient Egyptian calendar...
and Ethiopian calendar
Ethiopian calendar
The Ethiopian calendar , also called the Ge'ez calendar, is the principal calendar used in Ethiopia and also serves as the liturgical calendar for Christians in Eritrea belonging to the Eritrean Orthodox Church, Eastern Catholic Church and Lutheran Evangelical Church of Eritrea...
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 vernal equinox year. This means that the vernal equinox moves a day earlier in the calendar about every 131 years.
Revised Julian calendar
The Revised Julian calendarRevised Julian calendar
The Revised Julian calendar, also known as the Rectified Julian calendar, or, less formally, New calendar, is a calendar, originated in 1923, which effectively discontinued the 340 years of divergence between the naming of dates sanctioned by those Eastern Orthodox churches adopting it and the...
adds an extra day to February in years divisible by four, except for years divisible by 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
Tropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
, 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
The Chinese calendarChinese calendar
The Chinese calendar is a lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. It is not exclusive to China, but followed by many other Asian cultures as well...
is lunisolar
Lunisolar calendar
A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will...
, 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 complicated rule, which ensures that month 11 is always the month that contains the northern winter solstice
Solstice
A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes...
. 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" .
Hebrew calendar
The Hebrew calendarHebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
is also lunisolar with an embolismic month. This extra month is called Adar Alef (first Adar) and is added before Adar
Adar
Adar is the sixth month of the civil year and the twelfth month of the ecclesiastical year on the Hebrew calendar. It is a winter month of 29 days...
, which then becomes Adar Bet (second Adar). According to the Metonic cycle
Metonic cycle
In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...
, 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
Torah
Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five books of the bible—Genesis , Exodus , Leviticus , Numbers and Deuteronomy Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five...
(Pentateuch) in many verses relating to Pesah.
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
Week-day names
The names of the days of the week from the Roman period have been both named after the seven planets of classical astronomy and numbered, beginning with Monday. In Slavic languages, a numbering system was adopted, but beginning with Monday. There was an even older tradition of names in Ancient...
from 28 to 14, and regulate the location of certain religious holidays in relation to the Sabbath
Shabbat
Shabbat is the seventh day of the Jewish week and a day of rest in Judaism. Shabbat is observed from a few minutes before sunset on Friday evening until a few minutes after when one would expect to be able to see three stars in the sky on Saturday night. The exact times, therefore, differ from...
. 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" (לא אד"ו ראש), i.e. "Rosh [ha-Shanah, first day of the year] is not Sunday, Wednesday or Friday" (as the Hebrew word adu is written by three Hebrew letters
Hebrew alphabet
The Hebrew alphabet , known variously by scholars as the Jewish script, square script, block script, or more historically, the Assyrian script, is used in the writing of the Hebrew language, as well as other Jewish languages, most notably Yiddish, Ladino, and Judeo-Arabic. There have been two...
signifying Sunday, Wednesday and Friday). Accordingly, the first day of Pesah (Passover) is never Monday, Wednesday or Friday. This rule is known in Hebrew as "lo badu Pesah" (לא בד"ו פסח), which has a double meaning — "Pesah is not a legend", but also "Pesah is not Monday, Wednesday or Friday" (as the Hebrew word badu is written by three Hebrew letters signifying Monday, Wednesday and Friday).
One reason for this rule is that Yom Kippur
Yom Kippur
Yom Kippur , also known as Day of Atonement, is the holiest and most solemn day of the year for the Jews. Its central themes are atonement and repentance. Jews traditionally observe this holy day with a 25-hour period of fasting and intensive prayer, often spending most of the day in synagogue...
, the holiest day in the Hebrew calendar and the tenth day of the Hebrew year, now must never be adjacent to the weekly Sabbath
Shabbat
Shabbat is the seventh day of the Jewish week and a day of rest in Judaism. Shabbat is observed from a few minutes before sunset on Friday evening until a few minutes after when one would expect to be able to see three stars in the sky on Saturday night. The exact times, therefore, differ from...
(which is Saturday), i.e. it must never fall on Friday or Sunday, in order not to have two adjacent Sabbath days. (Ironically, if the belief that man was created on Rosh Hashanah and on Friday are both correct, then the Yom Kippur of that year would have been on a Sunday.) However, Yom Kippur can still be on Saturday.
Years consisting of 12 months have between 353 and 355 days. In a k'sidra ("in order") 354-day year, months have alternating 30 and 29 day lengths. In a chaser ("lacking") year, the month of Kislev
Kislev
Kislev Kislev Tiberian ; also Chislev is the third month of the civil year and the ninth month of the ecclesiastical year on the Hebrew calendar....
is reduced to 29 days. In a malei ("filled") year, the month of Cheshvan
Cheshvan
Marcheshvan , sometimes shortened to Cheshvan , is the second month of the civil year and the eighth month of the ecclesiastical year on the Hebrew...
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 calendarIslamic calendar
The Hijri calendar , also known as the Muslim calendar or Islamic calendar , is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to date events in many Muslim countries , and used by Muslims everywhere to determine the proper day on which to celebrate Islamic...
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
Tabular Islamic calendar
The Tabular Islamic 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 arithmetic rules rather than by observation or astronomical calculations...
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.
Calendars with leap years synchronized with Gregorian
The Indian National CalendarIndian national calendar
The Indian national calendar is the official civil calendar in use in India. It is used, alongside the Gregorian calendar, by The Gazette of India, news broadcasts by All India Radio, and calendars and communications issued by the Government of India.The term may also ambiguously refer to the...
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
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
. This makes it easy to convert dates to or from Gregorian.
The Bahá'í calendar
Bahá'í calendar
The Bahá'í calendar, also called the Badí‘ calendar , used by the Bahá'í Faith, is a solar calendar with regular years of 365 days, and leap years of 366 days. Years are composed of 19 months of 19 days each, plus an extra period of "Intercalary Days"...
is structured such that the leap day always falls within Ayyám-i-Há
Ayyám-i-Há
Ayyám-i-Há refers to a period of four or five intercalary days in the Bahá'í calendar, where Bahá'ís celebrate the Festival of Ayyám-i-Há...
, a period of four or five days corresponding to Gregorian February 26 – March 1. Because of this, Baha'i dates consistently line up with exactly one Gregorian date.
The Thai solar calendar
Thai solar calendar
The Thai solar calendar, Suriyakati was adopted by King Chulalongkorn in AD 1888 as the Siamese version of the Gregorian calendar. It is the legal calendar in Thailand, though Thai lunar calendar dates continue in use. Years are now counted in the Buddhist Era that is 543 years greater than...
uses the Buddhist Era (BE), but has been synchronized with the Gregorian since AD 1941.
Hindu calendar
In the Hindu calendarHindu calendar
The hindu calendar used in ancient times has undergone many changes in the process of regionalization, and today there are several regional Indian calendars, as well as an Indian national calendar. Nepali calendar, Bengali calendar, Malayalam calendar, Tamil calendar, Telugu calendar, Kannada...
, which is a lunisolar calendar
Lunisolar calendar
A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will...
, 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
Diwali
Diwali or DeepavaliThe name of the festival in various regional languages include:, , , , , , , , , , , , , popularly known as the "festival of lights," is a festival celebrated between mid-October and mid-December for different reasons...
festival tends to occur between October 22 and November 15. Buddhist calendar
Buddhist calendar
The Buddhist calendar is used on mainland Southeast Asia in the countries of Thailand, Cambodia, Laos, Burma and Sri Lanka in several related forms. It is a lunisolar calendar having months that are alternately 29 and 30 days, with an intercalated day and a 30-day month added at regular intervals...
s 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
Thai lunar calendar
The Thai lunar calendar , or Dai calendar , Tai calendar, is Thailand's version of the lunisolar Buddhist calendar used in the southeast Asian countries of Cambodia, Laos and Burma, for calculating lunar-regulated holy days...
, Myanmar (formerly Burma) and Sri Lanka.
The Hindu Calendar also known as Vikram Samvat is used in Nepal
Nepal
Nepal , officially the Federal Democratic Republic of Nepal, is a landlocked sovereign state located in South Asia. It is located in the Himalayas and bordered to the north by the People's Republic of China, and to the south, east, and west by the Republic of India...
as National Calendar. All the official work is done based on this calendar.
The calendar followed in some parts of South India
South India
South India is the area encompassing India's states of Andhra Pradesh, Karnataka, Kerala and Tamil Nadu as well as the union territories of Lakshadweep and Pondicherry, occupying 19.31% of India's area...
(mainly in Tamil Nadu) is solar
Solar calendar
A solar calendar is a calendar whose dates indicate the position of the earth on its revolution around the sun .-Tropical solar calendars:...
. It has a leap year every four years.
Iranian calendar
The Iranian calendarIranian calendar
The Iranian calendars or sometimes called Persian calendars are a succession of calendars invented or used for over two millennia in Greater Iran...
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. The system used is more accurate and more complicated, and is based on the time of the March equinox as observed from Tehran
Tehran
Tehran , sometimes spelled Teheran, is the capital of Iran and Tehran Province. With an estimated population of 8,429,807; it is also Iran's largest urban area and city, one of the largest cities in Western Asia, and is the world's 19th largest city.In the 20th century, Tehran was subject to...
. 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.
Folk traditions
On the British isles, it is a traditionTradition
A tradition is a ritual, belief or object passed down within a society, still maintained in the present, with origins in the past. Common examples include holidays or impractical but socially meaningful clothes , but the idea has also been applied to social norms such as greetings...
that women may propose marriage
Proposal of marriage
A marriage proposal is an event where one person in a relationship asks for the other's hand in marriage. If accepted, it marks the initiation of engagement. It often has a ritual quality, sometimes involving the presentation of an engagement ring and a formalized asking of a question such as "Will...
only on leap years. While it has been claimed that the tradition was initiated by Saint Patrick
Saint Patrick
Saint Patrick was a Romano-Briton and Christian missionary, who is the most generally recognized patron saint of Ireland or the Apostle of Ireland, although Brigid of Kildare and Colmcille are also formally patron saints....
or Brigid of Kildare
Brigid of Kildare
Saint Brigit of Kildare, or Brigit of Ireland , nicknamed Mary of the Gael is one of Ireland's patron saints along with Saints Patrick and Columba...
in 5th century Ireland
Ireland
Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...
, this is dubious, as the tradition has not been attested before the 19th century. Supposedly, a 1288 law by Queen Margaret of Scotland
Margaret, Maid of Norway
Margaret , usually known as the Maid of Norway , sometimes known as Margaret of Scotland , was a Norwegian princess who was Queen of Scots from 1286 until her death...
(then age five and living in Norway), required that fines be levied if a marriage proposal was refused by the man; compensation ranged from a kiss to £1 to a silk gown, in order to soften the blow. Because men felt that put them at too great a risk, the tradition was in some places 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—fair warning, if you will."
In Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
, the tradition is that women may propose on the bissextile leap day, February 24, and that refusal must be compensated with 12 pairs of gloves.
In Finland
Finland
Finland , officially the Republic of Finland, is a Nordic country situated in the Fennoscandian region of Northern Europe. It is bordered by Sweden in the west, Norway in the north and Russia in the east, while Estonia lies to its south across the Gulf of Finland.Around 5.4 million people reside...
, the tradition is that if a man refuses a woman's proposal on leap day, he should buy her the fabrics for a skirt.
Birthdays
A person born on February 29 may be called a "leapling" or a "leaper". In common years they usually celebrate their birthdayBirthday
A birthday is a day or anniversary where a person celebrates his or her date of birth. Birthdays are celebrated in numerous cultures, often with a gift, party or rite of passage. Although the major religions celebrate the birth of their founders , Christmas – which is celebrated widely by...
s on February 28 or March 1. 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
Gilbert and Sullivan
Gilbert and Sullivan refers to the Victorian-era theatrical partnership of the librettist W. S. Gilbert and the composer Arthur Sullivan . The two men collaborated on fourteen comic operas between 1871 and 1896, of which H.M.S...
's 1879 comic opera
Comic opera
Comic opera denotes a sung dramatic work of a light or comic nature, usually with a happy ending.Forms of comic opera first developed in late 17th-century Italy. By the 1730s, a new operatic genre, opera buffa, emerged as an alternative to opera seria...
The Pirates of Penzance
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. The opera's official premiere was at the Fifth Avenue Theatre in New York City on 31 December 1879, where the show was well received by both audiences...
, 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.
Republic of China
The Civil Code of the Republic of ChinaRepublic of China
The Republic of China , commonly known as Taiwan , is a unitary sovereign state located in East Asia. Originally based in mainland China, the Republic of China currently governs the island of Taiwan , which forms over 99% of its current territory, as well as Penghu, Kinmen, Matsu and other minor...
since 10 October 1929 implies that the legal birthday of a leapling is February 28 in common years:
Hong Kong
Since 1990 non-retroactively, Hong Kong considers the legal birthday of a leapling March 1 in common years:Major events
These events are or were held every four years during leap years- UEFA European Football ChampionshipUEFA European Football ChampionshipThe UEFA European Football Championship is the main football competition of the men's national football teams governed by UEFA . Held every four years since 1960, in the even-numbered year between World Cup tournaments, it was originally called the UEFA European Nations Cup, changing to the current...
- Summer Olympic GamesSummer Olympic GamesThe Summer Olympic Games or the Games of the Olympiad are an international multi-sport event, occurring every four years, organized by the International Olympic Committee. Medals are awarded in each event, with gold medals for first place, silver for second and bronze for third, a tradition that...
except 1900 - Republic of China presidential election, 1996 in Taiwan and subsequent elections
- United States presidential electionUnited States presidential electionElections for President and Vice President of the United States are indirect elections in which voters cast ballots for a slate of electors of the U.S. Electoral College, who in turn directly elect the President and Vice President...
- Winter Olympic GamesWinter Olympic GamesThe Winter Olympic Games is a sporting event, which occurs every four years. The first celebration of the Winter Olympics was held in Chamonix, France, in 1924. The original sports were alpine and cross-country skiing, figure skating, ice hockey, Nordic combined, ski jumping and speed skating...
through 1992
See also
- Century leap yearCentury leap yearIn the Gregorian calendar, an end-of-century leap year is a year that is exactly divisible by 400 and, as with every other leap year, qualifies for the intercalation of February 29. End-of-century years that are exactly divisible by 4 but not by 400 are common years...
- Leap week calendarLeap week calendarA leap week calendar is a calendar system with a whole number of weeks every year, and with every year starting on the same weekday. Most leap week calendars are proposed reforms to the civil calendar, but some - such as the ISO week number calendar - are simply conveniences for specific...
- Leap secondLeap secondA leap second is a positive or negative one-second adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official time-of-day radio broadcasts for civil time, is maintained using extremely precise atomic clocks...
- Zeller's congruenceZeller's congruenceZeller's congruence is an algorithm devised by Christian Zeller to calculate the day of the week for any Julian or Gregorian calendar date.- Formula :For the Gregorian calendar, Zeller's congruence is...
- SansculottidesSansculottidesThe Sansculottides are holidays following the last month of the year on the French Republican Calendar which was used following the French Revolution from approximately 1793 to 1805....
- List of leap years