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 and specific day within such a system. A calendar is ...
in many
culture
Culture ( ) is a concept that encompasses the social behavior, institutions, and Social norm, norms found in human societies, as well as the knowledge, beliefs, arts, laws, Social norm, customs, capabilities, Attitude (psychology), attitudes ...
s, that combines monthly
lunar cycle
A lunar phase or Moon phase is the apparent shape of the Moon's directly sunlit portion as viewed from the Earth. Because the Moon is tidally locked with the Earth, the same hemisphere is always facing the Earth. In common usage, the four majo ...
s with the
solar year
A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronom ...
. As with all calendars which divide the year into months, there is an additional requirement that the year have a whole number of months (Moon cycles). The majority of years have twelve months but every second or third year is an
embolismic year, which adds a thirteenth
intercalary, embolismic, or leap month.
Lunisolar calendars are
lunar calendar
A lunar calendar is a calendar based on the monthly cycles of the Moon's phases ( synodic months, lunations), in contrast to solar calendars, whose annual cycles are based on the solar year, and lunisolar calendars, whose lunar months are br ...
s but, in contrast to purely lunar calendars such as the
Islamic calendar
The Hijri calendar (), also known in English as the Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to determine the proper days of Islamic holidays and rituals, such as the Ramad ...
, have additional intercalation rules that reset them periodically into a rough agreement with the solar year and thus with the seasons.
Examples
The
Chinese,
Buddhist
Buddhism, also known as Buddhadharma and Dharmavinaya, is an Indian religion and List of philosophies, philosophical tradition based on Pre-sectarian Buddhism, teachings attributed to the Buddha, a wandering teacher who lived in the 6th or ...
,
Burmese,
Assyrian,
Hebrew
Hebrew (; ''ʿÎbrit'') is a Northwest Semitic languages, Northwest Semitic language within the Afroasiatic languages, Afroasiatic language family. A regional dialect of the Canaanite languages, it was natively spoken by the Israelites and ...
,
Jain, traditional Nepali,
Hindu
Hindus (; ; also known as Sanātanīs) are people who religiously adhere to Hinduism, also known by its endonym Sanātana Dharma. Jeffery D. Long (2007), A Vision for Hinduism, IB Tauris, , pp. 35–37 Historically, the term has also be ...
,
Japanese,
Korean
Korean may refer to:
People and culture
* Koreans, people from the Korean peninsula or of Korean descent
* Korean culture
* Korean language
**Korean alphabet, known as Hangul or Korean
**Korean dialects
**See also: North–South differences in t ...
,
Mongolian,
Tibetan, and
Vietnamese
Vietnamese may refer to:
* Something of, from, or related to Vietnam, a country in Southeast Asia
* Vietnamese people, or Kinh people, a Southeast Asian ethnic group native to Vietnam
** Overseas Vietnamese, Vietnamese people living outside Vietna ...
calendars (in the
East Asian Chinese cultural sphere), plus the ancient
Hellenic,
Coligny, and
Babylonian calendar
The Babylonian calendar was a lunisolar calendar used in Mesopotamia from around the 2nd millennium BC until the Seleucid Era ( 294 BC), and it was specifically used in Babylon from the Old Babylonian Period ( 1780s BC) until the Seleucid Era. ...
s are all lunisolar. Also, some of the ancient
pre-Islamic calendars in
south Arabia
South Arabia (), or Greater Yemen, is a historical region that consists of the southern region of the Arabian Peninsula in West Asia, mainly centered in what is now the Republic of Yemen, yet it has also historically included Najran, Jazan, ...
followed a lunisolar system.
[F.C. De Blois, "TAʾRĪKH": I.1.iv. "Pre-Islamic and agricultural calendars of the Arabian peninsula", ''The Encyclopaedia of Islam'', 2nd edition, X:260.] The Chinese, Coligny and
Hebrew lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon.
Chinese lunisolar calendar

The
Chinese calendar
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
(華夏曆法) or
Chinese lunisolar calendar
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
is also called Agricultural Calendar
��曆; 农历; Nónglì; 'farming calendar' or Yin Calendar
��曆; 阴历; Yīnlì; 'yin calendar', as movements of the sun (representing
Yang) and moon (representing Yin) are the references for the Chinese lunisolar calendar calculations. The Chinese lunisolar calendar is the origin of some variant calendars adopted by other neighboring countries, such as Vietnam and Korea.
Together with astronomical, horological, and
phenological
Phenology is the study of periodic events in biological life cycles and how these are influenced by seasonal and interannual variations in climate, as well as habitat factors (such as elevation).
Examples include the date of emergence of leave ...
observations, definitions, measurements, and predictions of years, months, and days were refined. Astronomical phenomena and calculations emphasized especially the efforts to mathematically correlate the solar and lunar cycles from the perspective of the earth, which however are known to require some degree of numeric approximation or compromise.
The earliest record of the Chinese lunisolar calendar was in the
Zhou dynasty
The Zhou dynasty ( ) was a royal dynasty of China that existed for 789 years from until 256 BC, the longest span of any dynasty in Chinese history. During the Western Zhou period (771 BC), the royal house, surnamed Ji, had military ...
(1050 BC – 771 BC, around 3000 years ago. Throughout history, the Chinese lunisolar calendar had many variations and evolved with different dynasties with increasing accuracy, including the "six ancient calendars" in the
Warring States period
The Warring States period in history of China, Chinese history (221 BC) comprises the final two and a half centuries of the Zhou dynasty (256 BC), which were characterized by frequent warfare, bureaucratic and military reforms, and ...
, the Qin calendar in the
Qin dynasty
The Qin dynasty ( ) was the first Dynasties of China, imperial dynasty of China. It is named for its progenitor state of Qin, a fief of the confederal Zhou dynasty (256 BC). Beginning in 230 BC, the Qin under King Ying Zheng enga ...
, the Han calendar or the Taichu calendar in the
Han dynasty
The Han dynasty was an Dynasties of China, imperial dynasty of China (202 BC9 AD, 25–220 AD) established by Liu Bang and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–206 BC ...
and
Tang dynasty
The Tang dynasty (, ; zh, c=唐朝), or the Tang Empire, was an Dynasties of China, imperial dynasty of China that ruled from 618 to 907, with an Wu Zhou, interregnum between 690 and 705. It was preceded by the Sui dynasty and followed ...
, the Shoushi calendar in the
Yuan dynasty
The Yuan dynasty ( ; zh, c=元朝, p=Yuáncháo), officially the Great Yuan (; Mongolian language, Mongolian: , , literally 'Great Yuan State'), was a Mongol-led imperial dynasty of China and a successor state to the Mongol Empire after Div ...
, and the Daming calendar in the
Ming dynasty
The Ming dynasty, officially the Great Ming, was an Dynasties of China, imperial dynasty of China that ruled from 1368 to 1644, following the collapse of the Mongol Empire, Mongol-led Yuan dynasty. The Ming was the last imperial dynasty of ...
, etc. Starting in 1912, the western solar calendar is used together with the lunisolar calendar in China.
The most celebrated Chinese holidays, such as the
Chinese New Year
Chinese New Year, or the Spring Festival (see also #Names, § Names), is a festival that celebrates the beginning of a New Year, new year on the traditional lunisolar calendar, lunisolar Chinese calendar. It is one of the most important holi ...
(華夏新年),
Lantern Festival
The Lantern Festival ( zh, t=wikt:元宵節, 元宵節, s=wikt:元宵节, 元宵节, first=t, hp=Yuánxiāo jié), also called Shangyuan Festival ( zh, t=上元節, s=上元节, first=t, hp=Shàngyuán jié) and Cap Go Meh ( zh, t=十五暝, ...
(元宵節),
Mid-Autumn Festival
The Mid-Autumn Festival (for other names, see § Etymology) is a harvest festival celebrated in Chinese culture. It is held on the 15th day of the 8th month of the Chinese lunisolar calendar with a full moon at night, corresponding to mid- ...
(中秋節), and
Dragon Boat Festival
The Dragon Boat Festival ( zh, s=端午节, t=端午節, first=t, p=Duānwǔ jié, cy=Dyūnńgh jit) is a traditional Chinese holiday that occurs on the fifth day of the fifth month of the Chinese calendar, which corresponds to late May or earl ...
(端午節) are all based upon the
Chinese lunisolar calendar
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
. In addition, the popular
Chinese zodiac
The Chinese zodiac is a traditional classification scheme based on the Chinese calendar that assigns an animal and its reputed attributes to each year in a repeating twelve-year (or duodenary) cycle. The zodiac is very important in traditional ...
is a classification scheme based on the
Chinese calendar
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
that assigns an animal and its reputed attributes to each year in a repeating twelve-year cycle. The traditional calendar used the
sexagenary cycle-based
''ganzhi'' system's mathematically repeating cycles of
Heavenly Stems
The ten Heavenly Stems (or Celestial Stems) are a system of ordinals indigenous to China and used throughout East Asia, first attested during the Shang dynasty as the names of the ten days of the week. They were also used in Shang-era ritual ...
and
Earthly Branches
The Earthly Branches (also called the Terrestrial Branches or the 12-cycle) are a system of twelve ordered symbols used throughout East Asia. They are indigenous to China, and are themselves Chinese characters, corresponding to words with no co ...
.
Movable feasts in the Christian calendars, related to the lunar cycle
The
Gregorian calendar
The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian cale ...
(the world's most commonly used) is a solar one but the
Western Christian churches use a lunar-based algorithm to determine the
date of Easter
As a moveable feast, the date of Easter is determined in each year through a calculation known as – often simply ''Computus'' – or as paschalion particularly in the Eastern Orthodox Church. Easter is celebrated on the first Sunday after the ...
and consequent
movable feasts. Briefly, the date is determined with respect to the
ecclesiastical full moon that follows the
ecclesiastical equinox in March. (These events are almost, but not quite, the same as the actual astronomical observations.) The
Eastern Christian churches have a similar algorithm that is based on the
Julian calendar
The Julian calendar is a solar calendar of 365 days in every year with an additional leap day every fourth year (without exception). The Julian calendar is still used as a religious calendar in parts of the Eastern Orthodox Church and in parts ...
.
Reconciling lunar and solar cycles
Determining leap months
A
tropical year
A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronom ...
is approximately 365.2422
days
A day is the time period of a full rotation of the Earth with respect to the Sun. On average, this is 24 hours (86,400 seconds). As a day passes at a given location it experiences morning, afternoon, evening, and night. This daily cyc ...
long and a
synodic month
In lunar calendars, a lunar month is the time between two successive Syzygy (astronomy), syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Variations
In Shona people, S ...
is approximately 29.5306 days long, so a tropical year is approximately months long. Because 0.36826 is between and , a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years. More precisely, 0.36826 is quite close to (about 0.3684211): several lunisolar calendars have 7 leap months in every cycle of 19 years (called a '
Metonic cycle
The Metonic cycle or enneadecaeteris (from , from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise obser ...
'). The
Babylonians
Babylonia (; , ) was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Kuwait, Syria and Iran). It emerged as an Akkadian-populated but Amorite-ru ...
applied the 19-year cycle in the late sixth century BCE.
Intercalation of leap months is frequently controlled by the "
epact
The epact (, from () = added days) used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 ...
", which is the difference between the lunar and solar years (approximately 11 days). The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year. Between the last year of one cycle and the first year of the next the increment is 12 the which causes the epacts to repeat every 19 years. When the epact reaches 30 or higher, an intercalary month is added and 30 is subtracted. The Metonic cycle states that 7 of 19 years will contain an additional intercalary month and those years are numbered: 3, 6, 8, 11, 14, 17 and 19. Both the Hebrew calendar and the Julian calendar use this sequence.
The Buddhist and Hebrew calendars restrict the leap month to a single month of the year; the number of common months between leap months is, therefore, usually 36, but occasionally only 24 months. Because the Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true apparent motion of the
Sun
The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...
, their leap months do not usually occur within a couple of months of
perihelion
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.
Apsides perta ...
, when the apparent speed of the Sun along the
ecliptic
The ecliptic or ecliptic plane is the orbital plane of Earth's orbit, Earth around the Sun. It was a central concept in a number of ancient sciences, providing the framework for key measurements in astronomy, astrology and calendar-making.
Fr ...
is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs, while reducing the number to about 29 months when only a common singleton occurs.
With uncounted time
An alternative way of dealing with the fact that a solar year does not contain an integer number of
lunar month
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Variations
In Shona, Middle Eastern, and Euro ...
s is by including uncounted time in a period of the year that is not assigned to a named month. Some
Coast Salish peoples
The Coast Salish peoples are a group of ethnically and linguistically related Indigenous peoples of the Pacific Northwest Coast, living in the Canadian province of British Columbia and the U.S. states of Washington and Oregon. They speak on ...
used a calendar of this kind. For instance, the
Chehalis began their count of lunar months from the arrival of spawning
chinook salmon
The Chinook salmon (''Oncorhynchus tshawytscha'') is the largest and most valuable species of Oncorhynchus, Pacific salmon. Its common name is derived from the Chinookan peoples. Other vernacular names for the species include king salmon, quinn ...
(in Gregorian calendar October), and counted 10 months, leaving an uncounted period until the next chinook
salmon run
A salmon run is an annual fish migration event where many salmonid species, which are typically hatched in fresh water and live most of their adult life downstream in the ocean, swim back against the stream to the upper reaches of rivers to s ...
.
[Suttles, Wayne P. ''Musqueam Reference Grammar'', UBC Press, 2004, p. 517.]
List of lunisolar calendars
The following is a list of lunisolar calendars sorted by family.
*
Babylonian calendar
The Babylonian calendar was a lunisolar calendar used in Mesopotamia from around the 2nd millennium BC until the Seleucid Era ( 294 BC), and it was specifically used in Babylon from the Old Babylonian Period ( 1780s BC) until the Seleucid Era. ...
family – common use of the Metonic cycle
**
Ancient Macedonian calendar
**
Hebrew calendar
The Hebrew calendar (), also called the Jewish calendar, is a lunisolar calendar used today for Jewish religious observance and as an official calendar of Israel. It determines the dates of Jewish holidays and other rituals, such as '' yahrze ...
**
Umma calendar
*
Hindu calendar
The Hindu calendar, also called Panchangam, Panchanga (), is one of various lunisolar calendars that are traditionally used in the Indian subcontinent and Southeast Asia, with further regional variations for social and Hindu religious purposes ...
family – shared astronomical roots
**
Vikram Samvat
Vikram Samvat (ISO: ''Vikrama Saṁvata''; abbreviated VS), also known as the Vikrami calendar is a Hindu calendar historically used in the Indian subcontinent and still also used in several Indian states and Nepal. It is a lunisolar calendar ...
**
Buddhist calendar
The Buddhist calendar is a set of lunisolar calendars primarily used in Tibet, Cambodia, Laos, Myanmar, Bangladesh, India, Sri Lanka, Thailand and Vietnam as well as in Malaysia and Singapore and by Chinese populations for religious or o ...
**
Burmese calendar
The Burmese calendar (, , or , ; Burmese Era (BE) or Myanmar Era (ME)) is a lunisolar calendar in which the months are based on lunar months and years are based on sidereal years. The calendar is largely based on an older version of the Hind ...
(
Pyu calendar)
***
Chula Sakarat
Chula Sakarat or Chulasakarat (; , ; , ; , , , abbrv. จ.ศ. ''Choso'') is a lunisolar calendar derived from the Burmese calendar, whose variants were in use by most mainland Southeast Asian kingdoms down to the late 19th century. The calendar is ...
**
Nepal Sambat
**
Thai lunar calendar
**
Vira Nirvana Samvat (
Jain calendar)
*
Chinese calendar
The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...
family – years start on second new moon after winter solstice (save for leaps)
**
Japanese calendar
Japanese calendar types have included a range of official and unofficial systems. At present, Japan uses the Gregorian calendar together with year designations stating the Japanese era name, year of the reign of the current Emperor. The written f ...
**
Korean calendar
Throughout its many years of history, various calendar systems have been used in Korea. Many of them were adopted from the Lunar calendar, lunar Chinese calendar system, with modifications occasionally made to accommodate Korea's geographic locat ...
**
Mongolian calendar
**
Tibetan calendar
The Tibetan calendar (), or the Phukpa calendar, known as the ''Tibetan lunar calendar'', is a lunisolar calendar composed of either 12 or 13 lunar months, each beginning and ending with a new moon. A thirteenth month is added every two or three y ...
**
Vietnamese calendar
The Vietnamese calendar (; ) is a lunisolar calendar that is mostly based on the lunisolar Chinese calendar. As Vietnam's official calendar has been the Gregorian calendar since 1954, the Vietnamese calendar is used mainly to observe lunisolar ...
* Unclassified or independent
**
Attic calendar
The Attic calendar or Athenian calendar is the lunisolar calendar beginning in midsummer with the lunar month of Hekatombaion, in use in ancient Attica, the ancestral territory of the Athenian polis. It is sometimes called the Greek calendar bec ...
** A lunisolar calendar devised by
Plethon
Georgios Gemistos Plethon (; /1360 – 1452/1454), commonly known as Gemistos Plethon, was a Byzantine Greeks, Greek scholar and one of the most renowned philosophers of the Late Byzantine era. He was a chief pioneer of the revival of Greek scho ...
, né Georgios Gemistos, in his Book of Laws
**
Ptolemic Egyptian calendar
**
Inca calendar
**
Celtic calendar, including
Coligny calendar
The Coligny calendar is a bronze plaque with an inscribed calendar, made in Roman Gaul in the 2nd century CE. It lays out a five-year cycle of a lunisolar calendar, each year with twelve lunar months. An intercalary month is inserted before eac ...
**
Muisca calendar
The Muisca calendar was a lunisolar calendar, lunisolar calendar used by the Muisca people, Muisca. The calendar was composed of a complex combination of months and three types of years were used; rural years (according to Pedro Simón, Chibcha la ...
**
Nisg̱a'a calendar
**
Old Eastern Ojibwe calendar
See also
*
List of calendars
A list is a Set (mathematics), set of discrete items of information collected and set forth in some format for utility, entertainment, or other purposes. A list may be memorialized in any number of ways, including existing only in the mind of t ...
*
*
Calendar reform
*
*Other non-solar calendars
**
Roman calendar
The Roman calendar was the calendar used by the Roman Kingdom and Roman Republic. Although the term is primarily used for Rome's pre-Julian calendars, it is often used inclusively of the Julian calendar established by Julius Caesar in 46&nbs ...
(probably a lunisolar calendar with
common year
A common year is a calendar year with 365 days, as distinguished from a ''leap year'', which has 366 days. More generally, a common year is one without Intercalation (timekeeping), intercalation. The Gregorian calendar, used by the majority of ...
s of 355 days and
leap year
A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) compared to a common year. The 366th day (or 13th month) is added to keep t ...
s of 378 days.)
**
Notes
References
Further reading
*
External links
Introduction to Calendars, US Naval Observatory, Astronomical Applications Department.
{{Chronology
Calendars
*