Lunar calendar

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Islamic Calendar, year 1280, Linden Museum, Stuttgart. Iran Kalender 1863 Linden-Museum.jpg
Islamic Calendar, year 1280, Linden Museum, Stuttgart.

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 only directly on the solar year. The most commonly used calendar, the Gregorian calendar, is a solar calendar system that originally evolved out of a lunar calendar system. A purely lunar calendar is also distinguished from a lunisolar calendar, whose lunar months are brought into alignment with the solar year through some process of intercalation. The details of when months begin varies from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.


Since each lunation is approximately 29+12 days, [1] it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of 12 such lunations, a lunar year, is 354 days, 8 hours, 48 minutes, 34 seconds (354.36707 days), [1] purely lunar calendars are 11 to 12 days shorter than the solar year. In purely lunar calendars, which do not make use of intercalation, like the Islamic calendar, the lunar months cycle through all the seasons of a solar year over the course of a 33–34 lunar-year cycle.

Although the Gregorian calendar is in common and legal use in most countries, traditional lunar and lunisolar calendars continue to be used throughout the world to determine religious festivals and national holidays. Such holidays include Rosh Hashanah (Hebrew calendar); Easter (the Computus); the Chinese, Japanese, Korean, Vietnamese, and Mongolian New Year (Chinese, Japanese, Korean, Vietnamese, and Mongolian calendars, respectively); the Nepali New Year (Nepali calendar); the Mid-Autumn Festival and Chuseok (Chinese and Korean calendars); Loi Krathong (Thai calendar); Sunuwar calendar; Vesak/Buddha's Birthday (Buddhist calendar); Diwali (Hindu calendars); Ramadan, Eid al-Fitr and Eid al-Adha (Islamic calendar).


A lunisolar calendar was found at Warren Field in Scotland and has been dated to c. 8000 BC, during the Mesolithic period. [2] Some scholars argue for lunar calendars still earlier—Rappenglück in the marks on a c.17,000 year-old cave painting at Lascaux and Marshack in the marks on a c.27,000 year-old bone baton—but their findings remain controversial. [3] [4] Scholars have argued that ancient hunters conducted regular astronomical observations of the Moon back in the Upper Palaeolithic. [5] Samuel L. Macey dates the earliest uses of the Moon as a time-measuring device back to 28,000–30,000 years ago. [6]

Lunisolar calendars

Most calendars referred to as "lunar" calendars are in fact lunisolar calendars. Their months are based on observations of the lunar cycle, with intercalation being used to bring them into general agreement with the solar year. The solar "civic calendar" that was used in ancient Egypt showed traces of its origin in the earlier lunar calendar, which continued to be used alongside it for religious and agricultural purposes. Present-day lunisolar calendars include the Chinese, Vietnamese, Hindu, and Thai calendars.

Synodic months are 29 or 30 days in length, making a lunar year of 12 months about 11 to 12 days shorter than a solar year. Some lunar calendars do not use intercalation, for example the lunar Hijri calendar used by most Muslims. For those that do, such as the Hebrew calendar, and Buddhist Calendars in Myanmar, the most common form of intercalation is to add an additional month every second or third year. Some lunisolar calendars are also calibrated by annual natural events which are affected by lunar cycles as well as the solar cycle. An example of this is the lunar calendar of the Banks Islands, which includes three months in which the edible palolo worms mass on the beaches. These events occur at the last quarter of the lunar month, as the reproductive cycle of the palolos is synchronized with the moon. [7]

Start of the lunar month

Lunar and lunisolar calendars differ as to which day is the first day of the month. In some lunisolar calendars, such as the Chinese calendar, the first day of a month is the day when an astronomical new moon occurs in a particular time zone. In others, such as some Hindu calendars, each month begins on the day after the full moon. Others are based on the first sighting of the lunar crescent, such as the lunar Hijri calendar (and, historically, the Hebrew calendar).

Length of the lunar month

The length of each lunar cycle varies slightly from the average value. In addition, observations are subject to uncertainty and weather conditions. Thus to avoid uncertainty about the calendar, there have been attempts to create fixed arithmetical rules to determine the start of each calendar month.

The average length of the synodic month is 29.53059 days. [1] Thus it is convenient if months generally alternate between 29 and 30 days (sometimes termed respectively "hollow" and "full"). The distribution of hollow and full months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day.

In the table below, the first column gives a sequence of such continued fractions. So to devise a calendar from each, one would take the number of days as given in the numerator and divide it into the number of months as given in the denominator. The second column shows, for reference, the time length of that cycle in years and days. The next double column shows how many of the months must be full and how many must be hollow; in each case, there is only one possible combination (how they are ordered within the cycle is not relevant).

The next column shows the decimal value of each fraction; that is the effective average length of a month over one cycle. It will be noted that each successive value comes closer to the length of the synodic month. Finally, the last two columns show roughly how long it will take (assuming one adheres to the pattern exactly) for the calendar months to be about a day off the synodic month, and which way off it will be.

Increasing accuracy with increasing period of repetition
FractionLength of one cycle
in years and days
Numbers of months ofAverage length of
calendar month
in days
After this much time
has elapsed
the calendar will be about
30 days
29 days
29 days/1 month0 years, 29 days01292 months1 day ahead of the moon phases
30 days/1 month0 years, 30 days10302 months1 day behind the moon phases
59 days/2 months0 years, 59 days1129.52.6 years1 day ahead of the moon phases
443 days/15 months1 non-leap year +
78 days
8729.53333...30 years1 day behind the moon phases
502 days/17 months1 non-leap year +
137 days
9829.529 411 76470 years1 day ahead of the moon phases
945 days/32 months2 non-leap years +
215 days
171529.53125122 years1 day behind the moon phases
1447 days/49 months3 non-leap years +
352 days
262329.530 612 2553000 years1 day behind the moon phases
25101 days/850 months68 years
incl. 17 leap years +
264 days
45139929.530 588 23531,000 years1 day behind the moon phases [lower-alpha 1]

These fractions can be used to construct a lunar calendar, or in combination with a solar calendar to produce a lunisolar calendar. A 49-month cycle was proposed as the basis of an alternative Easter computation by Isaac Newton around 1700. [8] The tabular Islamic calendar's 360-month cycle is equivalent to 24 of the 443 days15 months cycles, minus a correction of one day. It comes to 10,631 days (29 years, including 7 leap years + 39 days) with 191 months of 30 days and 169 months of 29 days.[ citation needed ]

List of lunar calendars

See also


  1. Theoretical. In reality, not accurate due to the multi-millennial change of the synodic month length.

Related Research Articles

Calendar System for organizing the days of year

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 date is the designation of a single, specific day within such a system. A calendar is also a physical record of such a system. A calendar can also mean a list of planned events, such as a court calendar or a partly or fully chronological list of documents, such as a calendar of wills.

Hebrew calendar Lunisolar calendar used for Jewish religious observances

The Hebrew calendar, also called Jewish calendar, is a lunisolar calendar used today for Jewish religious observance, and as an official calendar of the state of Israel. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits, and daily Psalm readings, among many ceremonial uses. In Israel, it is used for religious purposes, provides a time frame for agriculture, and is an official calendar for civil holidays, alongside the Gregorian calendar.

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 calendars may require intercalations of both days and months.

A leap year is a calendar year that contains an additional day added to keep the calendar year synchronized with the astronomical year or seasonal year. Because astronomical events and seasons do not repeat in a whole number of days, calendars that have 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 an additional day or month into some years, the drift between a civilization's dating system and the physical properties of the solar system can be corrected. A year that is not a leap year is a common year.

Lunisolar calendar Calendar with lunar month, solar year

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 predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.

A month is a unit of time, used with calendars, that is approximately as long as a natural orbital period of the Moon; the words month and Moon are cognates. The traditional concept arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth-Sun line, are still the basis of many calendars today, and are used to divide the year.

Lunar phase the shape of the Moons directly sunlit portion as viewed from Earth

The lunar phase or Moon phase is the shape of the Moon's directly sunlit portion as viewed from Earth. The lunar phases gradually change over a synodic month as the Moon's orbital positions around Earth and Earth around the Sun shift. The visible side of the moon is variously sunlit, depending on the position of the Moon in its orbit. Thus, this face's sunlit portion can vary from 0% to 100% . Each of the four "intermediate" lunar phases is approximately 7.4 days, with slight variation due to the Moon's orbit's elliptical shape.

Metonic cycle

The Metonic cycle or enneadecaeteris is a period of approximately 19 years after which the phases of the moon recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic lunar months is just 1 hour, 27 minutes and 33 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a lunisolar calendar.

A moveable feast or movable feast is an observance in a Christian liturgical calendar, borrowed from the Hebrew Lunisolar calendar, which therefore occurs on a different date in different years.

New moon Phase of the Moon

In astronomy, the new moon is the first lunar phase, when the Moon and Sun have the same ecliptic longitude. At this phase, the lunar disk is not visible to the unaided eye, but its presence may be detected because it occults stars behind it.

Eclipse cycle Calculation and prediction of eclipses

Eclipses may occur repeatedly, separated by certain intervals of time: these intervals are called eclipse cycles. The series of eclipses separated by a repeat of one of these intervals is called an eclipse series.

The Thai lunar calendar, or Tai calendar, is a lunisolar Buddhist calendar. It is used for calculating lunar-regulated holy days. Based on the SuriyaYatra, with likely influence from the traditional Hindu Surya Siddhanta, it has its own unique structure that does not require the Surya Siddhanta to calculate. Lunisolar calendars combine lunar and solar calendars for a nominal year of 12 months. An extra day or an extra 30-day month is intercalated at irregular intervals.

Date of Easter Calculation of the date of Easter

As a moveable feast, the date of Easter is determined in each year through a calculation known as computus. Easter is celebrated on the first Sunday after the Paschal full moon, which is the first full moon on or after 21 March. Determining this date in advance requires a correlation between the lunar months and the solar year, while also accounting for the month, date, and weekday of the Julian or Gregorian calendar. The complexity of the algorithm arises because of the desire to associate the date of Easter with the date of the Jewish feast of Passover which, Christians believe, is when Jesus was crucified.

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.

Babylonian calendar

The Babylonian calendar was a lunisolar calendar with years consisting of 12 lunar months, each beginning when a new crescent moon was first sighted low on the western horizon at sunset, plus an intercalary month inserted as needed by decree. The calendar is based on a Sumerian predecessor preserved in the Umma calendar of Shulgi.

The Buddhist calendar is a set of lunisolar calendars primarily used in mainly South and Southeast Asian countries such as Cambodia, Laos, Sri Lanka, Myanmar and Thailand as well as in Chinese populations of Malaysia and Singapore for religious or official occasions. While the calendars share a common lineage, they also have minor but important variations such as intercalation schedules, month names and numbering, use of cycles, etc. In Thailand, the name Buddhist Era is a year numbering system shared by the traditional Thai lunisolar calendar and by the Thai solar calendar.

The Hijri year or era is the era used in the Islamic lunar calendar, which begins its count from the Islamic New Year in 622 CE. During that year, Muhammad and his followers migrated from Mecca to Yathrib. This event, known as the Hijra, is commemorated in Islam for its role in the founding of the first Muslim community (ummah).

The Ancient Macedonian calendar is a lunisolar calendar that was in use in ancient Macedon in the 1st millennium BC. It consisted of 12 synodic lunar months, which needed intercalary months to stay in step with the seasons. By the time the calendar was being used across the Hellenistic world, seven total embolimoi were being added in each 19-year Metonic cycle. The names of the ancient Macedonian Calendar remained in use in Syria even into the Christian era.

The Burmese calendar 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 Hindu calendar, though unlike the Indian systems, it employs a version of the Metonic cycle. The calendar therefore has to reconcile the sidereal years of the Hindu calendar with the Metonic cycle's near tropical years by adding intercalary months and days at irregular intervals.

Lunar month Time between successive new moons

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.


  1. 1 2 3 P. Kenneth Seidelmann, ed. (1992). Explanatory Supplement to the Astronomical Almanac. p. 577. For convenience, it is common to speak of a lunar year of twelve synodic months, or 354.36707 days. (which gives a mean synodic month as 29.53059 days or 29 days 12 hours 44 minutes and 3 seconds)
  2. Nancy Owano, Scotland lunar-calendar find sparks Stone Age rethink,, 27 July 2013 Archived 9 August 2013 at the Wayback Machine
  3. James Elkins, Our beautiful, dry, and distant texts (1998) 63ff.
  4. "Oldest lunar calendar identified". BBC News . 2000-10-16. Retrieved 2013-03-14.
  5. Gurshtein, Alex (2005-01-01). "Did the Pre-Indo-Europeans Influence the Formation of the Western Zodiac?". Journal of Indo-European Studies. 33: 106.
  6. Macey, Samuel L. (1994). Encyclopedia of Time. Taylor & Francis. p. 75. ISBN   9780815306153.
  7. R.H.Codrington. The Melanesians: Their anthropology and folklore (1891) Oxford, Clarendon Press
  8. Reform of the Julian Calendar as Envisioned by Isaac Newton by Ari Belenkiy and Eduardo Vila Echagüe (pdf); Notes and Records of the Royal Society of London (vol. 59, no. 3, pp. 223–254).