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A lunar calendar is a calendar oriented at the moon phase.

This is normally done by having a month which corresponds to a lunation so that the day of month indicates the moon phase. If a calendar tracks the seasons, it is also a lunisolar calendar.

Since there are about twelve lunations (synodic months) in a solar year, this period (354.37 days) is sometimes referred to as lunar year, corresponding to thirteen sidereal months (355.18 days).


Most lunar calendars are also lunisolar, such as the Hebrew, Chinese, Tamil Calendar and Hindu calendar, and most calendar systems used in antiquity. The reason for this is that a year is not evenly divisible by an exact number of lunations, so without any correction the calendar year will drift with respect to the seasons. The only widely used purely lunar calendar is the Islamic calendar, whose year always consists of 12 lunations. As a result of this, it is mostly used for religious purposes, alongside a secular solar calendar, and Islamic feasts perform a full circle with respect to the seasons every 33 years.

Determining the start of the month[]

For some lunar calendars, such as the Chinese calendar, the first day of the month is determined by the day during which the moment of new moon arrives, according to a particular time zone. Many other lunar calendars are based on first sighting of the lunar crescent. Thus, different lunar calendars differ in which day is considered the first day of the month.

The length of a month orbit/cycle is difficult to predict and varies from its average value. Because observations are subject to uncertainty and weather conditions, and astronomical methods are highly complex, there have been attempts to create fixed arithmetical rules.

The average length of the synodic month is 29.530589 days. This means the length of a month is alternately 29 and 30 days (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 list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed:

   29 /   1   
   30 /   1   
   59 /   2   (error: 1 day after about 33 months)
  443 /  15   (error: 1 day after about 30 years) 
  502 /  17   (error: 1 day after about 70 years)
 1447 /  49   (error: 1 day after about 3 millennia)
25101 / 850   (error: dependent on change of synodic month value}

These fractions can be used in the construction of lunar calendars, or in combination with a solar calendar to produce a lunisolar calendar. The 49-month cycle was proposed as the basis of an alternative Easter computation by Isaac Newton around 1700 [1]. The tabular Islamic calendar's 360-month cycle is equivalent to 24×15 months minus a correction of one day.

The recently invented Yerm Lunar Calendar makes use of all of the above approximations.

Lunar year[]

Lunisolar calendars that try to reconcile lunations with the solar year have to operate with intercalary months, resulting in a thirteen-month year every two or three years.

In England, a calendar of thirteen months of 28 days each, plus one extra day, known as "a year and a day" was still in use up to Tudor times. This would be a hybrid calendar that had substituted regular weeks of seven days for actual quarter-lunations, so that one month had exactly four weeks, regardless of the actual moon phase. The "lunar year" is here considered to have 364 days, resulting in a solar year of "a year and a day".

As a religious tradition, the thirteen-month years survived among European peasants for more than a millennium after the adoption of the Julian Calendar.

The "Edwardian" (probably Edward II, late 13th or early 14th century) ballad of Robin Hood for example has "How many merry months be in the year? / There are thirteen, I say ...", amended by a Tudor editor to "...There are but twelve, I say....". Robert Graves in the introductions to Greek Myths comments on this with "Thirteen, the number of the sun's death-month, has never lost its evil reputation among the superstitious."

See also[]


  1. 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).

External links[]