Introduction to Calendars
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A calendar is a system of organizing units of time for the purpose of reckoning time over extended periods.

There are six principal calendars in current use. These are the Gregorian, Jewish, Islamic, Indian, Chinese, and Julian Calendars. These calendars replicate astronomical cycles according to fixed rules. The data and information on our web site are limited to the astronomical issues for these calendars.

The principal astronomical cycles are the day (based on the rotation of the Earth on its axis), the year (based on the revolution of the Earth around the Sun), and the month (based on the revolution of the Moon around the Earth). The complexity of calendars arises because the year does not comprise an integral number of days or an integral number of lunar months.

The civil calendar in use around the world (Gregorian calendar) is a solar calendar. Solar calendars are based on the progression through the seasons as the Earth revolves around the Sun, but neglect any attempt to keep the months synchronous with the lunar phases. A lunar calendar bases each month on a full cycle of the Moon's phases (called a lunation or synodic month) without regard to the solar year. Lunar calendars usually start each month with a New Moon or the first visible crescent moon after New Moon. Luni-solar calendars try to remain synchronous with both the solar year and the moon phases. However, a solar year does not contain an integral number of days or an integral number of lunar months. To compensate for this, many luni-solar calendars adjust the length of their years and months. Without such an adjustment the seasons will steadily drift through the months.


Historical records from around the world show continued efforts to build reliable luni-solar calendars. One of the methods used most often was to insert (intercalate) an extra month every few years. It might be done randomly, but usually it is not. In the fifth century BC, the Greek astronomer Meton of Athens set down specific rules for inserting these extra months. If one picks a year that starts with a New Moon and lets the months run in sequence, how many lunar months pass before another year comes that starts on a New Moon? The answer is 235 lunar months - or 19 years. In other words the Full Moon appears on the same day in that year as it did 19 years earlier. This 19-year period defines the Metonic Cycle. This cycle is useful for calendar makers. The same pattern of lunar phase and date in the year repeats every 19 years. This number was so important to ancient calendar makers that the Greeks inscribed this number in golden letters on a temple in Athens - hence the term The Golden Number, G. Today's almanacs, including The Astronomical Almanac, provide The Golden Number. As it turns out, the Metonic Cycle is not quite exactly 19 years. It is off by about 2 hours per cycle.

Principal Solar Calendars:

The Julian Calendar was introduced by Julius Caesar in 45 BC. It eventually standardized on 21 March as the date of the vernal equinox and introduced a simple leap year rule: insert an extra day every four years. Although this leap year rule is straightforward, it does not produce a precise match to the solar year. Over the centuries the date of the astronomical vernal equinox slowly drifted away from the date of 21 March. The ecclesiastical rules to compute the date of Easter defined 21 March as the date of the vernal equinox. The Gregorian Calendar resulted from a perceived need to reform the calculation method for the dates of Easter. Nonetheless, the Julian Calendar and variations of it are still in use by some groups to set the dates for liturgical events.

The Gregorian Calendar has become the internationally accepted civil calendar. The leap year rule for the Gregorian Calendar differs slightly from one for the Julian Calendar. The Gregorian leap year rule is: Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the year 2000 is. The Gregorian dates for Easter are computed from a set of ecclesiastical rules and tables.

Principal Lunar Calendars:

The Islamic Calendar is a purely lunar calendar in which months correspond to the lunar phase cycle. Thus the twelve months of the Islamic Calendar systematically shift with respect to the months of the international civil calendar. The cycle of twelve months regresses through the seasons over a period of about 33 years. For religious purposes, Muslims begin each month with the first visibility of the lunar crescent after conjunction. For civil purposes, a tabulated calendar that approximates the lunar phase cycle is often used, which is discussed further in our Islamic Calendar page with projected dates for the beginning of the year and Ramadan.

The astronomical date and time of each New Moon can be computed exactly; however, the time an observer first sees that young Moon cannot be computed exactly. The Crescent Moon Visibility page discusses the difficulties associated with visual sightings of the young Moon. Her Majesty's Nautical Almanac Office computes the time of New Moon and provides information sheets that give the date of earliest visibility of the new crescent Moon for each lunar month for a selection of cities in the UK and around the world.

Luni-solar Calendars:

The Jewish Calendar that dates from the time of Hillel II (359 CE, AM4119) is the official calendar of the State of Israel (though variations on the calendar exist). It is a luni-solar calendar based on calculation rather than observation (visual observations of the young crescent Moon were used in ancient times). The dates for Passover are computed from a set of defined rules; Passover begins on the same liturgical date, Nisan 15, each year

The National Calendar of India is a formalized luni-solar calendar in which leap years coincide with those of the Gregorian calendar. The Gregorian Calendar is used for administrative purposes. The Indian religious calendars require calculations of the motions of the Sun and Moon. Tabulations of the religious holidays are prepared by the India Meteorological Department and published annually in The Indian Astronomical Ephemeris. Many local variations exist.

The Chinese Calendar is a luni-solar calendar based on calculations of the positions of the Sun and Moon. Since this calendar uses the true positions of the Sun and Moon, its accuracy depends on the accuracy of the astronomical theories and calculations.

Special purpose calendars:

There are also many special purpose calendars. Some are based on abstract, perpetually repeating cycles of no astronomical significance. Some calendars are regulated by observations (not computed or tabulated times) of celestial events. Some calendars are codified in written laws; others are transmitted by oral tradition. Many of these calendars provide dates for religious events and depend upon, for example, the occurrence of a specific religious, cultural, or agricultural event. They may or may not tie this to a date on the international civil calendar. They may or may not tie this to other astronomical events such as the astronomical vernal equinox. Those calendars are outside the scope of this website.

For further information on calendars, see Richards, E.G. 2012, "Calendars," from the Explanatory Supplement to the Astronomical Almanac, 3rd edition, S.E Urban and P.K. Seidelmann eds., (Mill Valley, CA: University Science Books), Chapter 15, pp. 585-624.