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A calendar is a system for assigning dates to days. The dates may be based on the perceived motion of astronomical objects. A calendar can also be a physical device (often paper) that illustrates the system (for example, a desktop calendar). The term is also used to indicate a particular set of planned events (for example, court calendar).

Calendars assign a date to each solar day. A day may consist of the period between sunrise and sunset, with a following period of night, or it may be a period between successive events such as two sunsets. The length of the interval between two such successive events may be allowed to vary slightly during the year, or it may be averaged into a mean solar day.

A calendar that is based on precieved season changes is called a solar calendar and one which is based on moon phases is called a lunar calendar, one which is based on both is called a lunisolar calendar.

Nearly all calendar systems group consecutive days into "months" and also into "years". In a solar calendar a year approximates Earth's tropical year (that is, the time it takes for a complete cycle of seasons) traditionally used to facilitate the planning of agricultural activities. In a lunar calendar, the month approximates the cycle of the moon phase. Consecutive days may be grouped into other periods such as the week.

Because, the number of days in the tropical year is not a whole number, a solar calendar must have a different number of days in different years. This may be done with leap years. The same applies to months in a lunar calendar and also the number of months in a year in a lunisolar calendar. This is generally known as intercalation. Even if a calendar is solar, but not lunar, the year can not be divided entirely into months that never vary in length.

Not all calenders use the solar year as a unit. A lunar calendar is one in which days are numbered within each Moon phase cycle. Because the length of the lunar month is not an even fraction of the length of the tropical year, a purely lunar calendar quickly drifts against the seasons. It does, however, stay constant with respect to other phenomena, notably tides. A lunisolar calendar is a lunar calendar that compensates by adding an extra month as needed to realign the months with the seasons.

The primary practical use of a calendar is to identify days: to be informed about and/or to agree on a future event and to record an event that has happened. Days may be significant for civil, religious or social reasons. For example, a calendar provides a way to determine which days are religious or civil holidays, and also which days mark the beginning and end of business accounting periods, and which days have legal significance, such as the day taxes are due or a contract expires. Also a calendar may provide by identifying a day provide other useful information about the day such as its season.

Calendars are also used as part of a complete timekeeping[?] system: date and time of day[?] together specify a moment in time. In the modern world, written calendars are no longer an essential part of such systems, as the advent of accurate clocks has made it possible to record time independently of astronomical events.

Calendars in widespread use today include the Gregorian calendar, which is the de facto international standard, and is used almost everywhere in the world for civil purposes, including in China and India. The Hebrew calendar is the official calendar of Israel's government, however the Gregorian calendar is much more widely used in Israel's business and day-to-day affairs. The Persian calendar is used in Iran and Afghanistan. The Islamic calendar is used by Moslems the world over. Chinese, Hebrew and Hindu calendars are widely used for religious and/or social purposes.

In the Roman Empire, the year-based Julian calendar was adopted. It numbers days within months that are longer than the lunar cycle, so it is not convenient for tracking phases of the moon, but it does a better job tracking the seasons. Each calendar year has 365 days, except every 4th year which is a leap year of 366 days. So the mean calendar year is 365.25 days.

Unfortunately, Earth's tropical year is not a little less the 365.25 days(it is approximately 365.242 days), so it too slowly drifted out of sync with the seasons. For such reasons, the Gregorian calendar was later adopted by most of the Western World starting in 1582 and it has since become the world's dominant civic calendar.

Cultures may define other units of time, such as the week, for the purpose of scheduling regular activities that do not easily coincide with months or years.

There have been a number of proposals for reform of the calendar, such as the World calendar or Perpetual calendar. The United Nations considered adopting such a reformed calendar for a while in the 1950s, but these proposals have lost most of their popularity.

Even where there is a commonly used calendar such as the Gregorian calendar, alternate calendars may also be used, such as a Fiscal calendar.

One example of an alternate calendar is a Fiscal calendar, which might be a 5/4/4 calendar, which fixes each month at a specific number of weeks to facilitate comparisons from month to month and year to year. January always has exactly 5 weeks (Sunday through Saturday), February has 4 weeks, March has 4 weeks, etc. Note that this calendar will normally need to add a 53rd week to every 5th or 6th year, which might be added to December or might not be, depending on how the organization uses those dates. There exists an international standard way doing this (the ISO week). The ISO week runs Monday through Sunday and Week 1 is always the week that contains January 4 Gregorian.

Type of calendars

Calendars in use on Earth are most frequently lunar, solar, luni-solar or arbitrary. A lunar calendar is synchronized to the motion of the Moon; an example is the Islamic calendar. A solar calendar is synchronized to the motion of the Sun; an example is the Persian calendar. A luni-solar calendar is synchronized to the motions of both the Moon and the Sun; an example is the Jewish calendar. An arbitrary calendar is not synchronized to either the Moon or the Sun; an example is the Julian date used by astronomers. There are some calendars that appear to be synchronized to the motion of Venus, such as some of the ancient Egyptian calendars; synchronization to Venus appears to occur primarily in civilizations near the Equator.

Calendars may be either complete or incomplete. Complete calendars provide a way of naming each consecutive day, while incomplete calendars do not. The early Roman calendar, that had no way of designating the days of the winter months other than to lump them together as "winter" is an example of an incomplete calendar, while the Gregorian calendar is an example of a complete calendar.

Calendars may be pragmatic, theoretical, or mixed.

A pragmatic calendar is one that is based on observation; an example is the religious Islamic calendar. Such a calendar is also referred to as an observation-based or astronomical calendar. The advantage of such a calendar is that it is perfectly and perpetually accurate. The disadvantage is working out when a particular date would occur.

A theoretical calendar is one that is based on a strict set of rules; an example is the Jewish calendar. Such a calendar is also referred to a rule-based or arithmetical calendar. The advantage of such a calendar is the ease of working out when a particular date occurs. The disadvantage is imperfect accuracy. Furthermore if the calendar is very accurate, its accuracy perishes slowly over time owing to changes in Earth's rotation. This limits the lifetime of an accurate theoretical calendar to a few thousand years. After then, the rules would need to be modified from observations made since the invention of the calendar, resulting in a mixed calendar.

A mixed calendar combines the features of both pragmatic and theoretical calendars. Mixed calendars usually begin as theoretical calendars, but are adjusted pragmatically when some type of asynchrony becomes apparent; the shift from the Julian to the Gregorian calendar is such an example.

The Gregorian calendar, as a final example, is complete, solar, and mixed.

List of calendars (including some dating systems which aren't really calendars)

in use today:
Gregorian calendar, Julian calendar, Chinese calendar, Japanese calendar, Hebrew calendar, Iranian calendar, Islamic calendar, Hindu calendars, Revised Julian calendar, Coptic calendar, Thai solar calendar, Zoroastrian calendar (including Parsi), Malayalam calendar, Bahai calendar, Fiscal year, Julian date, ISO Week-Date calendar
no longer in common use
Roman calendar, Mayan calendar, Aztec calendar, Egyptian calendar, French Revolutionary Calendar, Soviet revolutionary calendar, Thai lunar calendar
not yet in common use
Darian calendar for use on Mars
calendar proposals[?]:
World calendar, International Perpetual calendar (also called the International Fixed calendar)
Compare liturgical year, calendar of saints, Christian calendar...

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