A calendar is a system of organising days for social, religious, commercial or administrative purposes. 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 (often paper) 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.
Periods in a calendar (such as years and months) are usually, though not necessarily, synchronised with the cycle of the sun or the moon. The most common type of pre-modern calendar was the lunisolar calendar, a lunar calendar that occasionally adds one intercalary month to remain synchronised with the solar year over the long term.
The term calendar is taken from calendae, the term for the first day of the month in the Roman calendar, related to the verb calare "to call out", referring to the "calling" of the new moon when it was first seen. Latin calendarium meant "account book, register" (as accounts were settled and debts were collected on the calends of each month). The Latin term was adopted in Old French as calendier and from there in Middle English as calender by the 13th century (the spelling calendar is early modern).
The course of the Sun and the Moon are the most evident forms of timekeeping, and the year and lunation were most commonly used in pre-modern societies worldwide as time units. Nevertheless, the Roman calendar contained very ancient remnants of a pre-Etruscan 10-month solar year. The first recorded calendars date to the Bronze Age, dependent on the development of writing in the Ancient Near East, the Egyptian and Sumerian calendars.
A large number of calendar systems which were based on the Babylonian calendar, and which were found in the Ancient Near East, date from the Iron Age. Amongst such calendar systems was the calendar system of the Persian Empire, which in turn gave rise to the Zoroastrian calendar as well as the Hebrew calendar.
A great number of Hellenic calendars developed in Classical Greece, and with the Hellenistic period also influenced calendars outside of the immediate sphere of Greek influence, giving rise to the various Hindu calendars as well as to the ancient Roman calendar.
Calendars in antiquity were lunisolar, depending on the introduction of intercalary months to align the solar and the lunar years. This was mostly based on observation, but there may have been early attempts to model the pattern of intercalation algorithmically, as evidenced in the fragmentary 2nd-century Coligny calendar.
A full calendar system has a different calendar date for every day. Thus the week cycle is by itself not a full calendar system; neither is a system to name the days within a year without a system for identifying the years.
The simplest calendar system just counts time periods from a reference date. This applies for the Julian day or Unix Time. Virtually the only possible variation is using a different reference date, in particular one less distant in the past to make the numbers smaller. Computations in these systems are just a matter of addition and subtraction.
Other calendars have one (or multiple) larger units of time.
Calendars that contain one level of cycles:
- week and weekday – this system (without year, the week number keeps on increasing) is not very common
- year and ordinal date within the year, e.g., the ISO 8601 ordinal date system
Calendars with two levels of cycles:
- year, month, and day – most systems, including the Gregorian calendar (and its very similar predecessor, the Julian calendar), the Islamic calendar, the Solar Hijri calendar and the Hebrew calendar
- year, week, and weekday – e.g., the ISO week date
Cycles can be synchronized with periodic phenomena:
- Lunar calendars are synchronized to the motion of the Moon (lunar phases); an example is the Islamic calendar.
- Solar calendars are based on perceived seasonal changes synchronized to the apparent motion of the Sun; an example is the Persian calendar.
- Lunisolar calendars are based on a combination of both solar and lunar reckonings; examples include the traditional calendar of China, the Hindu calendar in India, and the Hebrew calendar.
- The week cycle is an example of one that is not synchronized to any external phenomenon (although it may have been derived from lunar phases, beginning anew every month).