The Gregorian calendar is the calendar used in most parts of the world.[1][a] It went into effect in October 1582 following the papal bull Inter gravissimas issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years differently so as to make the average calendar year 365.2425 days long, more closely approximating the 365.2422-day 'tropical' or 'solar' year that is determined by the Earth's revolution around the Sun.

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.


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There were two reasons to establish the Gregorian calendar. First, the Julian calendar assumed incorrectly that the average solar year is exactly 365.25 days long, an overestimate of a little under one day per century, and thus has a leap year every four years without exception. The Gregorian reform shortened the average (calendar) year by 0.0075 days to stop the drift of the calendar with respect to the equinoxes.[3] Second, in the years since the First Council of Nicaea in AD 325,[b] the excess leap days introduced by the Julian algorithm had caused the calendar to drift such that the (Northern) spring equinox was occurring well before its nominal 21 March date. This date was important to the Christian churches because it is fundamental to the calculation of the date of Easter. To reinstate the association, the reform advanced the date by 10 days:[c] Thursday 4 October 1582 was followed by Friday 15 October 1582.[3] In addition, the reform also altered the lunar cycle used by the Church to calculate the date for Easter, because astronomical new moons were occurring four days before the calculated dates. Whilst the reform introduced minor changes, the calendar continued to be fundamentally based on the same geocentric theory as its predecessor.[4]

Gregorian years are identified by consecutive year numbers.[7] A calendar date is fully specified by the year (numbered according to a calendar era, in this case Anno Domini or Common Era), the month (identified by name or number), and the day of the month (numbered sequentially starting from 1). Although the calendar year currently runs from 1 January to 31 December, at previous times year numbers were based on a different starting point within the calendar (see the "beginning of the year" section below).

Calendar cycles repeat completely every 400 years, which equals 146,097 days.[d][e] Of these 400 years, 303 are regular years of 365 days and 97 are leap years of 366 days. A mean calendar year is .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}365+97/400 days = 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds.[f] During intervals that do not contain any century common years (such as 1800, 1900 and 2100), the calendar repeats every 28 years, during which 29 February will fall on each of the seven days of the week once and only once. All other dates of the year fall on each day exactly four times, each day of the week having gaps of 6 years, 5 years, 6 years, and 11 years, in that order.

The Gregorian calendar was a reform of the Julian calendar. It was instituted by papal bull Inter gravissimas dated 24 February 1582 by Pope Gregory XIII,[3] after whom the calendar is named. The motivation for the adjustment was to bring the date for the celebration of Easter to the time of year in which it was celebrated when it was introduced by the early Church. The error in the Julian calendar (its assumption that there are exactly 365.25 days in a year) had led to the date of the equinox according to the calendar drifting from the observed reality, and thus an error had been introduced into the calculation of the date of Easter. Although a recommendation of the First Council of Nicaea in 325 specified that all Christians should celebrate Easter on the same day, it took almost five centuries before virtually all Christians achieved that objective by adopting the rules of the Church of Alexandria (see Easter for the issues which arose).[g]

Lilius's proposal included reducing the number of leap years in four centuries from 100 to 97, by making three out of four centurial years common instead of leap years. He also produced an original and practical scheme for adjusting the epacts of the Moon when calculating the annual date of Easter, solving a long-standing obstacle to calendar reform.

Ancient tables provided the Sun's mean longitude.[h] The German mathematician Christopher Clavius, the architect of the Gregorian calendar, noted that the tables agreed neither on the time when the Sun passed through the vernal equinox nor on the length of the mean tropical year. Tycho Brahe also noticed discrepancies.[16][17] The Gregorian leap year rule (97 leap years in 400 years) was put forward by Petrus Pitatus of Verona in 1560. He noted that it is consistent with the tropical year of the Alfonsine tables and with the mean tropical year of Copernicus (De revolutionibus) and Erasmus Reinhold (Prutenic tables). The three mean tropical years in Babylonian sexagesimals as the excess over 365 days (the way they would have been extracted from the tables of mean longitude) were 0;14,33,9,57 (Alfonsine), 0;14,33,11,12 (Copernicus) and 0;14,33,9,24 (Reinhold).[i] In decimal notation, these are equal to 0.24254606, 0.24255185, and 0.24254352, respectively. All values are the same to two sexagesimal places (0;14,33, equal to decimal 0.2425) and this is also the mean length of the Gregorian year. Thus Pitatus's solution would have commended itself to the astronomers.[18]

Lilius's proposals had two components. First, he proposed a correction to the length of the year. The mean tropical year is 365.24219 days long.[19] A commonly used value in Lilius's time, from the Alfonsine tables, is 365.2425463 days.[13] As the average length of a Julian year is 365.25 days, the Julian year is almost 11 minutes longer than the mean tropical year. The discrepancy results in a drift of about three days every 400 years. Lilius's proposal resulted in an average year of 365.2425 days (see Accuracy). At the time of Gregory's reform there had already been a drift of 10 days since the Council of Nicaea, resulting in the vernal equinox falling on 10 or 11 March instead of the ecclesiastically fixed date of 21 March, and if unreformed it would have drifted further. Lilius proposed that the 10-day drift should be corrected by deleting the Julian leap day on each of its ten occurrences over a period of forty years, thereby providing for a gradual return of the equinox to 21 March.

The second component consisted of an approximation that would provide an accurate yet simple, rule-based calendar. Lilius's formula was a 10-day correction to revert the drift since the Council of Nicaea, and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. The proposed rule was that "years divisible by 100 would be leap years only if they were divisible by 400 as well".

The 19-year cycle used for the lunar calendar required revision because the astronomical new moon was, at the time of the reform, four days before the calculated new moon.[9] It was to be corrected by one day every 300 or 400 years (8 times in 2500 years) along with corrections for the years that are no longer leap years (i.e. 1700, 1800, 1900, 2100, etc.) In fact, a new method for computing the date of Easter was introduced. The method proposed by Lilius was revised somewhat in the final reform.[20]

A month after having decreed the reform, the pope (with a brief of 3 April 1582) granted to one Antoni Lilio the exclusive right to publish the calendar for a period of ten years. The Lunario Novo secondo la nuova riforma[j] was printed by Vincenzo Accolti, one of the first calendars printed in Rome after the reform, notes at the bottom that it was signed with papal authorization and by Lilio (Con licentia delli Superiori... et permissu Ant(onii) Lilij). The papal brief was revoked on 20 September 1582, because Antonio Lilio proved unable to keep up with the demand for copies.[21]

Prior to 1917, Turkey used the lunar Islamic calendar with the Hijri era for general purposes and the Julian calendar for fiscal purposes. The start of the fiscal year was eventually fixed at 1 March and the year number was roughly equivalent to the Hijri year (see Rumi calendar). As the solar year is longer than the lunar year this originally entailed the use of "escape years" every so often when the number of the fiscal year would jump. From 1 March 1917 the fiscal year became Gregorian, rather than Julian. On 1 January 1926, the use of the Gregorian calendar was extended to include use for general purposes and the number of the year became the same as in most other countries.

This section always places the intercalary day on 29 February even though it was always obtained by doubling 24 February (the bissextum (twice sixth) or bissextile day) until the late Middle Ages. The Gregorian calendar is proleptic before 1582 (calculated backwards on the same basis, for years before 1582), and the difference between Gregorian and Julian calendar dates increases by three days every four centuries (all date ranges are inclusive).

In common usage, 1 January was regarded as New Year's Day and celebrated as such,[47] but from the 12th century until 1751 the legal year in England began on 25 March (Lady Day).[48] So, for example, the Parliamentary record lists the execution of Charles I on 30 January as occurring in 1648 (as the year did not end until 24 March),[49] although later histories adjust the start of the year to 1 January and record the execution as occurring in 1649.[50] ff782bc1db

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