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The Gregorian calendar, also known as the Western calendar or the Christian calendar, is the internationally accepted civil calendar.[1][2][3] It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter gravissimas.[4] The reformed calendar was adopted later that year by a handful of countries, with other countries adopting it over the following centuries. The motivation for the Gregorian reform was that the Julian calendar assumes that the time between vernal equinoxes is 365.25 days, when in fact it is about 11 minutes less. The accumulated error between these values was about 10 days when the reform was made, resulting in the equinox occurring on March 11 and moving steadily earlier in the calendar. Since the equinox was tied to the celebration of Easter, the Roman Catholic Church considered that this steady movement was undesirable.

The Gregorian calendar reform contained two parts, a reform of the Julian calendar as used up to Pope Gregory's time, together with a reform of the lunar cycle used by the Church along with the Julian calendar for calculating dates of Easter. The reform was a modification of a proposal made by the Calabrian doctor Aloysius Lilius (or Lilio).[5] Lilius' proposal included reducing the number of leap years in four centuries from 100 to 97, by making 3 out of 4 centurial years common instead of leap years: this part of the proposal had been suggested before by, among others, Pietro Pitati. Lilio also produced an original and practical scheme for adjusting the epacts of the moon for completing the calculation of Easter dates, solving a long-standing difficulty that had faced proposers of calendar reform.

The Gregorian calendar continued the previous year-numbering system (Anno Domini), which counts years from the traditional Incarnation of Jesus, and which had spread throughout Europe during the Middle Ages. This year-numbering system is the predominant international standard today.[6]

The Gregorian calendar modified the Julian calendar's regular cycle of leap years, years exactly divisible by four,[7] including all centurial years, as follows:

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year.[8]

In addition to the change in the mean length of the calendar year from 365.25 days to 365.2425 days (a difference of 10.8 minutes per year), the Gregorian calendar also dealt with the past accumulated difference between these lengths. Due mostly to this discrepancy,[9] between AD 325 (when the Roman Catholic Church thought the First Council of Nicaea had fixed the vernal equinox on 21 March), and the time of Gregory's edict in 1582, the vernal equinox had moved backward in the calendar, until it was occurring on about 11 March, 10 days earlier. The Gregorian calendar therefore began by dropping 10 calendar days, to revert to the previous date of the vernal equinox.

Because of the Protestant Reformation, however, many Western European countries did not initially follow the Gregorian reform, and maintained their old-style systems. Eventually other countries followed the reform for the sake of consistency, but by the time the last adherents of the Julian calendar in Eastern Europe (Russia and Greece) changed to the Gregorian system in the 20th century, they had to drop 13 days from their calendars, due to the additional accumulated difference between the two calendars since 1582.