Century leap year

A century leap year is a year in the Gregorian calendar that is evenly divisible by 400 and is thus a leap year.[1]

Like all leap years, it has an extra day in February for a total of 366 days instead of 365. In the obsolete Julian calendar, all years that were divisible by 4, including end-of-century years, were considered leap years. The Julian rule, however, adds too many leap days (about 3 extra leap days in 400 years), which resulted in the calendar drifting gradually with respect to the astronomical seasons. To remedy this, Pope Gregory XIII introduced in 1582 a slightly modified version of the Julian calendar, the Gregorian calendar, where century years are leap years only if they are divisible by 400. This eliminates 3 of the 4 end-of-century years in a 400-year period. For example, the years 1600, 2000, 2400, and 2800 are century leap years since those numbers are evenly divisible by 400, while 1700, 1800, 1900, 2100, 2200, 2300, 2500, 2600, 2700, 2900, and 3000 are common years despite being evenly divisible by 4. This scheme brings the average length of the calendar year significantly closer to the astronomical length of the year, nearly eliminating the drift of the calendar against the seasons.

By coincidence rather than design, the Gregorian calendar repeats exactly every 400 years,[lower-alpha 1] so century leap years in the Gregorian calendar always start on a Saturday, and the leap day in those years always falls on a Tuesday. The start days of the end-of-century common years also varies; the century year begins on a Friday if the remainder obtained by dividing it by 400 is 100, Wednesday if the remainder is 200, and Monday if the remainder is 300. Thus, only leap years that start on a Monday, Wednesday, and Friday can be skipped in the Gregorian calendar.

The Gregorian calendar was introduced in 1582, but was adopted by various countries at different times over several centuries. Dates prior to 1582 are generally calculated using the Julian calendar, and different countries have different conventions about dates between 1582 and their adoption of the Gregorian calendar. (See, for example, Old Style and New Style dates.)

Notes
  1. It would repeat every 2800 years (400 years, the length of the full Gregorian leap-year cycle, times 7, the number of distinct weekdays), were it not for the fact that the 400-year cycle contains an integer number of weeks, as the number of days in 400 years happens to be an exact multiple of 7 ((365 · 303) + (366 · 97) = 146,097 = 7 · 20,871, the number of weeks in the 400-year Gregorian cycle).

References
  1. "Introduction to Calendars". United States Naval Observatory. n.d. Retrieved 9 May 2022. 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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