Portions of this entry contributed by Alejandra Mercado

The calendar currently in worldwide use for secular purposes based on a cycle of 400 years comprising 146,097 days, giving a year of average length 365.2425 days. The Gregorian calendar is a modification of the Julian calendar in which leap years are omitted in years divisible by 100 but not divisible by 400. By this rule, the year 1900 was not a leap year (1900 is divisible by 100 and not divisible by 400), but the year 2000 will be a leap year (2000 is divisible by 400). The total number of days in 400 years is therefore given by

This also gives an exact number of weeks per 400-year cycle.

The Gregorian calendar was constructed to give a close approximation to the tropical year, which is the actual length of time it takes for the Earth to complete one orbit around the Sun.

The Julian calendar was switched over to the Gregorian starting in 1582, at which point the 10 day difference between the actual time of year and traditional time of year on which calendrical events occurred became intolerable. The switchover was bitterly opposed by much of the populace, who feared it was attempt by landlords to cheat then out of a week and a half's rent. However, when Pope Gregory XIII decreed that the day after October 4, 1582 would be October 15, 1582, the Catholic countries of France, Spain, Portugal, and Italy complied. Various Catholic German countries (Germany was not yet unified), Belgium, the Netherlands, and Switzerland followed suit within a year or two, and Hungary followed in 1587.

Because of the Pope's decree, the reform of the Julian calendar came to be known as the Gregorian calendar. However, the rest of Europe did not follow suit for more than a century.

The Protestant German countries adopted the Gregorian reform in 1700. By this time, the calendar trailed the seasons by 11 days. England (and the American colonies) finally followed suit in 1752, and Wednesday, September 2, 1752 was immediately followed by Thursday, September 14, 1752. This traumatic change resulted in widespread riots and the populace demanding "Give us the eleven days back!"

English Calendar:

Sweden followed England's lead in 1753. Russia, however, did not follow suit until 1918, when January 31, 1918 was immediately followed by February 14th. In fact, however, the USSR is not on the Gregorian calendar, but on a more accurate one of their own devising. The USSR calendar is designed to more closely approximate the true length of the tropical year, thus has one additional rule for when a year is a leap year. It will remain in synchronization with the Gregorian calendar for thousands more years, by which time one or both will have probably fallen into disuse. Similarly, Iranian calendar is also a more accurate version of the Gregorian calendar (Ross).

Formulas for computing the Julian date from the Gregorian dates are given in Danby (1988) and Sinnott (1991). Let denote the integer part (sometimes known in mathematical circles as the floor function ), let Y be the Gregorian year, M the month number (1=January, 2=February, etc.), D the day of the month, and UT the universal time. For all AD dates in the Gregorian calendar,

	(1)

For Gregorian calendar dates 1901-2099, the formula can be simplified to

	(2)

Calendar, French Revolutionary Calendar, Iranian Calendar, Islamic Calendar, Julian Date, Julian Calendar, Julian Date, Leap Day, Leap Year, Tropical Year, Year