Gregorian Calendar - Other Aspects

Other Aspects

The day of the year is somewhat inconvenient to compute, partly because the leap day does not fall at the end of the year. But the calendar exhibits a repeating pattern for the number of days in the months March through July and August through December: 31, 30, 31, 30, 31, for a total of 153 days each. In fact, any five consecutive months not containing February contain exactly 153 days.

See also common year starting on Sunday and dominical letter.

The 400-year cycle of the Gregorian calendar has 146,097 days and hence exactly 20,871 weeks. So, for example, the days of the week in Gregorian 1612 were exactly the same as for 2012. The years that are divisible by 400 begin on a Saturday. In the 400-year cycle, more months begin on a Sunday (and hence have Friday the 13th) than any other day of the week (see above under Week for a more detailed explanation of how this happens). 688 out of every 4800 months (or 172/1200) begin on a Sunday, while only 684 out of every 4800 months (171/1200) begin on each of Saturday and Monday, the least common cases.

A smaller cycle is 28 years (1,461 weeks). For any given date of the year, the day of the week also repeats in one of the following patterns:

after 5, 11, and 22 years

after 6, 11, and 17 years

after 6, 17, and 23 years

after 11, 17, and 22 years

However, a dropped leap year (such as 1900) temporarily disrupts the 28-year cycle and the repetitions within it.

The Doomsday algorithm is a method to discern which of the 14 calendar variations should be used in any given year (after the Gregorian reformation). It is based on the last day in February, referred to as the Doomsday.