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A leap week calendar can take advantage of the 400-year cycle of the Gregorian calendar, as it has exactly 20,871 weeks: with 329 common years of 52 weeks plus 71 leap years of 53 weeks, a leap week calendar would synchronize with the Gregorian every 400 years since (329 × 52 + 71 × 53 = 20,871).
The common year of 365 days has 52 weeks and one day, hence a common year always begins and ends on the same day of the week (for example, January 1 and December 31 will fall on a Wednesday in 2025) and the year following a common year will start on the subsequent day of the week. In common years, February has exactly four weeks, so March ...
In every cycle there are 71 years with an additional 53rd week (corresponding to the Gregorian years that contain 53 Thursdays). An average year is exactly 52.1775 weeks long; months (1 ⁄ 12 year) average at exactly 4.348125 weeks/month. An ISO week-numbering year (also called ISO year informally) has 52 or 53 full weeks. That is 364 or 371 ...
A variation is the 52–53-week calendar. It is used by companies that want their fiscal year to always end on the same day of the week. Any day of the week may be used, and Saturday and Sunday are common because the business may more easily be closed for counting inventory and other end-of-year accounting activities.
In a Gregorian mean year, there are 365.2425 days, and thus exactly 52 + 71 ⁄ 400 or 52.1775 weeks (unlike the Julian year of 365.25 days or 52 + 5 ⁄ 28 ≈ 52.1786 weeks, which cannot be represented by a finite decimal expansion). There are exactly 20,871 weeks in 400 Gregorian years, so 7 January 1625 was a Tuesday just as was 7 January 2025.
Leap week calendar plans often restrict common years to 364 days, or 52 weeks, and expand leap years to 371 days, or 53 weeks. The added week may extend an existing month, or it may stand alone as an inserted seven-day month. The leap-week calendar may have been conceived originally by Rev. George M. Searle (1839-1918), around
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Unlike other perennial calendar reform proposals, such as the International Fixed Calendar and the World Calendar, it preserves the 7-day week by periodically intercalating an extra seven days to a common year of 52 weeks (364 days). In leap years, a one-week month called Pax would be inserted after Columbus.