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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.
The Gregorian calendar (like the earlier Julian calendar) employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days. 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 ...
The resulting pattern would be irregular. There would be 4 months of 5 weeks per normal, 52-week year, or 5 such months in a long, 53-week year. Although the days of a month (except February) always belong to 5 and sometimes 6 different weeks, there would never be 6 weeks belonging to a single month.
The ISO week date is an example of a leap week calendar that eliminate the month. 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 ...
[e] [f] Of these 400 years, 303 are regular years of 365 days and 97 are leap years of 366 days. A mean calendar year is 365 + 97 / 400 days = 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds.
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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.
While the ancient Germanic calendars were based on lunar months, the new Icelandic calendar introduced a purely solar reckoning, with a year having a fixed number of weeks (52 weeks or 364 days). This necessitated the introduction of "leap weeks" instead of the Julian leap days.