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A leap week calendar is a reformed calendar system in which each year consists of a whole number of weeks. Leap years have one week (or some other whole number of weeks) added, so each year begins on the same day of the week.

The ISO week is an example of such a calendar. It is a variation of the Gregorian calendar that is used (mainly) in government and business for fiscal years, as well as in timekeeping. In this system a year (ISO year) has 52 or 53 full weeks (364 or 371 days).

Leap week calendars vary on whether the concept of month is preserved and whether the month (if preserved) has a whole number of weeks. A more exotic variant is the Monotonic Calendar in which the year has a whole number of weeks plus one day, which means it starts on a different day every passing year.

Most leap week calendars take advantage of the fact that 400 Gregorian calendar years have exactly 20,871 weeks, so with non-leap years of 52 weeks, this means there are 71 leap weeks every 400 years. These include the Pax Calendar and CCC&T, as well as the ISO week dates.

One proposed calendar (The Bonavian Civil Calendar) has 159 leap weeks in a 896-year cycle, which has a mean year of 365.2421875 days. Josef Suran's World Calendar with Leap Weeks has a 62 year cycle with 11 leap weeks, which has a mean year of 365.241935 days. The Symmetry454 Calendar and others have a 293-year cycle with 52 leap weeks equivalent to 294 years of 52 weeks.

Advantages of week calendars
Pro Con
  • There are no variations between day of week between years for a specific date.
  • The calendar starts on the same day and week every year.
  • Unlike the regular calendar, variations of years are limited to a possible addition of a leap week.
  • There are no fragments of weeks at the end of the year.
  • Unlike certain proposed calendar reforms such as the World Calendar and International Fixed Calendar, there is no need to modify the week.
  • A year with a leap week is at least 7 days longer than a year without a leap week, consequently the equinoxes and solstices must vary over 7 days, (i.e. ±3 of the average date), or even more, such as 19 days in the Pax Calendar.
  • The mere fact that the year may vary by seven days may be a stumbling block to adoption. Contracts, for example, set to expire within "five years" need to determine whether any leap years are included, making a year longer and perhaps changing the rent or mortgage or salary for that year.

Year Structures[]

Calendars with leap week at the end
ISO week W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W53
13 × 4 M01 M02 M03 M04 M05 M06 M07 M08 M09 M10 M11 M12 M13 *
5:4:4 01 02 03 04 05 06 07 08 09 10 11 12 *
4:5:4 01 02 03 04 05 06 07 08 09 10 11 12 *
30:31:30 01 02 03 04 05 06 07 08 09 10 11 12 *
Gregorian, Monotonic January February March April May June July August September October November December
Quarter 1 2 3 4

Note that the new years of the calendars shown need not be synchronised.

Leap Year Cycles[]

Leap-week cycles used in calendars in this wiki
Years Days Weeks Leap Weeks Mean Year Comments
28 10227 1461 5 365.25 Solar cycle
62 22645 3235 11 365.241935... World Calendar with Leap Weeks
293 107016 15288 52 365.24231... Symmetry454 Calendar
400 146097 20871 71 365.2425 Gregorian 400-year cycle
896 327257 46751 159 365.2421875 Bonavian Civil Calendar

External links[]