Leap week calendar

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
Day
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

• Leap Week Calendars, an article by Karl Palmen
• List of ISO leap years - here the leap weeks are called Newton