Leap week calendar

A leap week calendar is a calendar system with a whole number of weeks every year, and with every year starting on the same weekday. Most leap week calendars are proposed reforms to the civil calendar, but some - such as the ISO week number calendar - are simply conveniences for specific purposes.

The ISO calendar in question 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.

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, CCC&T as well as the ISO week dates.

Advantages

• 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. This avoids opposition from religious groups who object to interruption of the seven-weekday sequence.

Disadvantages

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.

If the added week is intercalary then people born during a leap week have birthday problems similar to those born on February 29th and furthermore about 1 in 294 days would belong to a leap week rather than about 1 in 1506 days that are February 29th.

In the Gregorian cycle, the fourth quarter accounting statistics may not be consistent over a string of years unless the number of leap weeks are known. For example, a leap week may occur in 6 common years with one leap year or it may occur in 5 common years with two leap years.

Year structures

Calendars with leap week at the end

Week	01							02							03							04							05							06							07							08							09							10							11							12							13							14							15							16							17							18							19							20							21							22							23							24							25							26							27							28							29							30							31							32							33							34							35							36							37							38							39							40							41							42							43							44							45							46							47							48							49							50							51							52							53
Day
13 months	1																												2																												3																												4																												5																												6																												7																												8																												9																												10																												11																												12																												13																												*
Bonavian	1																																			2																												3																												4																																			5																												6																												7																																			8																												9																												10																																			11																												12																												*
Sym454	1																												2																																			3																												4																												5																																			6																												7																												8																																			9																												10																												11																																			12																												*
30-31-30	1																														2																															3																														4																														5																															6																														7																														8																															9																														10																														11																															12																														*
Quarter	1																																																																2																																																																3																																																																4
Gregorian	Jan																															Feb																												Mar																															Apr																														May																															Jun																														Jul																															Aug																															Sep																														Oct																															Nov																														Dec
ISO: Mon	Jan																												Feb																												Mar							Mar																												Apr																												May																																			Jun																												Jul																												Aug																																			Sep																												Oct																												Nov							Nov																												Dec
ISO: Tue	Jan																																			Feb																												Mar																												Apr																												May																																			Jun																												Jul																												Aug							Aug																												Sep																												Oct																																			Nov																												Dec
ISO: Wed	Jan																																			Feb																												Mar																												Apr																												May							May																												Jun																												Jul																																			Aug																												Sep																												Oct																																			Nov																												Dec																												Dec
ISO: Thu	Jan																																			Feb																												Mar																												Apr																																			May																												Jun																												Jul							Jul																												Aug																												Sep																												Oct																																			Nov																												Dec
ISO: Fri	Jan																												Feb																												Mar																												Apr							Apr																												May																												Jun																												Jul																																			Aug																												Sep																												Sep							Oct																												Nov																												Dec
ISO: Sat	Jan																												Feb																												Mar																																			Apr																												May																												Jun																																			Jul																												Aug																												Sep							Sep																												Oct																												Nov																												Dec							Dec
ISO: Sun	Jan																												Feb																												Mar																																			Apr																												May																												Jun							Jun																												Jul																												Aug																																			Sep																												Oct																												Nov																																			Dec

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

The years according to ISO week date applied to months, i.e. a month has as many weeks as it has Thursdays, are shown depending on the weekday of 1 January, shaded weeks belong to the month they are labeled with in regular years and to the other adjoining one in leap years.

External links

• Leap Week Calendars
• List of ISO leap years - here the leap weeks are called Newton
• Hermetic Leap Week Calendar - a leap week calendar with four quarters of three months each, suitable for business purposes