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The ISO week date system is a leap week calendar system that is part of the ISO 8601 date and time standard. The system is used (mainly) in government and business for fiscal years, as well as in timekeeping.

The system uses the same cycle of 7 weekdays as the Gregorian calendar. Weeks start with Monday. ISO years have a year numbering which is approximately the same as the Gregorian years, but not exactly (see below). An ISO year has 52 or 53 full weeks (364 or 371 days). The extra week is called a leap week, a year with such a week a leap year.

A date is specified by the ISO year in the format YYYY, a week number in the format ww prefixed by the letter W, and the weekday number, a digit d from 1 through 7, beginning with Monday and ending with Sunday. For example, 2006-W52-7 (or in its most compact form 06W527) is the Sunday of the 52nd week of 2006. In the Gregorian system this day is called December 31, 2006.

The system has a 400-year cycle of 146,097 days (20,871 weeks), with an average year length of exactly 365.2425 days, just like the Gregorian calendar. Since non-leap years have 52 weeks, in every 400 years there are 71 leap years.

Relation with the Gregorian calendar[edit | edit source]

The ISO year number deviates from the number of the Gregorian year on, if applicable, a Friday, Saturday, and Sunday, or a Saturday and Sunday, or just a Sunday, at the start of the Gregorian year (which are at the end of the previous ISO year) and a Monday, Tuesday and Wednesday, or a Monday and Tuesday, or just a Monday, at the end of the Gregorian year (which are in week 01 of the next ISO year). In the period 4 January–28 December and on all Thursdays the ISO year number is always equal to the Gregorian year number.

Mutually equivalent definitions for week 01 are:

  • the week with the year's first Thursday in it
  • the week with the year's first working day in it (if Saturdays, Sundays, and 1 January are no working days)
  • the week with January 4 in it
  • the first week with the majority (four or more) of its days in the starting year
  • the week starting with the Monday in the period 29 December - 4 January
  • the week with the Thursday in the period 1 - 7 January
  • If 1 January is on a Monday, Tuesday, Wednesday or Thursday, it is in week 01. If 1 January is on a Friday, Saturday or Sunday, it is in week 52 or 53 of the previous year.

Note that while most definitions are symmetric with respect to time reversal, one definition in terms of working days happens to be equivalent.

The last week of the ISO year is the week before week 01; in accordance with the symmetry of the definition, equivalent definitions are:

  • the week with the year's last Thursday in it
  • the week with December 28 in it
  • the last week with the majority (four or more) of its days in the ending year
  • the week starting with the Monday in the period 22 - 28 December
  • the week with the Thursday in the period 25 - 31 December
  • the week ending with the Sunday in the period 28 December - 3 January
  • If 31 December is on a Monday, Tuesday, or Wednesday, it is in week 01, otherwise in week 52 or 53.

The following years have 53 weeks:

  • years starting with Thursday
  • leap years starting with Wednesday

Examples[edit | edit source]

  • 2005-01-01 is 2004-W53-6
  • 2005-01-02 is 2004-W53-7
  • 2005-12-31 is 2005-W52-6
  • 2007-01-01 is 2007-W01-1 (both years 2007 start with the same day)
  • 2007-12-30 is 2007-W52-7
  • 2007-12-31 is 2008-W01-1
  • 2008-01-01 is 2008-W01-2 (Gregorian year 2008 is a leap year, ISO year 2008 is 2 days shorter: 1 day longer at the start, 3 days shorter at the end)
  • 2008-12-29 is 2009-W01-1
  • 2008-12-31 is 2009-W01-3
  • 2009-01-01 is 2009-W01-4
  • 2009-12-31 is 2009-W53-4 (ISO year 2009 is a leap year, extending the Gregorian year 2009, which starts and ends with Thursday, at both ends with three days)
  • 2010-01-03 is 2009-W53-7

Examples where the ISO year is three days into the next Gregorian year[edit | edit source]

  • "{{ISOWEEKDATE|2009|12|31}}" gives "2009-W53-4" [1]
  • "{{ISOWEEKDATE|2010|1|1}}" gives "2009-W53-5" [2]
  • "{{ISOWEEKDATE|2010|1|2}}" gives "2009-W53-6" [3]
  • "{{ISOWEEKDATE|2010|1|3}}" gives "2009-W53-7" [4]
  • "{{ISOWEEKDATE|2010|1|4}}" gives "2010-W01-1" [5]

Examples where the ISO year is three days into the previous Gregorian year[edit | edit source]

  • "{{ISOWEEKDATE|2008|12|28}}" gives "2008-W52-7" [6]
  • "{{ISOWEEKDATE|2008|12|29}}" gives "2009-W01-1" [7]
  • "{{ISOWEEKDATE|2008|12|30}}" gives "2009-W01-2" [8]
  • "{{ISOWEEKDATE|2008|12|31}}" gives "2009-W01-3" [9]
  • "{{ISOWEEKDATE|2009|1|1}}" gives "2009-W01-4" [10]

The system does not need the concept of month and is not well connected with the Gregorian system of months: some months January and December are divided over two ISO years.

Week number[edit | edit source]

Dates with a fixed week number in every year other than a leap year starting on Thursday (DC)
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
Jan04 Jan11 Jan18 Jan25 Feb01 Feb08 Feb15 Feb22 Mar01 Mar08 Mar15 Mar22 Mar29 Apr05 Apr12 Apr19 Apr26 May03 May10 May17 May24 May31 Jun07 Jun14 Jun21 Jun28 Jul05 Jul12 Jul19 Jul26 Aug02 Aug09 Aug16 Aug23 Aug30 Sep06 Sep13 Sep20 Sep27 Oct04 Oct11 Oct18 Oct25 Nov01 Nov08 Nov15 Nov22 Nov29 Dec06 Dec13 Dec20 Dec27

The day of the week for these days are related to Doomsday because for any year, the Doomsday is the day of the week that the last day of February falls on. These dates are one day after the Doomsdays, except that in January and February of leap years the dates themselves are Doomsdays. In leap years the week number is the rank number of its Doomsday.

All other month dates can fall in one of two weeks, except for 29 December through 2 January which can be in W52, W53 or W01, i.e. either in the first week of the new year or the last week of the old year, which can have two different designations.


Dates of ISO weeks in common years
Type Jan01 Jan02 Jan03 Jan04 Jan05 Jan06 Jan07 Jan08 Jan09 Jan10 Jan11 Jan12 Jan13 Jan14 Jan15 Jan16 Jan17 Jan18 Jan19 Jan20 Jan21 Jan22 Jan23 Jan24 Jan25 Jan26 Jan27 Jan28 Jan29 Jan30 Jan31 Feb01 Feb02 Feb03 Feb04 Feb05 Feb06 Feb07 Feb08 Feb09 Feb10 Feb11 Feb12 Feb13 Feb14 Feb15 Feb16 Feb17 Feb18 Feb19 Feb20 Feb21 Feb22 Feb23 Feb24 Feb25 Feb26 Feb27 Feb28 Mar01 Mar02 Mar03 Mar04 Mar05 Mar06 Mar07 Mar08 Mar09 Mar10 Mar11 Mar12 Mar13 Mar14 Mar15 Mar16 Mar17 Mar18 Mar19 Mar20 Mar21 Mar22 Mar23 Mar24 Mar25 Mar26 Mar27 Mar28 Mar29 Mar30 Mar31 Apr01 Apr02 Apr03 Apr04 Apr05 Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 Apr14 Apr15 Apr16 Apr17 Apr18 Apr19 Apr20 Apr21 Apr22 Apr23 Apr24 Apr25 Apr26 Apr27 Apr28 Apr29 Apr30 May01 May02 May03 May04 May05 May06 May07 May08 May09 May10 May11 May12 May13 May14 May15 May16 May17 May18 May19 May20 May21 May22 May23 May24 May25 May26 May27 May28 May29 May30 May31 Jun01 Jun02 Jun03 Jun04 Jun05 Jun06 Jun07 Jun08 Jun09 Jun10 Jun11 Jun12 Jun13 Jun14 Jun15 Jun16 Jun17 Jun18 Jun19 Jun20 Jun21 Jun22 Jun23 Jun24 Jun25 Jun26 Jun27 Jun28 Jun29 Jun30 Jul01 Jul02 Jul03 Jul04 Jul05 Jul06 Jul07 Jul08 Jul09 Jul10 Jul11 Jul12 Jul13 Jul14 Jul15 Jul16 Jul17 Jul18 Jul19 Jul20 Jul21 Jul22 Jul23 Jul24 Jul25 Jul26 Jul27 Jul28 Jul29 Jul30 Jul31 Aug01 Aug02 Aug03 Aug04 Aug05 Aug06 Aug07 Aug08 Aug09 Aug10 Aug11 Aug12 Aug13 Aug14 Aug15 Aug16 Aug17 Aug18 Aug19 Aug20 Aug21 Aug22 Aug23 Aug24 Aug25 Aug26 Aug27 Aug28 Aug29 Aug30 Aug31 Sep01 Sep02 Sep03 Sep04 Sep05 Sep06 Sep07 Sep08 Sep09 Sep10 Sep11 Sep12 Sep13 Sep14 Sep15 Sep16 Sep17 Sep18 Sep19 Sep20 Sep21 Sep22 Sep23 Sep24 Sep25 Sep26 Sep27 Sep28 Sep29 Sep30 Oct01 Oct02 Oct03 Oct04 Oct05 Oct06 Oct07 Oct08 Oct09 Oct10 Oct11 Oct12 Oct13 Oct14 Oct15 Oct16 Oct17 Oct18 Oct19 Oct20 Oct21 Oct22 Oct23 Oct24 Oct25 Oct26 Oct27 Oct28 Oct29 Oct30 Oct31 Nov01 Nov02 Nov03 Nov04 Nov05 Nov06 Nov07 Nov08 Nov09 Nov10 Nov11 Nov12 Nov13 Nov14 Nov15 Nov16 Nov17 Nov18 Nov19 Nov20 Nov21 Nov22 Nov23 Nov24 Nov25 Nov26 Nov27 Nov28 Nov29 Nov30 Dec01 Dec02 Dec03 Dec04 Dec05 Dec06 Dec07 Dec08 Dec09 Dec10 Dec11 Dec12 Dec13 Dec14 Dec15 Dec16 Dec17 Dec18 Dec19 Dec20 Dec21 Dec22 Dec23 Dec24 Dec25 Dec26 Dec27 Dec28 Dec29 Dec30 Dec31
A W52 W−01 W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01
B/B* W52/3 W−01 W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01
C W53 W−01 W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01
D W01 W−53 W02 W−52 W03 W−51 W04 W−50 W05 W−49 W06 W−48 W07 W−47 W08 W−46 W09 W−45 W10 W−44 W11 W−43 W12 W−42 W13 W−41 W14 W−40 W15 W−39 W16 W−38 W17 W−37 W18 W−36 W19 W−35 W20 W−34 W21 W−33 W22 W−32 W23 W−31 W24 W−30 W25 W−29 W26 W−28 W27 W−27 W28 W−26 W29 W−25 W30 W−24 W31 W−23 W32 W−22 W33 W−21 W34 W−20 W35 W−19 W36 W−18 W37 W−17 W38 W−16 W39 W−15 W40 W−14 W41 W−13 W42 W−12 W43 W−11 W44 W−10 W45 W−09 W46 W−08 W47 W−07 W48 W−06 W49 W−05 W50 W−04 W51 W−03 W52 W−02 W53 W−01
E W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01 W01 W−52
F W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01 W01 W−52
G W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01 W01 W−52
Dates of ISO weeks in leap years
Type Jan01 Jan02 Jan03 Jan04 Jan05 Jan06 Jan07 Jan08 Jan09 Jan10 Jan11 Jan12 Jan13 Jan14 Jan15 Jan16 Jan17 Jan18 Jan19 Jan20 Jan21 Jan22 Jan23 Jan24 Jan25 Jan26 Jan27 Jan28 Jan29 Jan30 Jan31 Feb01 Feb02 Feb03 Feb04 Feb05 Feb06 Feb07 Feb08 Feb09 Feb10 Feb11 Feb12 Feb13 Feb14 Feb15 Feb16 Feb17 Feb18 Feb19 Feb20 Feb21 Feb22 Feb23 Feb24 Feb25 Feb26 Feb27 Feb28 Feb29 Mar01 Mar02 Mar03 Mar04 Mar05 Mar06 Mar07 Mar08 Mar09 Mar10 Mar11 Mar12 Mar13 Mar14 Mar15 Mar16 Mar17 Mar18 Mar19 Mar20 Mar21 Mar22 Mar23 Mar24 Mar25 Mar26 Mar27 Mar28 Mar29 Mar30 Mar31 Apr01 Apr02 Apr03 Apr04 Apr05 Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 Apr14 Apr15 Apr16 Apr17 Apr18 Apr19 Apr20 Apr21 Apr22 Apr23 Apr24 Apr25 Apr26 Apr27 Apr28 Apr29 Apr30 May01 May02 May03 May04 May05 May06 May07 May08 May09 May10 May11 May12 May13 May14 May15 May16 May17 May18 May19 May20 May21 May22 May23 May24 May25 May26 May27 May28 May29 May30 May31 Jun01 Jun02 Jun03 Jun04 Jun05 Jun06 Jun07 Jun08 Jun09 Jun10 Jun11 Jun12 Jun13 Jun14 Jun15 Jun16 Jun17 Jun18 Jun19 Jun20 Jun21 Jun22 Jun23 Jun24 Jun25 Jun26 Jun27 Jun28 Jun29 Jun30 Jul01 Jul02 Jul03 Jul04 Jul05 Jul06 Jul07 Jul08 Jul09 Jul10 Jul11 Jul12 Jul13 Jul14 Jul15 Jul16 Jul17 Jul18 Jul19 Jul20 Jul21 Jul22 Jul23 Jul24 Jul25 Jul26 Jul27 Jul28 Jul29 Jul30 Jul31 Aug01 Aug02 Aug03 Aug04 Aug05 Aug06 Aug07 Aug08 Aug09 Aug10 Aug11 Aug12 Aug13 Aug14 Aug15 Aug16 Aug17 Aug18 Aug19 Aug20 Aug21 Aug22 Aug23 Aug24 Aug25 Aug26 Aug27 Aug28 Aug29 Aug30 Aug31 Sep01 Sep02 Sep03 Sep04 Sep05 Sep06 Sep07 Sep08 Sep09 Sep10 Sep11 Sep12 Sep13 Sep14 Sep15 Sep16 Sep17 Sep18 Sep19 Sep20 Sep21 Sep22 Sep23 Sep24 Sep25 Sep26 Sep27 Sep28 Sep29 Sep30 Oct01 Oct02 Oct03 Oct04 Oct05 Oct06 Oct07 Oct08 Oct09 Oct10 Oct11 Oct12 Oct13 Oct14 Oct15 Oct16 Oct17 Oct18 Oct19 Oct20 Oct21 Oct22 Oct23 Oct24 Oct25 Oct26 Oct27 Oct28 Oct29 Oct30 Oct31 Nov01 Nov02 Nov03 Nov04 Nov05 Nov06 Nov07 Nov08 Nov09 Nov10 Nov11 Nov12 Nov13 Nov14 Nov15 Nov16 Nov17 Nov18 Nov19 Nov20 Nov21 Nov22 Nov23 Nov24 Nov25 Nov26 Nov27 Nov28 Nov29 Nov30 Dec01 Dec02 Dec03 Dec04 Dec05 Dec06 Dec07 Dec08 Dec09 Dec10 Dec11 Dec12 Dec13 Dec14 Dec15 Dec16 Dec17 Dec18 Dec19 Dec20 Dec21 Dec22 Dec23 Dec24 Dec25 Dec26 Dec27 Dec28 Dec29 Dec30 Dec31
AG W52 W−01 W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01 W01 W−52
BA W52 W−01 W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01
CB W53 W−01 W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01
DC W01 W−53 W02 W−52 W03 W−51 W04 W−50 W05 W−49 W06 W−48 W07 W−47 W08 W−46 W09 W−45 W10 W−44 W11 W−43 W12 W−42 W13 W−41 W14 W−40 W15 W−39 W16 W−38 W17 W−37 W18 W−36 W19 W−35 W20 W−34 W21 W−33 W22 W−32 W23 W−31 W24 W−30 W25 W−29 W26 W−28 W27 W−27 W28 W−26 W29 W−25 W30 W−24 W31 W−23 W32 W−22 W33 W−21 W34 W−20 W35 W−19 W36 W−18 W37 W−17 W38 W−16 W39 W−15 W40 W−14 W41 W−13 W42 W−12 W43 W−11 W44 W−10 W45 W−09 W46 W−08 W47 W−07 W48 W−06 W49 W−05 W50 W−04 W51 W−03 W52 W−02 W53 W−01
ED W01 W−53 W02 W−52 W03 W−51 W04 W−50 W05 W−49 W06 W−48 W07 W−47 W08 W−46 W09 W−45 W10 W−44 W11 W−43 W12 W−42 W13 W−41 W14 W−40 W15 W−39 W16 W−38 W17 W−37 W18 W−36 W19 W−35 W20 W−34 W21 W−33 W22 W−32 W23 W−31 W24 W−30 W25 W−29 W26 W−28 W27 W−27 W28 W−26 W29 W−25 W30 W−24 W31 W−23 W32 W−22 W33 W−21 W34 W−20 W35 W−19 W36 W−18 W37 W−17 W38 W−16 W39 W−15 W40 W−14 W41 W−13 W42 W−12 W43 W−11 W44 W−10 W45 W−09 W46 W−08 W47 W−07 W48 W−06 W49 W−05 W50 W−04 W51 W−03 W52 W−02 W53 W−01
FE W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01 W01 W−52
GF W01 W−52 W02 W−51 W03 W−50 W04 W−49 W05 W−48 W06 W−47 W07 W−46 W08 W−45 W09 W−44 W10 W−43 W11 W−42 W12 W−41 W13 W−40 W14 W−39 W15 W−38 W16 W−37 W17 W−36 W18 W−35 W19 W−34 W20 W−33 W21 W−32 W22 W−31 W23 W−30 W24 W−29 W25 W−28 W26 W−27 W27 W−26 W28 W−25 W29 W−24 W30 W−23 W31 W−22 W32 W−21 W33 W−20 W34 W−19 W35 W−18 W36 W−17 W37 W−16 W38 W−15 W39 W−14 W40 W−13 W41 W−12 W42 W−11 W43 W−10 W44 W−09 W45 W−08 W46 W−07 W47 W−06 W48 W−05 W49 W−04 W50 W−03 W51 W−02 W52 W−01 W01 W−52

Months[edit | edit source]

The assignment of weeks to months does not form part of the ISO standard. It only assigns weeks to years and thereby implicitly to the months of January and December. If week months were defined to begin on the nearest Monday to the first day of the Gregorian month, or, in other words, weeks belonged to the calendar month the majority of their days (and thus their Thursday) are in, then seemingly irregular patterns would be the result.

Weeks per month, year and quarter depending on the weekday of 1 January
1 Jan: Mon Tue Wed Thu Fri Sat Sun
01 4 5 5 5 4 4 4
02 4+ 4 4 4 4 4 4
03 5– 4 4 4 4+ 5 5
04 4 4 4+ 5 5– 4 4
05 5 5 5– 4 4 4 4+
06 4 4 4 4 4+ 5 5–
07 4 4+ 5 5 5– 4 4
08 5 5– 4 4 4 4+ 5
09 4 4 4 4+ 5 5– 4
10 4+ 5 5 5– 4 4 4
11 5– 4 4 4 4 4+ 5
12 4 4 4+ 5 5 5– 4
Year 52 52 52+ 53 52 52 52
Q1 13 13 13 13 12+ 13 13
Q2 13 13 13 13 13 13 13
Q3 13 13 13 13+ 14– 13 13
Q4 13 13 13+ 14 13 13 13


Many ordinal weeks would always be in the same month, but some would fluctuate between two months.

Weeks that change their month depending on the weekday of 1 January or Dominical Letter
Jan01 Friday Saturday Sunday Monday Tuesday Wednesday Thursday
DL C CB B BA A AG G GF F FE E ED D DC
W05 February January
W09 March February
W13 April March
W18 May April
W22 June May
W26 July June
W31 August July
W35 September August
W40 October Sept.
W44 November October
W48 December November
W53 December

Months could also be assigned regularly to the weeks, but the months of such a mapping will deviate from the Gregorian months by more days. See Week & Month Calendar for an example.

Advantages[edit | edit source]

  • The date directly tells the weekday.
  • All years start with a Monday and end with a Sunday.
  • When used by itself without using the concept of month, all years are the same except that leap years have a leap week at the end.
  • The weeks are the same as in the Gregorian calendar.

Disadvantages[edit | edit source]

Each equinox and solstice varies over a range of at least seven days. This is because each equinox and solstice may occur any day of the week and hence on at least seven different ISO week dates. For example, there are summer solstices on 2004-W12-7 and 2010-W11-7.

It cannot replace the Gregorian calendar, because it relies on it to define the new year day (Week 1 Day 1).

Leap year cycle[edit | edit source]

The three types of long or leap-week year are D (Thursday–Thursday), DC (Thursday–Friday) and ED (Wednesday–Thursday).

Dominical letters and Doomsdays
DL Doomsday 31 December
A, BA Tuesday Sunday
B, CB Monday Saturday
C, DC Sunday Friday
D, ED Saturday Thursday
E, FE Friday Wednesday
F, GF Thursday Tuesday
G, AG Wednesday Monday
400-year cycle of years by dominical letter, grouped by Olympiad, long years highlighted
Years 16xy 17xy 18xy 19xy
20xy 21xy 22xy 23xy
00 BA C E G
01 29 57 85 G B D F
02 30 58 86 F A C E
03 31 59 87 E G B D
04 32 60 88 DC FE AG CB
05 33 61 89 B D F A
06 34 62 90 A C E G
07 35 63 91 G B D F
08 36 64 92 FE AG CB ED
09 37 65 93 D F A C
10 38 66 94 C E G B
11 39 67 95 B D F A
12 40 68 96 AG CB ED GF
13 41 69 97 F A C E
14 42 70 98 E G B D
15 43 71 99 D F A C
16 72 44 CB ED GF BA
73 45 17 A C E G
74 46 18 G B D F
75 47 19 F A C E
76 48 20 ED GF BA DC
77 49 21 C E G B
78 50 22 B D F A
79 51 23 A C E G
80 52 24 GF BA DC FE
81 53 25 E G B D
82 54 26 D F A C
83 55 27 C E G B
84 56 28 BA DC FE AG
Long years per 400-year cycle
(28-year subcycles arranged horizontally)
DC D D ED D
+004 +009 +015 +020 +026
+032 +037 +043 +048 +054
+060 +065 +071 +076 +082
+088 +093 +099
+105 +111 +116 +122
+128 +133 +139 +144 +150
+156 +161 +167 +172 +178
+184 +189 +195
+201 +207 +212 +218
+224 +229 +235 +240 +246
+252 +257 +263 +268 +274
+280 +285 +291 +296
+303 +308 +314
+320 +325 +331 +336 +342
+348 +353 +359 +364 +370
+376 +381 +387 +392 +398

There are 13 Julian 28-year subcycles with 5 leap years each, and 6 remaining leap years in the remaining 36 years (the absence of leap days in the Gregorian calendar in 2100, 2200, and 2300 interrupts the subcycles). The leap years are 5 years apart 27 times, 6 years 43 times and 7 years once. (A slightly more even distribution would be possible: 5 years apart 26 times and 6 years 45 times.)

The Gregorian years corresponding to the 71 long, ISO leap-week years can be subdivided as follows:

Thus 27 ISO years are 5 days longer than the corresponding Gregorian year, and 44 are 6 days longer. Of the other 329 Gregorian years (neither starting nor ending with Thursday), 70 are Gregorian leap years, and 259 are non-leap years, so 70 week years are 2 days shorter, and 259 are 1 day shorter than their corresponding month years.

Alternative leap year rules[edit | edit source]

Karl Palmen[edit | edit source]

The best leap week calendars to convert to Gregorian would be those based on the ISO week or a similar week numbering scheme. Karl Palmen thought of another that interlocks with the 28-year subcycle that such calendars have, which is interrupted by a dropped leap day in three out of four century years.

+002   +008   +014   +020   +026
+030   +036   +042   +048   +054
+058   +064   +070   +076   +082
+086   +092   +098   +104   +110   +116   +122
+126   +132   +138   +144   +150
+154   +160   +166   +172   +178
+182   +188   +194   +200   +206   +212   +218
+222   +228   +234   +240   +246
+250   +256   +262   +268   +274
+278   +284   +290   +296   +302   +308   +314
+318   +324   +330   +336   +342
+346   +352   +358   +364   +370
+374   +380   +386   +392   +398

In each row, the leap years are six years apart and the first of each row is four years after the last of the previous row. Each row covers 28 years unless it contains a dropped Gregorian leap day, in which case it covers 40 years. The rows are synchronized to the 28-year cycles that occur in any week-number calendar like ISO week date. In particular, the 2nd year of each row is a leap year starting on Tuesday (GF). A simpler leap week rule would have rows alternating between 28 and 34, but this would be harder to convert to and from the Gregorian calendar.

The following variation, offset by 12 years, matches all even-numbered years with 53 ISO weeks.[1] The italic years are a year later than ISO and the underlined years are a year early. Gregorian leap years are shown in bold.

+014   +020   +026   +032   +038
+042   +048   +054   +060   +066
+070   +076   +082   +088   +094   +100   +106
+110   +116   +122   +128   +134
+138   +144   +150   +156   +162
+166   +172   +178   +184   +190
+194   +200   +206   +212   +218   +224   +230
+234   +240   +246   +252   +258
+262   +268   +274   +280   +286
+290   +296   +302   +308   +314   +320   +326
+330   +336   +342   +348   +354
+358   +364   +370   +376   +382
+386   +392   +398   +004   +010

As with Karl Palmen's original proposal, every row has leap-week years six years apart. The first year of each row is four years after the previous. Each row has five, unless it spans a dropped leap year, then it has seven. Unlike the original proposal, it is not symmetrical.

To get a leap week rule where every leap week occurs in a Gregorian leap year and furthermore every Gregorian leap year that also has 53 ISO weeks is included among them, take the previously mentioned proposal, make the leap weeks in the 1st and 3rd columns occur two years later, the leap week in the 5th and 7th column occur two years earlier. Then move +100 to +096 and +200 to +204.

+016   +020   ---   +028   +032   +036   ---
+044   +048   ---   +056   +060   +064   ---
+072   +076   ---   +084   +088   +092   +096   <<<   +104   ---
+112   +116   ---   +124   +128   +132   ---
+138   +144   ---   +152   +156   +160   ---
+166   +172   ---   +180   +184   +188   ---
+196    >>>  +204   +208   +212   +216   ---   +224   +228   ---
+236   +240   ---   +248   +252   +256   ---
+264   +268   ---   +276   +280   +284   ---
+292   +296   ---   +304   +308   +312   ---   +320   +324   ---
+332   +336   ---   +344   +348   +352   ---
+360   +364   ---   +372   +376   +380   ---
+388   +392   ---   +000   +004   +008   ---

The Gregorian leap years with 53 ISO weeks remain in bold. Other changes can be made to the years not shown in bold. For example, the 4th row could be changed to

+108   ---   +116   +120   ---   +128   +132   ---

Christoph Päper[edit | edit source]

Constraints:

  • Long leap year: Every year that has a leap week also has a leap day. 
  • Olympiad: The number of each leap year is divisible by four (as established over two millennia ago).

This way, years with dominical letter D never occur, just DC and ED. Since we need 97 leap days and just 71 leap weeks, there are 26 leap days per cycle in short years (i.e. ones without a 53rd week).

There are two distributions that are as even as possible under these constraints:

  • Round down
+000   +004   +008     –    +016   +020     –   
+028   +032   +036     –    +044   +048     –   
+056   +060   +064     *    +072   +076     –   
+084   +088   +092     –    +100   +104     –   
+112   +116   +120     –    +128   +132     –    +140   +144     –    
+152   +156   +160     –    +168   +172     –   
+180   +184   +188     –    +196   +200     *    
+208   +212   +216     –    +224   +228     –    
+236   +240   +244     –    +252   +256     –    +264   +268     –    
+276   +280   +284     –    +292   +296     –    
+304   +308   +312     –    +320   +324     *    
+332   +336   +340     –    +348   +352     –    
+360   +364   +368     –    +376   +380     –    +388   +392     –
  • Round up
  –    +020   +024     –    +032   +036   +040   
  –    +048   +052     –    +060   +064   +068
  *    +076   +080     –    +088   +092   +096   
  –    +104   +108     –    +116   +120   +124     –    +132   +136 
  –    +144   +148     –    +156   +160   +164 
  –    +172   +176     –    +184   +188   +192 
  *    +200   +204     –    +212   +216   +220 
  –    +228   +232     –    +240   +244   +248     –    +256   +260   
  –    +268   +272     –    +280   +284   +288   
  –    +296   +300     –    +308   +312   +316   
  –    +324   +328     *    +336   +340   +344   
  –    +352   +356     –    +364   +368   +372   
  –    +380   +384     –    +392   +396   +000     –    +008   +012

Rounding down matches 27, rounding up just 20 of the 71 long years according to ISO 8601.

In a final step, one would need to select three of the empty places, which do not contain a “leap+leap year” but are a Julian “leap-day year”, to have no leap day (like 100, 200 and 300 by Gregorian rules), e.g. – as marked above with asterisks – 068, 204 and 328 for round-down and 072, 196 and 332 for round-up.

Other week numbering systems[edit | edit source]

For an overview of week numbering systems see week number. The US system has weeks from Sunday through Saturday, and partial weeks at the beginning and the end of the year. An advantage is that no separate year numbering like the ISO year is needed, while correspondence of lexicographical order and chronological order is preserved.

External links[edit | edit source]

  1. List of ISO leap years Dick Henry – leap weeks are called Newton
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