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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 calendarEdit
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
ExamplesEdit
- 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
"{{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
"{{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 numberEdit
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.
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 |
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A | W52 | 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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
B | W52 | 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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
B* | W53 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
C | W53 | 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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
D | 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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
E | 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 | W01 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
F | 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 | W01 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
G | 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 | W01 |
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 |
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AG | W52 | 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 | W01 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
BA | W52 | 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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
CB | W53 | 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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
ED | 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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
FE | 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 | W01 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
GF | 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 | W01 |
AdvantagesEdit
- 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.
DisadvantagesEdit
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 cycleEdit
The three types of week leap year are D, DC, and ED.
DL | Doomsday | 1 January |
---|---|---|
A or BA | Tuesday | Sunday |
B or CB | Monday | Saturday |
C or DC | Sunday | Friday |
D or ED | Saturday | Thursday |
E or FE | Friday | Wednesday |
F or GF | Thursday | Tuesday |
G or AG | Wednesday | Monday |
Centuries | 1600 | 1700 | 1800 | 1900 | |||
---|---|---|---|---|---|---|---|
2000 | 2100 | 2200 | 2300 | ||||
Years | |||||||
00 | BA | C | E | G | |||
85 | 57 | 29 | 01 | G | B | D | F |
86 | 58 | 30 | 02 | F | A | C | E |
87 | 59 | 31 | 03 | E | G | B | D |
88 | 60 | 32 | 04 | DC | FE | AG | CB |
89 | 61 | 33 | 05 | B | D | F | A |
90 | 62 | 34 | 06 | A | C | E | G |
91 | 63 | 35 | 07 | G | B | D | F |
92 | 64 | 36 | 08 | FE | AG | CB | ED |
93 | 65 | 37 | 09 | D | F | A | C |
94 | 66 | 38 | 10 | C | E | G | B |
95 | 67 | 39 | 11 | B | D | F | A |
96 | 68 | 40 | 12 | AG | CB | ED | GF |
97 | 69 | 41 | 13 | F | A | C | E |
98 | 70 | 42 | 14 | E | G | B | D |
99 | 71 | 43 | 15 | D | F | A | C |
72 | 44 | 16 | 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 | |
Years | |||||||
Centuries | 1600 | 1700 | 1800 | 1900 | |||
2000 | 2100 | 2200 | 2300 |
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 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 27 times 5 years apart, 43 times 6 years, and once 7 years. (A slightly more even distribution would be possible: 26 times 5 years apart, and 45 times 6 years.)
The Gregorian years corresponding to the 71 ISO leap years can be subdivided as follows:
- 27 Gregorian leap years:
- 13 leap years starting on Thursday – Doomsday is Sunday, dominical letter is DC.
- 14 leap years starting on Wednesday, hence ending with Thursday) – Doomsday is Saturday, dominical letter is ED.
- 44 common years starting, hence also ending, with Thursday – Doomsday is Saturday, dominical letter is D.
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 ISO years are 2 days shorter, and 259 are 1 day shorter.
Alternative leap year rules Edit
KARL PALMENEdit
The best leap week calendars to convert to Gregorian would be those based on the ISO week or a similar week numbering scheme. I thought of another that interlocks with 28-year cycle that such calendars have, which is interrupted by a dropped leap day.
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 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 synchronised 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 in the Gregorian calendar a leap year starting on Tuesday. A simpler leap week rule would have rows alternating between 28 and 34, but this would be harder to convert to/from the Gregorian calendar.
The following variation matches all even-numbered years with 53 ISO weeks. Red years are one year later than ISO and the blue 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 my original proposal every row has 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 my 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 amongst them. Take the previously mentioned proposal make the leap weeks in the first and third columns occur two years later, the leap week in the 5th and 7th column occur two years earlier. Then move 100 to 96 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 PÄPEREdit
- Every year that has a leap week, also has a leap day.
- Leap years are divisible by four.
There are 26 leap days per cycle in years without a 53rd week.
distribution as evenly as possible under these constraintsEdit
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:
000 – 008 012 – 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
The former matches 27, the latter just 20 of the 71 long years according to ISO 8601.
One would now need to select three of the empty places, which do not contain a “leap+leap year”, to remain empty for leap-day years, e.g. – as marked above with plus signs –
068, 204, 328
072, 196, 332
Other week numbering systemsEdit
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 linksEdit
- List of ISO leap years Dick Henry. - Here the leap weeks are called Newton
- The Mathematics of the ISO 8601 Calendar Robert H. van Gent
- A generic Excel Calendar with ISO Week numbers