14th  Top calendars 
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 weeknumbering years have a year numbering which is approximately the same as the Gregorian years, but not exactly (see below). An ISO weeknumbering year has 52 or 53 full weeks (364 or 371 days). The extra week is here called a leap week (ISO 8601 does not use the term).
A date is specified by the ISO weeknumbering 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, 2006W527 (or in compact form 2006W527) is the Sunday of the 52nd week of 2006. In the Gregorian system this day is called 31 December 2006.
The system has a 400year cycle of 146 097 days (20 871 weeks), with an average year length of exactly 365.2425 days, just like the Gregorian calendar. In every 400 years there are 71 years with 53 weeks.
The first week of a year is the week that contains the first Thursday of a year.
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The ISO weeknumbering 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 weeknumbering year number is always equal to the Gregorian year number.
Mutually equivalent definitions for week 01 are:
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 weeknumbering year is the week before week 01; in accordance with the symmetry of the definition, equivalent definitions are:
<< January 2010 >>  
Wk  Mo  Tu  We  Th  Fr  Sa  Su 
(53)  28  29  30  31  1  2  3 
(1)  4  5  6  7  8  9  10 
(2)  11  12  13  14  15  16  17 
(3)  18  19  20  21  22  23  24 
(4)  25  26  27  28  29  30  31 
The 53week ISO weeknumbering year years can be described by any of the following equivalent definitions:
All other weeknumbering years have 52 weeks.
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.
Overview of dates with a fixed week number in any year other than a leap year starting on Thursday:
Month  Dates  Week numbers 

January  4, 11, 18, 25  0104 
February  1, 8, 15, 22  0508 
March  1, 8, 15, 22, 29  0913 
April  5, 12, 19, 26  1417 
May  3, 10, 17, 24, 31  1822 
June  7, 14, 21, 28  2326 
July  5, 12, 19, 26  2730 
August  2, 9, 16, 23, 30  3135 
September  6, 13, 20, 27  3639 
October  4, 11, 18, 25  4043 
November  1, 8, 15, 22, 29  4448 
December  6, 13, 20, 27  4952 
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.
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 spring equinoxes on 2004W127 and 2010W117.
It does not replace the Gregorian calendar, which it uses to define the new year day (Week 1 Day 1). However, it could be defined without reference to Gregorian. One needs at most a defined start and a table of yearlengths over the 400year cycle.
Not all parts of the world have a work week that begins with Monday. For example, in some Muslim countries, the work week may begin on Saturday while in other Muslim countries it may begin on Sunday.
There are 13 28year subcycles with 5 leap years (53week 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:
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 nonleap years, so 70 ISO years are 2 days shorter, and 259 are 1 day shorter.
One can calculate the week number of any date given its ordinal date (i.e. position within the year) and its day of the week. If one does not know the ordinal date, it can be computed by any of several methods; perhaps the most direct is a table such as the following.
To the day of: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Add: 0 31 59 90 120 151 181 212 243 273 304 334 For leap years: 0 31 60 91 121 152 182 213 244 274 305 335
Method: Using ISO weekday numbers (running from 1 for Monday to 7 for Sunday), subtract the weekday from the ordinal date, then add 10. Divide the result by 7. Ignore the remainder; the quotient equals the week number. If the week number thus obtained equals 0, it means that the given date belongs to the preceding (weekbased) year. If a week number of 53 is obtained, one must check that the date is not actually in week 1 of the following year.
Example: Friday, September 26, 2008
This method requires that one know the weekday of January 4 of the year in question. ^{[1]} Add 3 to the number of this weekday, giving a correction to be used for dates within this year.
Method: Multiply the week number by 7, then add the weekday. From this sum subtract the correction for the year. The result is the ordinal date, which can be converted into a calendar date using the table in the preceding section. If the ordinal date thus obtained is zero or negative, the date belongs to the previous calendar year; if greater than the number of days in the year, to the following year.
Example: year 2008, week 39, Friday (day 5)
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.



