This week numbering scheme was introduced earlier by the ISO with the standard ISO 2015:1976 (Numbering of Weeks) and was repealed on 1 June 1988 with the imminent introduction of ISO 8601. The calendar defined in the ISO standards 2015 and 8601 is commonly referred to as the “ISO calendar”.
The ISO calendar corresponds with the Gregorian calendar (sect. 3.2.1 on pp. 7-8) and uses the same year number but as its length is defined to be an integral number of weeks, its beginning can deviate up to a few days from 1 January and its end likewise can deviate up to a few days from 31 December. On average, however, it remains in step with the Gregorian calendar.
The week in the ISO calendar is defined (sect. 2.2.8 on p. 5) as a:
time interval of seven calendar days starting with a Monday [...] identified by its ordinal number within its calendar year.
The numbering of the ISO calendar weeks is defined (sect. 2.2.10 on p. 5) as:
[...] the first calendar week of a year is that one which includes the first Thursday of that year and [...] the last calendar week of a calendar year is the week immediately preceding the first calendar week of the next calendar year.
Another way of stating the above rule is that the first week of the ISO calendar year is the earliest week that contains at least four days of the month of January. Likewise, the last week of the ISO calendar year is the last week that contains at least four days of the month of December.
According to this rule the first week of the ISO calendar year can begin as late as 4 January and as early as 29 December of the previous year. Likewise, the last week of the ISO calendar year can end as early as 28 December and as late as 3 January of the following year. Examples of these extreme cases in the recent past are
| December 2014 | January 2015 | |||||||||||||||||||
| 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Mo | Tu | We | Th | Fr | Sa | Su | Mo | Tu | We | Th | Fr | Sa | Su | Mo | Tu | We | Th | Fr | Sa | Su |
| ISO week 52 (2014) | ISO week 01 (2015) | ISO week 02 (2015) | ||||||||||||||||||
and
| December 2009 | January 2010 | |||||||||||||||||||
| 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mo | Tu | We | Th | Fr | Sa | Su | Mo | Tu | We | Th | Fr | Sa | Su | Mo | Tu | We | Th | Fr | Sa | Su |
| ISO week 52 (2009) | ISO week 53 (2009) | ISO week 01 (2010) | ||||||||||||||||||
As Thursday is the “middle day” of the ISO week, each Thursday in a Gregorian calendar year belongs to the same ISO calendar year. Thus, if a Gregorian year contains 52 Thursdays then the corresponding ISO calendar year has 52 weeks and if the Gregorian year contains 53 Thursdays then the corresponding ISO calendar year has 53 weeks.
The ISO week number of an arbitrary date and the day number in that week can be determined from several online calendar converters: