ISO week date

Leap week calendar system

The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 (last revised in 2019) and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year. The Gregorian leap cycle, which has 97 leap days spread across 400 years, contains a whole number of weeks (20871). In every cycle there are 71 years with an additional 53rd week (corresponding to the Gregorian years that contain 53 Thursdays). An average year is exactly 52.1775 weeks long; months (1/12 year) average at exactly 4.348125 weeks/month. An ISO week numbering year (also called ISO year informally) has 52 or 53 full weeks. That is 364 or 371 days instead of the usual 365 or 366 days. These 53 week years occur on all years that have Thursday as the 1st of January and on leap years that start on Wednesday the 1st. The extra week is sometimes referred to as a leap week, although ISO 8601 does not use this term. Weeks start with Monday and end on Sunday. Each week's year is the Gregorian year in which the Thursday falls. The first week of the year, hence, always contains 4 January. ISO week year numbering therefore usually deviates by 1 from the Gregorian for some days close to 1 January. + Examples of contemporary dates around New Year's DayEnglish short ISO Sat 1 Jan 1977 1977 01 01 1976 W53 6Sun 2 Jan 1977 1977 01 02 1976 W53 7 Sat 31 Dec 1977 1977 12 31 1977 W52 6 Sun 1 Jan 1978 1978 01 01 1977 W52 7 Mon 2 Jan 1978 1978 01 02 1978 W01 1 Sun 31 Dec 1978 1978 12 31 1978 W52 7 Mon 1 Jan 1979 1979 01 01 1979 W01 1 Sun 30 Dec 1979 1979 12 30 1979 W52 7 Mon 31 Dec 1979 1979 12 31 1980 W01 1 Tue 1 Jan 1980 1980 01 01 1980 W01 2 Sun 28 Dec 1980 1980 12 28 1980 W52 7 Mon 29 Dec 1980 1980 12 29 1981 W01 1 Tue 30 Dec 1980 1980 12 30 1981 W01 2 Wed 31 Dec 1980 1980 12 31 1981 W01 3 Thu 1 Jan 1981 1981 01 01 1981 W01 4 Thu 31 Dec 1981 1981 12 31 1981 W53 4 Fri 1 Jan 1982 1982 01 01 1981 W53 5 Sat 2 Jan 1982 1982 01 02 1981 W53 6 Sun 3 Jan 1982 1982 01 03 1981 W53 7 Notes:

Both years 1979 start with the same day. 1980 is a leap year. 1980W is 2 days shorter:
1 day longer at the start,
3 days shorter at the end. 1981W begins three days before the end of 1980. 1981W has 53 weeks and ends three days into 1982. A precise date is specified by the ISO week numbering 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, the Gregorian date , corresponds to day number in the week number of , and is written as (in extended form) or (in compact form). The ISO year is slightly offset to the Gregorian year; for example, Monday 30 December 2019 in the Gregorian calendar is the first day of week 1 of 2020 in the ISO calendar, and is written as 2020 W01 1 or 2020W011.

The ISO week year number deviates from the Gregorian year number in one of three ways. The days differing are a Friday through 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 through 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 to 28 December the ISO week year number is always equal to the Gregorian year number. The same is true for every Thursday.

The ISO standard does not define any association of weeks to months. A date is either expressed with a month and day of the month, or with a week and day of the week, never a mix. Weeks are a prominent entity in accounting where annual statistics benefit from regularity throughout the years. Therefore, a fixed length of 13 weeks per quarter is usually chosen in practice. These quarters may then be subdivided into 5 + 4 + 4 weeks, 4 + 5 + 4 weeks or 4 + 4 + 5 weeks. The final quarter has 14 weeks in it when there are 53 weeks in the year. When it is necessary to allocate a week to a single month, the rule for first week of the year might be applied, although ISO 8601 1 does not consider this case explicitly. The resulting pattern would be irregular. There would be 4 months of 5 weeks per normal, 52 week year, or 5 such months in a long, 53 week year. They meet one of the following three criteria:

The first day of the month is a
Thursday and the month has 29 through 31 days. Wednesday and the month has 30 or 31 days. Tuesday and the month has 31 days, ending on a Thursday. Equivalently, the last day of the month is a
Thursday and it is not the 28th. Friday and it is not in February. Saturday and it is the 31st.

All weeks have exactly 7 days, i. e. there are no fractional weeks. Every week belongs to a single year, i. e. there are no ambiguous or double assigned weeks. The date directly tells the weekday. All week numbering years start with a Monday and end with a Sunday. When used by itself without using the concept of month, all week numbering years are the same except that some years have a week 53 at the end. The weeks are the same as used with the Gregorian calendar.

Solar astronomic phenomena, such as equinoxes and solstices, vary in the Gregorian calendar over a range spanning three days, over the course of each 400 year cycle, while the ISO Week Date calendar has a range spanning 9 days. For example, there are March equinoxes on 1920 W12 6 and 2077 W11 5 in UT. The year number of the ISO week very often differs from the Gregorian year number for dates close to 1 January. For example, 29 December 1986 is ISO 1987 W01 1, i. e., it is in year 1987 instead of 1986. A programming bug confusing these two year numbers is probably the cause of some Android users of Twitter being unable to log in around midnight of 29 December 2014 UTC. The ISO week calendar relies on the Gregorian calendar, which it augments, to define the new year day (Monday of week 01). As a result, extra weeks are spread across the 400 year cycle in a complex, seemingly random pattern. (However, a relatively simple algorithm to determine whether a year has 53 weeks from its ordinal number alone is shown under "Weeks per year" above.) Most calendar reform proposals using leap week designs strive to simplify and harmonize this pattern, some by choosing a different leap cycle (e. g. 293 years). Not all parts of the world consider the week to begin with Monday. For example, in some Muslim countries, the normal work week begins on Saturday, while in Israel it begins on Sunday. In much of the Americas, although the work week is usually defined to start on Monday, the calendar week is often considered to start on Sunday.

The US system has weeks from Sunday through Saturday, and partial weeks at the beginning and the end of the year, i. e. 52 full and 1 partial week of 1 or 2 days if the year starts on Sunday or ends on Saturday, 52 full and 2 single day weeks if a leap year starts on Saturday and ends on Sunday, otherwise 51 full and 2 partial weeks. An advantage is that no separate year numbering like the ISO year is needed. Correspondence of lexicographical order and chronological order is preserved (just like with the ISO year week weekday numbering), but partial weeks make some computations of weekly statistics or payments inaccurate at the end of December or the beginning of January or both. The US broadcast calendar designates the week containing 1 January (and starting Monday) as the first of the year, but otherwise works like ISO week numbering without partial weeks. Up to six days of the previous December may be part of the first week of the year. A mix of those, wherein weeks start Sunday and "containing 1 January" defines the first week, is used in US accounting, resulting in a system with years having also 52 or 53 weeks.