ISO Week Number Calculator (and the Two Conventions That Disagree)

ISO 8601 week number, week-based year, day of week and day of year — beside the Sunday-start spreadsheet convention and the broadcast calendar, because all three are in use. 1 January 2027 is 2026-W53-5 and also week 1 of 2027.

One day number, three ways of counting weeks

Three conventions, and what each one actually says

The cases where the conventions part company

52 or 53 ISO weeks, year by year

Two conventions, three answers, and 1 January in the middle

Two different week-numbering conventions are in daily use and they disagree, and there is a third that disagrees with both about which year a week belongs to. ISO 8601 says weeks begin on Monday and week 1 is the week containing the first Thursday of the year — equivalently, the week containing 4 January. The North American convention, which is what Excel’s WEEKNUM does if you give it no second argument, says weeks begin on Sunday and week 1 is the week containing 1 January. Microsoft documents these as System 2 and System 1 respectively. And the broadcast calendar used by American television says weeks run Monday to Sunday and a week belongs to the month its SUNDAY falls in. Put a date into all three and you can get three different answers.

The case that breaks spreadsheets is 1 January. Under ISO, if 1 January falls on a Friday, Saturday or Sunday, it is in the last week of the PREVIOUS ISO year. 1 January 2027 is a Friday, so it is 2026-W53-5 — week 53 of 2026, not week 1 of 2027. The Sunday-start convention calls the same day week 1 of 2027. If a report groups by ISO week and a spreadsheet groups by WEEKNUM, the first week of January will not line up, and neither system is broken. The same thing happens at the other end: 31 December 2026 is a Thursday and sits in 2026-W53, while 31 December 2021, a Friday, sits in 2021-W52 — but 1 January 2022, a Saturday, is also 2021-W52. ISO’s week-based year is a separate thing from the calendar year and the page prints it as such.

A year has 52 or 53 ISO weeks, and the rule everybody repeats is slightly wrong. The correct statement is that an ISO year is long — 53 weeks — if it starts or ends on a Thursday. The version usually given, “a common year starting on Thursday or a leap year starting on Wednesday”, is also correct; the version that drops the word common and says “a year starting Thursday or a leap year starting Wednesday” looks the same and fails thirteen times per 400-year cycle. R.H. van Gent’s analysis at Utrecht gives 71 long years in each 400-year cycle, and 2004 — a leap year that begins on a Thursday — is one of the cases the sloppy form misses. The long years between 2000 and 2040 are 2004, 2009, 2015, 2020, 2026, 2032, 2037. There is a neat reason the pattern repeats exactly every 400 years: the Gregorian cycle is 146,097 days, which is 20,871 weeks precisely, and 52 × 400 + 71 = 20,871. The Julian calendar had no such property.

The Sunday-start convention can produce a week 54, which nothing else does. If 1 January falls on a Saturday in a leap year, week 1 holds a single day and 31 December starts the fifty-fourth week. It happens in 1916, 1944, 1972, 2000, 2028 and so on, every 28 years. No ISO year ever exceeds 53 and no broadcast year does either. If you have ever seen “week 54” in a report, this is where it came from.

How the day of the week is found, with no loop and no lookup. Every date becomes a Julian Day Number — the running day count used in astronomy — and the weekday is that number modulo seven. That is exact and it involves no calendar rules at all. Zeller’s congruence and the Sakamoto method get the same answer with fewer operations and are the classical hand methods; the day-number route was chosen here because the page needs the day number anyway for the week arithmetic, and because a single integer is easier to verify than a formula with a table of month offsets in it. The leap rule is the Gregorian one: divisible by 4, except centuries, except multiples of 400 — so 1900 was not a leap year and 2000 was.

How this was checked. The ISO week date was computed for every single day from 1 January 1583 to 31 December 2500 — over 335,000 consecutive dates — and compared with Python’s datetime.date.isocalendar(), an independent implementation written in C, with no disagreements. The Sunday-start convention reproduces Microsoft’s own published worked example: 9 March 2012 returns 10 with weeks beginning Sunday and 11 with weeks beginning Monday. The published week date 1953-W31-7 for 2 August 1953, from Tøndering’s calendar FAQ, is reproduced. And the broadcast week number was shown identical to Excel’s Monday-start variant on every day of every year from 1900 to 2100 — a result that was not assumed but tested.

Range and scope. 1583 to 9999. ISO 8601 describes the Gregorian calendar, which began on 15 October 1582, and applying week dates to earlier years means agreeing first about which calendar you are in — so the page starts at the following January rather than extrapolating. The week-date rules moved to ISO 8601-1:2019 when the standard was split into parts; there is an Amendment 1 of 2022 carrying technical corrections, and a further edition in development. The standard itself is paywalled and is cited by number here, not reproduced. For converting an Islamic date, the Hijri to Gregorian converter. For clock time as a decimal fraction of an hour, the time to decimal hours converter.

Frequently asked questions

Related calculators

References

1. ISO 8601-1:2019, Date and time — Representations for information interchange — Part 1: Basic rules, edition 1, published February 2019, with Amendment 1:2022 (technical corrections). It replaced ISO 8601:2004, and a further edition is in development. The standard is paywalled and was not read; the number, title, date and replacement record above are from ISO’s own catalogue entry, which was fetched. Its week-date rule is reproduced from the free sources below and checked against 335,000 dates.
2. Tøndering, Claus. Frequently Asked Questions about Calendars, the ISO 8601 section (tondering.dk/claus/cal). “Week 1 of any year is the week that includes the first Thursday of that year”; “Monday is the first day of the week”; and the worked example this page checks against: 2 August 1953 is 1953-W31-7.
3. van Gent, R.H., Utrecht University. The Mathematics of the ISO 8601 Calendar — Long and Short Years. Fetched. Gives 71 long years of 53 weeks in each 400-year cycle of 20 871 weeks, and corrects the rule everybody repeats: a year is long if it begins on a Thursday, OR if it is a leap year beginning on a Wednesday — stated as “common year starting Thursday or leap year starting Wednesday” it misses leap years that start on a Thursday, of which 2004 is one, and fails thirteen times per cycle.
4. Microsoft. WEEKNUM function (support.microsoft.com). The authority for the other convention in daily use: System 1, which is the default, is “the week containing January 1 is the first week of the year, and is numbered week 1” with weeks beginning Sunday; System 2 is “the week containing the first Thursday of the year … the methodology specified in ISO 8601”. Its own worked example, 9 March 2012, returns 10 with weeks beginning Sunday and 11 with weeks beginning Monday; this page reproduces both, and the ISO answer for that date is also week 10.
5. Television Bureau of Advertising. Broadcast Calendar — Nielsen Survey Dates (tvb.org). “The standard broadcast week starts on Monday and ends on Sunday” and “the standard broadcast month ends on the last Sunday of the calendar month”. That is a third convention, and it is the one the brief for this page confused with the Sunday-start spreadsheet convention above; the two are different rules that happen to give the same week NUMBER as Excel’s Monday-start variant, which this page checks over two centuries.
6. Wikipedia, Broadcast calendar. “Every week in the broadcast calendar starts on a Monday and ends on a Sunday”; “the number of weeks in a broadcast month is based on the number of Sundays that fall in that month”; and it states the difference from ISO explicitly — both start the week on Monday, but ISO starts with the week containing the first Thursday and 4 January instead of the first Sunday and 1 January.