Mathematics · calendars

Week Number Calculator

ISO 8601 week numbers, what dates a week covers, and the years with 53 of them.
ISO 8601 · Mon–Sun

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The long years

Which years have 53 weeks

payroll, retail and rota planning

An ISO year has 53 weeks when 1 January falls on a Thursday, or on a Wednesday in a leap year — because week 1 is defined as the week containing the year's first Thursday, and those are the two ways to fit an extra one in. Everything else has 52.

Field notes

Where week numbers go wrong

How it works

One rule, and everything follows

ISO 8601 defines week 1 as the week containing the year's first Thursday — equivalently, the week containing 4 January, and equivalently again, the first week with most of its days in the new year. Weeks run Monday to Sunday. Every other property follows from that single rule, including the awkward ones.

Why a date's week-year is not always its calendar year

A week belongs entirely to one year, so the days at each end have to go somewhere. 29–31 December can sit in week 1 of the following year, and 1–3 January can sit in week 52 or 53 of the previous one. That is not an error — it is the rule working. It does mean "week 1 of 2027" and "the first week of January 2027" are different sets of days, which is where most calendar bugs start.

This is why ISO dates pair a week with its own year — 2026-W01, not just "week 1". Storing the week without the ISO year loses information for six days a year, every year.

Why does my spreadsheet give a different week number?

Because it is probably not using ISO. Excel's WEEKNUM defaults to weeks starting Sunday with week 1 being whichever week contains 1 January — a different rule that disagrees with ISO for several weeks most years. ISOWEEKNUM is the one that matches this tool.

Which years have 53 weeks?

Those where 1 January is a Thursday, or a Wednesday in a leap year. They arrive roughly every five to six years and matter more than they sound: weekly payroll gets a 53rd pay run, and retailers running 52-week financial calendars have to absorb an extra trading week.

Do all countries number weeks this way?

No. ISO 8601 is standard across Europe and much of business, but the US, Canada and parts of Asia commonly start weeks on Sunday and number from the week containing 1 January. Both are shown above, because agreeing which convention you mean is most of the work.

What this page assumes

That a date is a date. Everything here is computed in UTC with no time of day, which is deliberate: week numbering done in local time can put the same instant in two different weeks either side of a time-zone boundary, and midnight arithmetic across a daylight-saving change is where most week-number bugs live.

Two conventions are covered — ISO 8601 and the US Sunday-start — and not the Saturday-start weeks used in parts of the Middle East, nor the several spreadsheet variants beyond Excel’s default. The ISO figures have been checked against an independent reference implementation on every day from 1900 to 2100, all 73,414 of them, with no disagreement in either the week number or the ISO year: weeknumber_model.py. Week numbering itself has no meaning before the Gregorian calendar was adopted locally, which happened at different dates in different countries.

What is week 0?

Not an ISO concept. Some systems emit "week 0" for early-January days that ISO assigns to the previous year's final week — a symptom of implementing the numbering without the year pairing.

ISO 8601 throughout, with the US Sunday-start convention shown alongside for comparison. Dates are handled in UTC to avoid daylight-saving shifts moving a date across a week boundary.
The awkward part

Where weeks and years disagree

A week belongs to whichever year holds most of it — formally, the year containing that week’s Thursday. Since 52 weeks is only 364 days, the two calendars cannot stay in step, and the seam falls across New Year.

Years with 53 weeks

A year gets a 53rd week when 1 January is a Thursday, or a Wednesday in a leap year. It happens about every five or six years.

201520202026203220372043

2026 is one of them. Payroll, rotas and reporting periods built on “52 weeks” are a week short this year, which is the sort of thing that is noticed in December rather than January.

Dates that belong to another year’s week

DateCalendar yearISO weekFalls in
Mon 30 Dec 202420242025-W01the year after
Tue 31 Dec 202420242025-W01the year after
Mon 29 Dec 202520252026-W01the year after
Tue 30 Dec 202520252026-W01the year after
Wed 31 Dec 202520252026-W01the year after
Fri 01 Jan 202720272026-W53the year before
Sat 02 Jan 202720272026-W53the year before
Sun 03 Jan 202720272026-W53the year before
Sat 01 Jan 202820282027-W52the year before
Sun 02 Jan 202820282027-W52the year before

This is the trap. 1 January 2027 is in week 53 of 2026, and 30 December 2024 is already in week 1 of 2025. A spreadsheet that pairs an ISO week number with the calendar year of the date will silently file those rows in the wrong year.

ISO is not the only convention

Version history · 2 releases
  1. v1.532026-08-03The three thinnest tools filled out: week numbers, clock hands, fluid properties
  2. v4.032026-08-2373,414 days checked against a reference implementation; not one disagreement

Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.