ISO Week Date Calculator
Convert between a Gregorian calendar date and its ISO 8601 week date. In the ISO system every week starts on Monday and week 1 is the week that contains the year's first Thursday (equivalently 4 January), so a week-numbering year has 52 or 53 weeks and can straddle the calendar year boundary — e.g. 29 December 2014 is 2014-W01-1 and 31 December 2020 is 2020-W53-4. Enter a date to get its ISO week number, week-numbering year, day-of-week (Mon=1..Sun=7), day-of-year, leap-year flag, and the number of weeks in that ISO year, or go the other way and enter a year/week/day to recover the calendar date. Everything runs locally in your browser.
Date → week date
Week date → date
The math. The ISO 8601 week date pins week 1 to the first Thursday of the year, which is the same as the week containing 4 January. To find the week date of a given day: compute its day-of-week (Mon=1..Sun=7) from the Julian Day Number (JDN, a continuous day count), locate the Thursday of the surrounding week (date + (4 − dow) days), and read that Thursday's calendar year as the week-numbering year; the week number is then how many Thursdays elapsed since week 1's Thursday. A year has 53 weeks exactly when 1 January is a Thursday, or when 1 January is a Wednesday in a leap year (equivalently, the ISO week of 28 December — always in the final week — is 53); otherwise 52. Because week 1 may start in late December of the previous year and week 52/53 may spill into January of the next, the ISO year can differ from the calendar year by ±1 around New Year. Leap years follow the Gregorian rule (÷4 but not ÷100, unless ÷400). All arithmetic uses integer JDN so it is exact and timezone-independent for the proleptic Gregorian calendar, years 1–9999. Pairs with the Julian Day Number, Day-of-Year, and Date Duration tools. Everything runs locally — nothing leaves your browser.