ISO Week Number & Date Calculator
Convert a Gregorian calendar date to its ISO week date, or enter an ISO week-year, week number, and weekday to resolve the calendar date. The result also compares ISO numbering with the Sunday-start and Monday-start POSIX week systems.
ISO week date2026-W39-7
- Resolved calendar date
- 2026-09-27
- ISO week number
- 39
- ISO week-year
- 2,026
- ISO week date range
- 2026-09-21 to 2026-09-27
- Weeks in ISO week-year
- 53
- Sunday-start week number (%U)
- 39
- Monday-start week number (%W)
- 38
- Year-boundary explanation
- The Gregorian year and ISO week-year both equal 2026; ISO week 39 runs Monday through Sunday. POSIX %U and %W report 39 and 38 because they count from the first Sunday and first Monday of the calendar year.
Week numbering comparison
| System | Week starts | Year rule | Result |
|---|---|---|---|
| ISO 8601 | Monday | Week 1 contains January 4 and the first Thursday | 2026-W39-7 |
| POSIX %U | Sunday | Days before the first Sunday are week 00 | 39 |
| POSIX %W | Monday | Days before the first Monday are week 00 | 38 |
Uses the proleptic Gregorian calendar for all supported years.
ISO weeks begin on Monday; POSIX %U begins on Sunday and POSIX %W begins on Monday after possible week 00 days.
How to use this calculator
- Choose date-to-week mode when you have a calendar date.
- Enter the calendar year, month, and day, then read the ISO week date and POSIX comparison.
- Choose ISO week-to-date mode when you have an ISO week-year, week number, and weekday.
- Use the boundary explanation to check New Year dates and week 00 cases.
How the ISO week number is calculated
ISO 8601 weeks start on Monday, and ISO week 1 is the week that contains January 4. The same rule is often described as the first-Thursday rule: the ISO week-year belongs to the Gregorian year that contains the Thursday in that week. Because of that, dates near January 1 and December 31 can belong to a different ISO week-year than their calendar year.
For a Gregorian date D in calendar year y, the calculator first finds the ordinal day N and the ISO weekday u, where Monday is 1 and Sunday is 7. The provisional week is:
V = floor((N - u + 10) / 7)
Let L(g) be the number of ISO weeks in year g. An ISO year has 53 weeks when January 1 is a Thursday, or when January 1 is a Wednesday in a Gregorian leap year; otherwise it has 52 weeks. If V < 1, the date belongs to week L(y - 1) of the prior ISO week-year. If V > L(y), it belongs to week 1 of the next ISO week-year. Otherwise, V is the ISO week number for year y.
Converting an ISO week back to a date
For reverse conversion, the calculator finds the Monday of ISO week 1. It starts from January 4 in the requested ISO week-year, then moves back to that week's Monday. The resolved date is:
date = week1Monday + 7 x (weekNumber - 1) + (isoWeekday - 1)
Week 53 is accepted only when that ISO week-year actually has 53 weeks. A request such as week 53 in a 52-week ISO year is rejected instead of rolling into the next year.
How POSIX %U and %W differ
The POSIX %U week number starts weeks on Sunday. Dates before the first Sunday of the calendar year are week 00. The POSIX %W week number starts weeks on Monday, and dates before the first Monday are week 00. These systems are calendar-year week counters, not ISO week-years, so they often disagree with ISO near New Year and can also differ from each other during the same year.
What this calculator leaves out
The calculation uses the proleptic Gregorian calendar for all supported years, including years before modern calendar adoption. It does not apply custom fiscal calendars, payroll calendars, retail 4-5-4 calendars, holiday rules, business-day counting, or locale settings that label weeks differently from ISO 8601 or POSIX.
Worked example
For September 27, 2026, the ordinal day is 270 and the ISO weekday is 7 because it is a Sunday. The ISO provisional week is floor((270 - 7 + 10) / 7) = 39. ISO year 2026 has 53 weeks because January 1, 2026 is a Thursday, so the date is 2026-W39-7.
The ISO week runs from September 21, 2026 through September 27, 2026. Under POSIX rules, the Sunday-start %U week is 39 and the Monday-start %W week is 38, because those systems count from the first Sunday or Monday in the calendar year.
Common questions
Why can the ISO week-year differ from the calendar year?
ISO weeks belong to the year that contains the Thursday of that week. A few early January dates can still be in the last ISO week of the prior year, and a few late December dates can be in ISO week 1 of the next year.
When does an ISO year have week 53?
An ISO year has 53 weeks when January 1 is a Thursday, or when January 1 is a Wednesday in a Gregorian leap year. All other ISO years have 52 weeks.
Does an ISO week begin on Sunday or Monday?
An ISO week begins on Monday. ISO weekdays are numbered Monday 1 through Sunday 7, so Sunday is the last day of the ISO week.
What is the difference between ISO week numbers and U.S. week numbers?
Many U.S. calendars use Sunday as the first day of the week, while ISO uses Monday. POSIX %U is Sunday-starting and tied to the calendar year; ISO uses a week-year that can differ near New Year.
Why do some calendars show week 00?
Week 00 appears in POSIX-style systems for dates before the first Sunday or first Monday of the calendar year. ISO does not use week 00; those dates belong to the final ISO week of the prior year or ISO week 1 of the current year.
Which dates belong to ISO week 1?
ISO week 1 is the Monday-through-Sunday week that contains January 4. Equivalently, it is the week with the first Thursday of the Gregorian year.