What is the ISO Week Number?
The ISO 8601 standard defines a way to number the weeks of a year from 1 to 52 or 53. Under this system every week starts on a Monday, and week 1 is the week that contains the first Thursday of the year (equivalently, the week containing January 4th). Because of this rule, the first few days of January can belong to the last week of the previous year, and the last few days of December can belong to week 1 of the next year. The "ISO week-year" reported here reflects that adjustment.
How to use this calculator
Choose a year, month and day, then submit. The calculator returns the ISO week number, the ISO week-year the week belongs to, the ordinal date (day of the year), and the ISO weekday (Monday = 1 through Sunday = 7).
The formula explained
The core calculation is:
$$\text{Week} = \left\lfloor \frac{\text{ordinalDate} - \text{isoWeekday} + 10}{7} \right\rfloor$$
Here ordinalDate is how many days into the year the date falls (Jan 1 = 1), and isoWeekday is the weekday with Monday as 1 and Sunday as 7. Adding 10 and dividing by 7 shifts the count so the Thursday rule is satisfied. If the result is less than 1, the date belongs to the last week (52 or 53) of the previous year. If the result is 53 but the year does not actually have 53 weeks, the date is week 1 of the next year.
Worked example
Take 1 January 2024. It is a Monday, so isoWeekday = 1, and it is the first day of the year, so ordinalDate = 1. $$\text{Week} = \left\lfloor \frac{1 - 1 + 10}{7} \right\rfloor = \left\lfloor \frac{10}{7} \right\rfloor = \lfloor 1.43 \rfloor = 1$$ So January 1, 2024 falls in ISO week 1 of 2024.
FAQ
Can a year have 53 weeks? Yes. Years that start on a Thursday, and leap years that start on a Wednesday, contain 53 ISO weeks.
Why does January 1 sometimes show week 52 or 53? Because ISO weeks start on Monday and week 1 must contain the first Thursday, early-January dates can still belong to the previous ISO week-year.
Is this the same as the "week of the year" in my spreadsheet? Not always. Many tools count week 1 as the week containing January 1 with weeks starting on Sunday. This calculator uses the stricter ISO 8601 definition.
