How to Calculate a Week Number by Hand

What you need

To find the ISO week number of a date by hand you need two numbers. The first is the day of the year, counted from 1 for 1 January, so that 1 February is 32 and 22 October 2026 is 295. The second is the weekday number, counted from 1 for Monday to 7 for Sunday. 22 October 2026 is a Thursday, which is 4.

With these two numbers, a single formula gives a first estimate of the week. Two checks at the year boundaries then fix the cases in which the date belongs to the previous or the next year's numbering. The method is exact for every date from the year 1 to 9999.

The formula

Calculate the week as the day of the year minus the weekday number plus 10, divided by 7, rounded down. In short: week = floor((day of year − weekday + 10) / 7).

For Thursday 22 October 2026: 295 − 4 + 10 = 301. 301 divided by 7 is 43, and rounded down it is 43. The ISO week is 43, which agrees with the calculator.

Why does the formula work? Subtracting the weekday and adding 4 gives the day of the year of the Thursday of that week. For 22 October 2026 that is 295 − 4 + 4 = 295, because the date itself is a Thursday. The week number is the number of whole weeks up to that Thursday, plus one: floor((Thursday − 1) / 7) + 1. Written in terms of the date, this is the same as floor((day of year − weekday + 10) / 7). The idea is the Thursday rule in arithmetic form.

Correction 1: the result is 0

If the formula gives 0, the date belongs to the last week of the previous year. Friday 1 January 2027 is day 1 and weekday 5, and 1 − 5 + 10 = 6, which divided by 7 is 0. The date is in the last week of 2026. To find out whether it is week 52 or 53, check whether 2026 is a long year. It is, so the answer is week 53 of 2026.

To check whether a year has 53 weeks, use the Thursday rule or the following test. Add the year, a quarter of the year, subtract a hundredth and add a four-hundredth, all rounded down, then divide the sum by 7 and look at the remainder. If the remainder is 4 for the year, or 3 for the year before, the year has 53 weeks. For 2026: 2026 + 506 − 20 + 5 = 2517, and the remainder after dividing by 7 is 4, so 2026 has 53 weeks. For 2027 the remainder is 5, and for 2026 it is 4, not 3, so 2027 has 52.

Correction 2: the result is too large

If the formula gives 53 and the year has only 52 weeks, the date is in week 1 of the next year. Monday 29 December 2025 is day 363 and weekday 1: 363 − 1 + 10 = 372, and 372 divided by 7 gives 53. But 2025 has only 52 weeks, because the test above gives a remainder of 3 for 2025, not 4, and 2 for 2024, not 3. The date is therefore in week 1 of 2026.

Tuesday 31 December 2024 works the same way. It is day 366 and weekday 2: 366 − 2 + 10 = 374, and 374 divided by 7 gives 53. 2024 has 52 weeks, so the date is in week 1 of 2025. The week number 53 is valid only if the year is long, and this simple check catches every case.

Worked examples

Example 1: Sunday 1 January 2023. Day 1, weekday 7. 1 − 7 + 10 = 4, divided by 7 is 0. The date is in the last week of 2022. 2022 has 52 weeks, so the answer is week 52 of 2022. The calculator shows the same.

Example 2: Thursday 31 December 2026. Day 365, weekday 4. 365 − 4 + 10 = 371, divided by 7 is exactly 53. 2026 has 53 weeks, so the date is in week 53 of 2026.

Example 3: Tuesday 15 June 2027. 15 June is day 166 in a common year (31 + 28 + 31 + 30 + 31 + 15). Weekday 2. 166 − 2 + 10 = 174, divided by 7 is 24.86, rounded down 24. The ISO week is 24.

Finding the day of the year

The day of the year needs the number of days in the months before. In a common year, the months before March add up to 59, so 1 March is day 60. In a leap year add 1. The cumulative days at the start of each month are 0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304 and 334 in a common year, and one more from March on in a leap year.

For 22 October 2026: the days before October are 273, plus 22 gives 295. For 29 February 2028: 31 + 29 = 60, and the year 2028 is a leap year. Remember that a century year is a leap year only if it is divisible by 400, so 2100 is not.

When to use hand methods

Doing this by hand is useful for checks, exams and for understanding. In daily work, use a tool. A calculator or a spreadsheet function is faster, and it does not make errors at New Year.

The hand method is still a good test of a tool. If you have written your own week function or you doubt a result, calculate three dates with this method: one near the start of January, one near the end of December and one in the middle of the year. If the tool agrees on those, it is almost certainly right.