Week number and day of year

How many weeks are in a year?

A year has 52 weeks and 1 day, or 52 weeks and 2 days in a leap year: 365 ÷ 7 = 52.14 and 366 ÷ 7 = 52.29. Numbered weeks work differently. An ISO 8601 year has 52 or 53 weeks, and 2026 has 53 because it starts on a Thursday.

An ISO year has 53 weeks when 1 January is a Thursday, or a Wednesday in a leap year. Being a leap year is not enough: 2024 and 2028 have 52 weeks, while 2020, 2026, 2032 and 2037 have 53.

52-week and 53-week years

The last column is the number of the ISO week that contains 28 December, which is always the final week of its ISO year. Checking 1 January or 31 December instead can land in a week of the neighboring year.

How ISO 8601 week numbers work

• Weeks run from Monday to Sunday.
• Week 1 is the week with the year's first Thursday, so it always contains 4 January.
• Each week belongs to the year that holds its Thursday. 29 to 31 December can fall in week 1 of the next year, and 1 to 3 January in week 52 or 53 of the previous one.

To number a week by hand, find the Thursday of the date's week and take its day of the year d; the week is ⌊(d − 1) ÷ 7⌋ + 1. For Monday 5 October 2026 that Thursday is 8 October, day 281, so the week is ⌊280 ÷ 7⌋ + 1 = 41.

ISO writes the result as a week date, 2026-W41-1: the ISO year, the week, then the weekday with Monday = 1 and Sunday = 7. Keep the ISO year with the week, because for a few days around New Year it differs from the calendar year.

US week numbers start on Sunday

The US count, Excel's WEEKNUM(date, 1), starts weeks on Sunday and makes week 1 the week containing 1 January, however short. With d the day of the year and s the weekday of 1 January (Sunday = 0), the week is ⌊(d − 1 + s) ÷ 7⌋ + 1.

For 5 October 2026, d = 278 and s = 4 (a Thursday), so the week is ⌊281 ÷ 7⌋ + 1 = 41, as in ISO. In 2026 the two systems agree from Monday to Saturday and differ by one on Sundays, which end an ISO week but start a US one.

In 2027, which starts on a Friday, the US number is one higher than the ISO number, or two higher on Sundays. Microsoft's WEEKNUM reference lists both systems and their return types.

Week number and day-of-year examples

31 December 2028 falls in US week 54 because that leap year starts on a Saturday and ends on a Sunday, leaving one-day US weeks at both ends. In ISO terms it is the last day of week 52.

Week numbers in Excel, Google Sheets and Python

• =ISOWEEKNUM(A2), or =WEEKNUM(A2, 21), returns the ISO week. Microsoft's ISOWeekNum notes explain why early January can belong to the previous ISO year.
• =WEEKNUM(A2) gives the Sunday-start US count. =WEEKNUM(A2, 2) starts weeks on Monday but still puts 1 January in week 1, so it is not ISO.
• Python's date.isocalendar() returns the ISO year, week and weekday. In strftime, pair %G with %V: %Y-W%V prints 2024-W01 for 30 December 2024, whose ISO week is 2025-W01.
• Python's %U counts Sunday-start weeks from 0, so it is one lower than WEEKNUM(date, 1) except in years that begin on a Sunday.

Day of the year, days left and quarter

• Day of the year counts 1 January as day 1, so 31 December is day 365, or 366 in a leap year.
• Days left excludes the date itself: 5 October 2026 is day 278 with 87 days left. Add 1 to include that day.
• The share of the year elapsed is the day of the year ÷ days in the year, counting the date as complete: 278 ÷ 365 = 76.2%.
• Quarters follow calendar months: January to March is Q1, and October to December is Q4. A fiscal year that starts in another month numbers its quarters differently.

Why some years have 53 paydays

A 365-day year contains 53 of the weekday it starts on, and a leap year 53 of each of its first two weekdays. 2026 starts on a Thursday, so it has 53 Thursdays, and a weekly payroll paid on Thursdays makes 53 payments that year.

2028 starts on a Saturday and has 366 days, so it has 53 Saturdays and 53 Sundays. A schedule that repeats every 52 weeks covers only 364 days, so it starts a day earlier in the calendar each year, or two days after a leap day.

Related calendar tools

For the number of weeks between two dates, use the date difference calculator. The day of the week calculator names the weekday of any date, and the leap year checker shows whether a year has 365 or 366 days.