What day of the week was it? Find the weekday of any date

How to use the day of the week finder

1. Pick a Date. It starts on 20 July 1969, the day of the first Moon landing.
2. The weekday appears next to the date, for example “20 July 1969: Sunday”.
3. You also see the Day of year and the ISO week.
4. Read the Working box to follow Zeller’s congruence step by step, or to check homework.

What it does and when to use it

People use it to find the weekday they were born, to check that an old letter or diary entry is consistent, to plan anniversaries, or to see what day a holiday falls on years ahead. Students meet Zeller’s congruence in maths and programming classes, and the worked steps show where each number comes from.

For a week number rather than a weekday, use the ISO week number tool. To find Easter or the dates that depend on it, use the Easter date finder. To count how many Mondays or Fridays fall in a period, use the weekday counter.

How it works

Zeller’s congruence for the Gregorian calendar is:

h = (q + ⌊13(m + 1) / 5⌋ + K + ⌊K / 4⌋ + ⌊J / 4⌋ + 5J) mod 7

The brackets ⌊ ⌋ mean “round down”. January and February are moved to months 13 and 14 of the previous year. The answer h runs from 0 to 6, where 0 = Saturday, 1 = Sunday, 2 = Monday and so on up to 6 = Friday. The formula was cross-checked against a separate day-count method for dates from 1582 to 2400. It works on calendar dates only, so time zones play no part.

Worked examples

29 February 2024. February becomes month 14 of 2023, so q = 29, m = 14, K = 23 and J = 20. The terms are 29 + 39 + 23 + 5 + 5 + 100 = 201, and h = 201 mod 7 = 5, which is Thursday. It was day 60 of the year, in ISO week 9.

4 July 1776. No month shift is needed: q = 4, m = 7, K = 76, J = 17. The sum is 208, and 208 mod 7 = 5, so 4 July 1776: Thursday.

20 July 1969. The default date gives 20 July 1969: Sunday, the day of the Apollo 11 landing.

Limits and tips

• Dates must be real calendar dates between years 1 and 9999; 30 February is rejected.
• Countries adopted the Gregorian calendar at different times, so for dates before the switch in a given country, the weekday printed in local records may differ.
• To do it by hand, remember the order of h: Saturday comes first, not Sunday or Monday.