📅 Day of the Week Calculator
Find the day of the week for any date, from birthdays and historic events to future plans, with the maths shown step by step.
Quick answer: July 20, 1969 – the day of the Apollo 11 Moon landing – was a Sunday: Zeller’s congruence gives 20 + 20 + 69 + 17 + 4 + 95 = 225, and 225 mod 7 = 1, which means Sunday.
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Day of the Week Calculator inputs
Result
July 20, 1969
Sunday
20,902 days ago
- Day of the year
- 201
- ISO week
- 29
- Leap year
- No
Zeller's congruence, step by step
| Day q | 20 |
| Month m | 7 |
| K = year of century | 69 |
| J = century | 19 |
| q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J | 20 + 20 + 69 + 17 + 4 + 95 = 225 |
| h = sum mod 7 | 1 → Sunday |
h: 0 = Saturday, 1 = Sunday, 2 = Monday, 3 = Tuesday, 4 = Wednesday, 5 = Thursday, 6 = Friday.
Zeller's congruence
Christian Zeller's 19th-century formula turns any Gregorian date into a weekday using only whole-number arithmetic. Treat January and February as months 13 and 14 of the previous year, then:
h = (q + ⌊13(m + 1) ÷ 5⌋ + K + ⌊K ÷ 4⌋ + ⌊J ÷ 4⌋ + 5J) mod 7
where q is the day, m the month, K the year within the century and J the century. The result h = 0 is Saturday, 1 Sunday, 2 Monday and so on to 6 Friday.
Worked example: July 20, 1969
- q = 20, m = 7, K = 69, J = 19
- ⌊13 × 8 ÷ 5⌋ = 20, ⌊69 ÷ 4⌋ = 17, ⌊19 ÷ 4⌋ = 4, 5 × 19 = 95
- 20 + 20 + 69 + 17 + 4 + 95 = 225, and 225 mod 7 = 1 → Sunday
The Doomsday rule (mental method)
Each century has an anchor day; for 1900–1999 it is Wednesday and for 2000–2099 it is Tuesday. Add the number of 12s in the last two digits of the year, the remainder, and the number of 4s in that remainder; reduce mod 7 and step forward from the anchor to get the year's doomsday. For 1969: 5 + 9 + 2 = 16 → 2 days after Wednesday = Friday. July 11 is a doomsday, so July 18 is also a Friday and July 20 is a Sunday.
| Month | Doomsday dates |
|---|---|
| Jan / Feb | Jan 3 (Jan 4 in leap years), last day of Feb |
| Even months | 4/4, 6/6, 8/8, 10/10, 12/12 |
| Odd months | 5/9, 9/5, 7/11, 11/7, and March 14 (Pi Day) |
Tips
- The calendar repeats every 400 years exactly, so 1626 and 2026 share the same weekdays.
- The same date moves forward one weekday each year, or two after February 29.
Frequently asked questions
What day of the week was I born?
Enter your date of birth and the calculator shows the weekday. It works for any date from the year 1000 to 9999 using the Gregorian calendar.
How does Zeller’s congruence work?
It adds the day, a month term, the year of the century, a quarter of it, a quarter of the century and five times the century, then takes the remainder after dividing by 7. January and February are treated as months 13 and 14 of the previous year.
What is the Doomsday rule?
John Conway’s mental method: in any year, certain easy dates – 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7 and the last day of February – all fall on the same weekday, the year’s "doomsday". Find it, then count to your date.
What about dates before 1582?
The Gregorian calendar was introduced in October 1582. Earlier dates here use the proleptic Gregorian calendar, so they may differ from Julian-calendar dates in historical sources.