How to use the day of the week calculator
- Enter the date. You can pick it from the calendar or type it, including years far in the past or future.
- Read the weekday, with the day of the year, the ISO week number, whether it's a leap year and how far the date is from today.
- Follow the two lists under the answer to see the weekday worked out with Zeller's congruence and checked with the Doomsday rule.
How the weekday is calculated
Zeller's congruence, published by Christian Zeller in the 1880s, turns any Gregorian date into a number from 0 to 6:
January and February are treated as months 13 and 14 of the year before, so that the leap day falls at the very end of the counting year. The term ⌊13(m + 1) ÷ 5⌋ adds up the uneven month lengths, and K ÷ 4 and J ÷ 4 add the leap days, including the rule that century years are leap years only when they divide by 400. The ⌊ ⌋ brackets mean "round down to a whole number".
Worked example
The calculator opens with July 4, 1776, the day the U.S. Declaration of Independence was adopted:
- q = 4, m = 7, K = 76, J = 17.
- ⌊13 × 8 ÷ 5⌋ = ⌊20.8⌋ = 20.
- ⌊76 ÷ 4⌋ = 19, ⌊17 ÷ 4⌋ = 4, and 5 × 17 = 85.
- Sum: 4 + 20 + 76 + 19 + 4 + 85 = 208.
- 208 mod 7 = 5 (because 7 × 29 = 203), and 5 means Thursday.
The Doomsday rule agrees. The anchor day for the 1700s is Sunday. For '76: 76 ÷ 12 = 6 remainder 4, and 4 ÷ 4 = 1, so Sunday + 6 + 4 + 1 = 11 days on, which is Thursday. July 11 is always a "doomsday", and July 4 is exactly a week earlier, so it's a Thursday too.
The Doomsday rule for mental math
John Conway's Doomsday rule is the easier method to do in your head. In any year, these dates all fall on the same weekday, called the doomsday:
| Month | Doomsday dates | Memory aid |
|---|---|---|
| January | 3rd (4th in leap years) | – |
| February | 28th (29th in leap years) | last day of February |
| March | 14th | Pi Day, 3/14 |
| April, June, August, October, December | 4th, 6th, 8th, 10th, 12th | 4/4, 6/6, 8/8, 10/10, 12/12 |
| May, July, September, November | 9th, 11th, 5th, 7th | "9 to 5 at the 7-Eleven" |
The century anchors repeat every 400 years: 1700s Sunday, 1800s Friday, 1900s Wednesday, 2000s Tuesday. In 2026 the doomsday is a Saturday (Tuesday + 2 + 2 + 0), so October 10 is a Saturday and October 29, 19 days later, is a Thursday.
Which calendar is used?
The calculator uses the Gregorian calendar, which began on October 15, 1582. Dates before that are shown in the proleptic Gregorian calendar, meaning the same rules run backward. Many countries switched later: Britain and its American colonies in September 1752, Russia in 1918 and Greece in 1923. A date written in an old Julian-calendar document may fall on a different weekday here.
Frequently asked questions
What day of the week was I born?
Enter your date of birth and the calculator gives the weekday straight away. The age calculator shows it too, along with your exact age and the weekdays of your next five birthdays.
Why does the same date move by one weekday each year?
A common year is 365 days, which is 52 weeks plus 1 day, so a date usually falls one weekday later the next year. After February 29 in a leap year it moves by two. That's why your birthday "skips" a weekday every few years.
When does the calendar repeat?
A year's calendar repeats when it starts on the same weekday and has the same leap-year status. That happens after 6, 11 or 28 years for common years. The full Gregorian cycle, including the century rule, repeats exactly every 400 years.
Is Zeller's congruence accurate for every date?
Yes, for the Gregorian calendar it's exact for any date. Errors usually come from forgetting to treat January and February as months 13 and 14 of the previous year. For dates near the switch from the Julian calendar, check which calendar your source uses.
Related calculators
- Date Calculator — Add or subtract years, months, weeks and days from a date, or count the days and weekdays between two dates.
- Age Calculator — Your exact age in years, months and days, with totals in weeks, days and hours and the date of your next birthday.
- Day Counter — Count the days or weekdays between two dates, with or without the end date, or count down the days to an event.
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