Day of the Week Calculator
Enter any date from year 1 to year 9999 and find out which day of the week it was or will be. Choose the proleptic Gregorian or Julian calendar, or the calendar a country actually used at the time, and see the answer worked out step by step with Zeller's congruence and Conway's Doomsday rule. Runs entirely in your browser — nothing is uploaded.
A date in an old document is in the calendar its country used then. Pick that place to read it correctly.
Enter a year and a day.
How to Use the Day of the Week Calculator
- 1. Enter the date. Type the year, pick the month and type the day. The form opens on today's date.
- 2. Choose the calendar. Gregorian runs today's calendar back in time; Julian runs the old one. For a date in an old document, pick the place — Britain, France, Russia and others — and the calculator reads the date in the calendar that place used on that day.
- 3. Read the weekday. You get the day name, its ISO number (Monday is 1, Sunday is 7), the day of the year, whether it is a leap year, and the same day in the other calendar.
- 4. Follow the working. Two tables show how Zeller's congruence and the Doomsday rule reach the answer. Both are checked against a day count that never fails.
Three Ways to Find a Weekday
The most reliable method counts days. Number every day from a fixed starting point and take the remainder after dividing by 7; the weekday of the starting day does the rest. That is what the calculator uses as its reference, following the fixed-day system of Reingold and Dershowitz, Calendrical Calculations: The Ultimate Edition (Cambridge University Press, 2018).
Zeller's congruence, published by Christian Zeller in the 1880s, packs the same count into one formula. For the Gregorian calendar it is h = (q + ⌊13(m + 1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J) mod 7, where q is the day of the month, m the month counted from March = 3 to February = 14 (January and February belong to the previous year), K the year of the century and J the century. The result h is 0 for Saturday, 1 for Sunday and so on to 6 for Friday. The Julian version replaces the last two terms with 5 − J.
John Conway's Doomsday rule is meant for mental arithmetic. In any year, the last day of February, 4 April, 6 June, 8 August, 10 October and 12 December fall on the same weekday, as do 9 May, 5 September, 11 July and 7 November. That weekday is the year's doomsday. January's is the 3rd (the 4th in leap years), February's the 28th (the 29th), and March's the 14th. Find the doomsday of the year, then count forward from the nearest doomsday date.
| Years | Anchor day |
|---|---|
| 1700–1799 | Sunday |
| 1800–1899 | Friday |
| 1900–1999 | Wednesday |
| 2000–2099 | Tuesday |
| 2100–2199 | Sunday |
The year's doomsday is the anchor day plus ⌊y/12⌋ + (y mod 12) + ⌊(y mod 12)/4⌋ days, where y is the last two digits of the year. The anchors repeat every 400 years in the Gregorian calendar, because 400 years is exactly 20,871 weeks. The Julian calendar's pattern repeats every 700 years.
Worked Examples
- 20 July 1969, the Apollo 11 landing, was a Sunday. Zeller: q = 20, m = 7, K = 69, J = 19, so h = (20 + 20 + 69 + 17 + 99) mod 7 = 225 mod 7 = 1, which is Sunday. Doomsday: the 1900s anchor is Wednesday, 1969 adds 2 days, so the doomsday is Friday; 11 July is a doomsday, and 20 July is 9 days later, which is 2 days after Friday — Sunday.
- 17 October 2026 is a Saturday. The doomsday of 2026 is Saturday and 10 October is a doomsday, so 17 October, a week later, is a Saturday too.
- 14 October 1066, the Battle of Hastings, was a Saturday in the Julian calendar then in use. Read in the Gregorian calendar, the same day is labelled 20 October.
Proleptic or Historical
The seven-day cycle never broke when countries moved from the Julian to the Gregorian calendar: Thursday 4 October 1582 was followed by Friday, which Spain, Portugal and Italy called 15 October. In Britain and its colonies Wednesday 2 September 1752 was followed by Thursday 14 September. So a date has the same weekday in both calendars, but a label does not. 1 January 1500 is a Monday in the proleptic Gregorian calendar and a Wednesday in the Julian one. If a letter, register or treaty is dated in the calendar its country used, choose that country here and the answer matches the original. Labels that the switch dropped, such as 5–14 October 1582 in Spain, are rejected.
Frequently Asked Questions
- How can I find out what day of the week I was born?
- Enter your birth date with the Gregorian calendar selected. The result gives the weekday, the day of the year, and the full Zeller and Doomsday working. For a birth date before the 20th century, pick the country's calendar only if the record is in an old-style form that predates its calendar change.
- What is Zeller's congruence?
- It is a formula that returns the weekday of any date from the day, month and year. January and February are treated as months 13 and 14 of the previous year, which pushes the leap day to the end of the counting year and keeps the formula simple. The remainder after division by 7 is the weekday, starting from Saturday as 0.
- How does the Doomsday rule work?
- Every year has a doomsday: a weekday shared by memorable dates such as 4 April, 6 June, 8 August, 10 October and 12 December. Take the century's anchor day, add the year's shift to get the doomsday, then count from the nearest doomsday date to your date. With practice it can be done in a few seconds in your head.
- How often does Friday the 13th happen?
- At least once and at most three times in a calendar year. The Gregorian calendar repeats every 400 years, and in that cycle the 13th falls on a Friday 688 times, more than on any other day (684 to 687 times for the others). The difference is tiny, but a Friday 13th is slightly more common than a Monday or a Saturday 13th.
- Did the weekday change when the Gregorian calendar was introduced?
- No. Countries dropped 10 to 13 days from the date count but kept the weekday cycle going. That is why a letter written on a Friday in Julian-calendar England and one written on the same day in Gregorian France carry different dates but the same weekday. This is also a handy check on a conversion.
- How far back and forward does the calculator work?
- From 1 January of year 1 to 31 December 9999, in the Gregorian or Julian calendar. Dates before the calendar existed are proleptic: the calendar is run backwards as if it had always been in use. Whether anyone knew the weekday that way then is another matter — the weekday itself is exact.