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Formula
h = (q + ⌊13(m + 1) ÷ 5⌋ + K + ⌊K ÷ 4⌋ + ⌊J ÷ 4⌋ + 5J) mod 7
- h
- the day of the week, where 0 = Saturday, 1 = Sunday, 2 = Monday … 6 = Friday
- q
- the day of the month
- m
- the month, from 3 (March) to 14 (February); January and February count as months 13 and 14 of the previous year
- K
- the year of the century (year mod 100), using the previous year for January and February
- J
- the zero-based century (⌊year ÷ 100⌋), so 19 for 1900–1999
What the calculator shows
Enter any date and the day of the week calculator tells you which weekday it falls on. Alongside the answer you get:
- The full date, written out, such as “Friday, December 25, 2026”.
- Day of the year, for example day 359 of 365.
- ISO week number, the week number used in business calendars and planning.
- Weekday or weekend.
- The year’s doomsday, the anchor weekday used in the mental method described below.
- Whether the year is a leap year.
- Zeller’s congruence worked out with the numbers from your date.
It handles past and future dates alike, from the year 1 to 9999, so you can look up the weekday you were born on, check the day of a historical event or plan an event years ahead.
How to use it
Pick a date in the day of the week calculator, or type it. The field starts on today’s date. The result updates as soon as the date is valid. For dates before October 15, 1582, a note reminds you that the result is on the proleptic Gregorian calendar.
How to calculate the day of the week with Zeller’s congruence
Zeller’s congruence, published by Christian Zeller in the 1880s, turns a date into a weekday with whole-number arithmetic. Here it is for March 14, 1879.
- Write down the parts: q = 14 (day), m = 3 (March), K = 79 (year of the century), J = 18 (century).
- Month term: ⌊13 × (3 + 1) ÷ 5⌋ = ⌊52 ÷ 5⌋ = 10.
- Year terms: K = 79, ⌊79 ÷ 4⌋ = 19, ⌊18 ÷ 4⌋ = 4 and 5 × 18 = 90.
- Add everything: 14 + 10 + 79 + 19 + 4 + 90 = 216.
- Take the remainder after dividing by 7: 216 mod 7 = 6.
- Look it up: 0 = Saturday, 1 = Sunday, 2 = Monday, 3 = Tuesday, 4 = Wednesday, 5 = Thursday, 6 = Friday. March 14, 1879 was a Friday.
For a January or February date, use the previous year and add 12 to the month. February 3, 2025 becomes month 14 of 2024, so K = 24 and J = 20.
The Doomsday rule: a method you can do in your head
John Conway’s Doomsday rule relies on the fact that certain easy-to-remember dates always share a weekday within a year, called the year’s doomsday:
- 4/4, 6/6, 8/8, 10/10 and 12/12
- 5/9, 9/5, 7/11 and 11/7 (“9 to 5 at the 7-Eleven”)
- The last day of February, and March 14 (Pi Day)
- January 3 in common years, January 4 in leap years
To find a year’s doomsday, start from the century’s anchor: Friday for the 1800s, Wednesday for the 1900s, Tuesday for the 2000s and Sunday for the 2100s. Then, for the last two digits of the year:
- Divide by 12: the quotient and the remainder.
- Divide the remainder by 4, ignoring any fraction.
- Add the three numbers and count that many days forward from the anchor.
For 2026: 26 ÷ 12 = 2 remainder 2, and 2 ÷ 4 = 0. Adding 2 + 2 + 0 = 4, and four days after Tuesday is Saturday. So every doomsday in 2026 is a Saturday. December 12 is a Saturday, so December 25, thirteen days later, is a Friday.
Weekdays of common dates
| Year | January 1 | July 4 | December 25 |
|---|---|---|---|
| 2025 | Wednesday | Friday | Thursday |
| 2026 | Thursday | Saturday | Friday |
| 2027 | Friday | Sunday | Saturday |
| 2028 | Saturday | Tuesday | Monday |
| 2029 | Monday | Wednesday | Tuesday |
| 2030 | Tuesday | Thursday | Wednesday |
Notice the two-day jump between 2027 and 2028 for July 4 and December 25: the leap day, February 29, 2028, falls in between. January 1 jumps two days a year later, from 2028 to 2029.
Historic dates and the Julian calendar
The Gregorian calendar replaced the Julian calendar in parts of Europe in October 1582, when Thursday, October 4 was followed directly by Friday, October 15. Britain and its American colonies did not switch until 1752, when Wednesday, September 2 was followed by Thursday, September 14.
The day of the week calculator always uses the Gregorian calendar. It correctly gives Thursday for September 14, 1752, but for September 2, 1752 it gives Saturday, the weekday of that date on the Gregorian calendar, while people in London at the time recorded a Wednesday under the Julian calendar. George Washington was born on February 11, 1731 by the Julian calendar then in use, which is February 22, 1732 on the Gregorian calendar, a Friday.
For genealogy or history research, check which calendar a record used before reading too much into the weekday.
Real-life uses
- Finding the weekday you or a relative were born on.
- Checking whether a holiday, deadline or anniversary lands on a weekend. To count working days between two dates, use the business days calculator.
- Planning events years ahead, together with the date calculator to add or subtract days.
- Verifying dates in historical documents, letters and diaries.
Glossary
- Gregorian calendar. The calendar used in the United States today, with leap years every 4 years except century years not divisible by 400.
- Proleptic calendar. A calendar extended backward to dates before it was introduced.
- Doomsday. The weekday shared by a set of easy-to-remember dates in a given year.
- ISO week. A Monday-to-Sunday week numbered under ISO 8601.
Worked examples
The first Moon landing
Apollo 11 landed on the Moon on July 20, 1969.
Inputs: Date = 1969-07-20
Zeller's congruence: q = 20, m = 7, K = 69, J = 19 h = (20 + ⌊13 × 8 ÷ 5⌋ + 69 + ⌊69 ÷ 4⌋ + ⌊19 ÷ 4⌋ + 5 × 19) mod 7 h = (20 + 20 + 69 + 17 + 4 + 95) mod 7 = 225 mod 7 = 1 h = 1 → Sunday (0 = Saturday, 1 = Sunday, 2 = Monday … 6 = Friday)
Answer: Sunday, July 20, 1969.
The Declaration of Independence
The Declaration of Independence was adopted on July 4, 1776.
Inputs: Date = 1776-07-04
Zeller's congruence: q = 4, m = 7, K = 76, J = 17 h = (4 + ⌊13 × 8 ÷ 5⌋ + 76 + ⌊76 ÷ 4⌋ + ⌊17 ÷ 4⌋ + 5 × 17) mod 7 h = (4 + 20 + 76 + 19 + 4 + 85) mod 7 = 208 mod 7 = 5 h = 5 → Thursday (0 = Saturday, 1 = Sunday, 2 = Monday … 6 = Friday)
Answer: Thursday, July 4, 1776.
A leap day
February 29, 2000, a leap day in a century year divisible by 400. January and February are treated as months 13 and 14 of 1999.
Inputs: Date = 2000-02-29
Zeller's congruence: q = 29, m = 14 (January and February count as months 13 and 14 of the previous year), K = 99, J = 19 h = (29 + ⌊13 × 15 ÷ 5⌋ + 99 + ⌊99 ÷ 4⌋ + ⌊19 ÷ 4⌋ + 5 × 19) mod 7 h = (29 + 39 + 99 + 24 + 4 + 95) mod 7 = 290 mod 7 = 3 h = 3 → Tuesday (0 = Saturday, 1 = Sunday, 2 = Monday … 6 = Friday)
Answer: Tuesday, February 29, 2000.
The first day of the Gregorian calendar
October 15, 1582, the day the Gregorian calendar took effect in Catholic Europe, straight after Julian Thursday, October 4.
Inputs: Date = 1582-10-15
Zeller's congruence: q = 15, m = 10, K = 82, J = 15 h = (15 + ⌊13 × 11 ÷ 5⌋ + 82 + ⌊82 ÷ 4⌋ + ⌊15 ÷ 4⌋ + 5 × 15) mod 7 h = (15 + 28 + 82 + 20 + 3 + 75) mod 7 = 223 mod 7 = 6 h = 6 → Friday (0 = Saturday, 1 = Sunday, 2 = Monday … 6 = Friday)
Answer: Friday, October 15, 1582.
Assumptions and limitations
- Dates use the Gregorian calendar, the calendar used in the United States today. Dates before it took effect on October 15, 1582 are calculated with the proleptic Gregorian calendar, extending today's leap-year rules backward.
- Many historic records use the Julian calendar instead, including British and American colonial records before September 1752. For those dates, convert to Gregorian first or the weekday may be wrong.
- Years from 1 to 9999 are supported. There is no year 0.
- The ISO week number follows ISO 8601. Weeks start on Monday and week 1 is the week containing the year's first Thursday, so early January or late December can belong to a neighboring year's week.
- The doomsday shown is the weekday of the year's "doomsday" dates in John Conway's method, such as 4/4, 6/6, 8/8, 10/10 and 12/12.
Frequently asked questions
What day of the week was I born?
Enter your date of birth and the calculator shows the weekday immediately, along with the day of the year and the ISO week number. It works for any date from the year 1 to 9999, so it also covers parents' and grandparents' birthdays.
How do you calculate the day of the week for any date?
Use a formula such as Zeller's congruence, or a mental method such as Conway's Doomsday rule. Both rely on the calendar repeating every 400 years and count how far the weekday shifts each year and month. The steps under the result show Zeller's formula with your date's numbers.
Why are January and February treated as months 13 and 14?
Moving them to the end of the previous year puts the leap day, February 29, at the very end of the counting year. That way the leap day never shifts the months that follow it, which keeps the formula simple.
Does the calculator work for dates before 1582?
It returns the weekday on the proleptic Gregorian calendar, which extends today's calendar backward. That is the correct answer for astronomy and for comparing dates, but historical documents from the time almost always used the Julian calendar, which by 1582 was 10 days out of step with the Gregorian calendar.
How often does the calendar repeat?
The Gregorian calendar repeats exactly every 400 years, because 400 years contain exactly 20,871 weeks. Individual years repeat more often. A common year's calendar usually recurs after 6 or 11 years, and a leap year's after 28 years, unless a skipped leap year in a century year gets in the way.
What day of the week is Christmas next year?
Christmas 2026 falls on a Friday, and Christmas 2027 on a Saturday. Each year a fixed date usually moves one weekday later, or two when a February 29 falls in between.
Sources
- Zeller's congruence — Wikipedia. Checked October 10, 2026.
- Determination of the day of the week — Wikipedia. Checked October 10, 2026.
- Doomsday rule — Wikipedia. Checked October 10, 2026.