How to Find the Day of the Week for Any Date (Doomsday and Zeller)

You can find the day of the week for any date with arithmetic alone. The quickest mental method is John Conway’s Doomsday rule: every year has a “doomsday” weekday shared by easy-to-remember dates such as 4/4, 6/6, 8/8, 10/10, 12/12 and the last day of February. Find the year’s doomsday, then count from the nearest doomsday date. For 2026 the doomsday is Saturday, so 12/12/2026 is a Saturday and Christmas, December 25, is a Friday. For a formula you can apply mechanically or in code, use Zeller’s congruence.

Method 1: the Doomsday rule

Step 1: Memorize the doomsday dates

In every year, these dates fall on the same weekday, the doomsday:

Step 2: Find the century anchor

The pattern repeats every 400 years: Sunday, Friday, Wednesday, Tuesday.

Step 3: Calculate the year’s doomsday

Let y be the last two digits of the year.

Example: 2026. y = 26.

• 26 ÷ 12 = 2 remainder 2
• 2 ÷ 4 = 0 (whole part)
• Sum: 2 + 2 + 0 = 4
• Tuesday (2000s anchor) + 4 days = Saturday

Step 4: Count from the nearest doomsday date

December 25, 2026: December 12 is a Saturday. December 26 is also a doomsday, so it is Saturday too, and December 25 is the day before: Friday.

October 11, 2026: October 10 is a doomsday (Saturday), so October 11 is a Sunday.

Two historical examples

July 4, 1776. Anchor for the 1700s: Sunday. y = 76: 76 ÷ 12 = 6 remainder 4; 4 ÷ 4 = 1. Sum: 6 + 4 + 1 = 11, and 11 mod 7 = 4. Sunday + 4 = Thursday. July 4 is a doomsday date, so it was a Thursday.

July 20, 1969 (the first Moon landing). Anchor for the 1900s: Wednesday. y = 69: 69 ÷ 12 = 5 remainder 9; 9 ÷ 4 = 2. Sum: 5 + 9 + 2 = 16, and 16 mod 7 = 2. Wednesday + 2 = Friday. July 11 was a Friday, and July 20 is 9 days later: 9 mod 7 = 2, so Friday + 2 = Sunday.

Method 2: Zeller’s congruence

Zeller’s congruence, published by Christian Zeller in the 1880s, gives the weekday directly. For the Gregorian calendar:

• q = day of the month
• m = month, with March = 3 through December = 12, and January = 13 and February = 14 of the previous year
• K = year of the century (year mod 100)
• J = century (⌊year ÷ 100⌋)
• h = weekday: 0 = Saturday, 1 = Sunday, 2 = Monday, 3 = Tuesday, 4 = Wednesday, 5 = Thursday, 6 = Friday

Example: December 25, 2026. q = 25, m = 12, K = 26, J = 20.

195 mod 7 = 6, which is Friday, matching the Doomsday result.

Example: January 1, 2026. January counts as month 13 of 2025, so q = 1, m = 13, K = 25, J = 20. The sum is 1 + 36 + 25 + 6 + 5 + 100 = 173, and 173 mod 7 = 5: Thursday.

The month adjustment is the usual source of errors: forgetting to move January and February into the previous year gives an answer that is off by one or two days. The modulo calculator helps with the final step.

Doomsdays for nearby years

The doomsday advances one weekday per year and two after a leap year, for the same reason your birthday moves forward. See how leap years work for why.

Why the methods work

Both methods rest on one fact: weekdays repeat every 7 days, so only the remainder after dividing a day count by 7 matters. A common year is 365 days, or 52 weeks plus 1 day, which is why a date’s weekday advances by one each year and by two after a leap day. The doomsday dates are chosen because they are a whole number of weeks apart: from 4/4 to 6/6 is 63 days, from 6/6 to 8/8 is 63 days, and from 8/8 to 10/10 is 63 days, all exactly 9 weeks. The ⌊y ÷ 12⌋ step works because 12 years contain 12 + 3 = 15 extra weekday shifts (12 years plus 3 leap days), and 15 mod 7 = 1. Zeller’s odd-looking ⌊13(m + 1) ÷ 5⌋ term encodes the uneven month lengths from March onward, which is why January and February are moved to the end of the previous year. Counting the days between two dates and reducing mod 7 is the same idea in its simplest form; see how to count days between dates.

Tips for speed

• Use the closest doomsday date, including the extras: July 4, Halloween (10/31) and December 26.
• Count by weeks: dates 7, 14, 21 or 28 days apart share a weekday, so reduce any gap with mod 7.
• The “odd + 11” variant: if y is odd, add 11; halve it; if the result is odd, add 11; then take 7 minus (result mod 7) and count forward from the anchor. Some people find it easier than dividing by 12.
• Check with a known date: you probably know what weekday today is; compute today as a test.

When you just need the answer

The day of the week calculator shows the weekday of any date along with the Doomsday and Zeller steps, and the birthday calculator shows which weekday you were born on and future birthdays. For a month view, the printable calendar builds any month or year. To move forward or backward from a date by a number of days, the date calculator does the counting.