The Doomsday Algorithm: How to Find the Day of the Week for Any Date in Your Head

Every date maps to exactly one day of the week. But how do you figure that out without a calendar?

In 1973, mathematician John Conway invented an algorithm that lets you determine — entirely in your head — what day of the week any date falls on. Whether it’s October 4, 1582, or your next birthday.

The method is built on the observation that every year contains anchor dates that always land on the same day of the week. That shared day is called the Doomsday for that year.

The Doomsday Algorithm Step 1: Memorize the Anchor Dates

Here is the list of anchor dates for non-leap years:

• April 4 → 4/4
• June 6 → 6/6
• August 8 → 8/8
• October 10 → 10/10
• December 12 → 12/12
• September 5 → 9/5
• May 9 → 5/9
• July 11 and November 7 → 7/11 and 11/7
• February 28 (or 29 in a leap year)

All of these dates fall on the same day of the week within any given year — and that is the day you need to find.

Step 2: Find the Doomsday for a Specific Year

Use the last two digits of the year (call them yy) and follow these steps:

1. Take the last two digits of the year → call this A
2. Divide A by 12 → take the integer part → B
3. Find the remainder of A divided by 12 → C
4. Divide C by 4 → take the integer part → D
5. Add them up: B + C + D
6. Add the century anchor (see below)
7. Take the result modulo 7 → this gives the day of the week (0 = Sunday, 1 = Monday, … 6 = Saturday)

Century anchors:

• 1900–1999 → Tuesday (2)
• 2000–2099 → Tuesday (2)
• 2100–2199 → Sunday (0)
• 1800–1899 → Friday (5)

Step 3: Find the Nearest Anchor Date and Count the Offset

Once you know the Doomsday for the year, find the anchor date closest to your target date, then count forward or backward from there.

Doomsday Algorithm in Practice: A Worked Example

What day of the week is September 10, 2025?

Year: 2025, last two digits: A = 25

1. A = 25
2. B = 25 ÷ 12 = 2
3. C = 25 mod 12 = 1
4. D = 1 ÷ 4 = 0
5. B + C + D = 2 + 1 + 0 = 3
6. Century anchor (2000–2099) = 2
7. 3 + 2 = 5 → 5 mod 7 = 5

The Doomsday for 2025 is Friday.

The nearest anchor date to September 10 is September 5, which — as we just established — falls on a Friday.

September 10 is 5 days later, so:

• September 5 → Friday
• September 6 → Saturday
• September 7 → Sunday
• September 8 → Monday
• September 9 → Tuesday
• September 10 → Wednesday

Answer: September 10, 2025 is a Wednesday.

Why the Doomsday Algorithm Is Worth Learning for Mental Math

The algorithm looks involved at first glance, but it sticks quickly. After a few practice runs, you will be computing this in 10–15 seconds — leaving people with the impression that you have a built-in calendar running somewhere in your head.