Learn Conway's Doomsday Algorithm — the mental math method that lets you name the day of the week for any date in history in seconds. Practice with a free interactive trainer, master the reference dates and formulas, and compete on a global leaderboard.
Play the Doomsday Trainer → free, no sign-inThe Doomsday Algorithm is a method invented by British mathematician John Horton Conway in 1973 for mentally calculating the day of the week for any date — past, present, or future — without a calendar or calculator.
The key insight is that certain dates within any year always fall on the same day of the week. Conway called this day the doomsday. Once you know the doomsday for a given year, you can find the weekday for any other date by counting days from the nearest doomsday anchor.
Conway was reportedly able to calculate the day for any date in the Gregorian calendar in under two seconds. With practice, most people can reach speeds of 3–5 seconds per date.
Beyond the party trick, the Doomsday Algorithm is a genuine exercise in mental arithmetic. Practitioners develop stronger intuition for modular arithmetic, calendar structure, and working memory — the same cognitive building blocks used in competitive memory sports.
Each century has a fixed anchor day. Memorise these four: 1800s → Friday, 1900s → Wednesday, 2000s → Tuesday, 2100s → Sunday. They cycle every 400 years, shifting back 5 days per century.
Take the last two digits of the year — call it YY. Calculate: a = YY ÷ 12, b = YY mod 12, c = b ÷ 4. Add a + b + c + anchor, then take mod 7. The result is the year's doomsday (0 = Sun, 1 = Mon … 6 = Sat).
Look up the doomsday reference date for your target month (see the table below). Pick whichever doomsday anchor is closest to your target date.
Count the days from the doomsday anchor to your target date. Add that offset (mod 7) to the year's doomsday. The result is the weekday for your target date.
Example: What day was 15 March 2026? Century anchor for 2000s = Tuesday (2). Year 26: a = 26÷12 = 2, b = 26 mod 12 = 2, c = 2÷4 = 0. Doomsday = (2+2+0+2) mod 7 = 6 = Saturday. Doomsday for March: 7th (since 7/7 is a doomsday — count 7 days from Feb 28 = March 7). March 7 is a Saturday. March 15 is 8 days later → 8 mod 7 = 1 extra day → Sunday. March 15, 2026 is a Sunday.
| Month | Doomsday dates | Mnemonic |
|---|---|---|
| January | 3 (common year), 4 (leap year) | Jan 3 or 4 |
| February | Last day (28 or 29) | End of Feb |
| March | 7, 14, 21, 28 | Every 7 days from March 7 |
| April | 4 | 4/4 |
| May | 9 | 9-to-5 at 7-Eleven |
| June | 6 | 6/6 |
| July | 11 | 9-to-5 at 7-Eleven |
| August | 8 | 8/8 |
| September | 5 | 9-to-5 at 7-Eleven |
| October | 10 | 10/10 |
| November | 7 | 9-to-5 at 7-Eleven |
| December | 12 | 12/12 |
The mnemonic "I work 9-to-5 at 7-Eleven" gives you four odd-month doomsdays: May 9, September 5, July 11, November 7. The even-month doubles (4/4, 6/6, 8/8, 10/10, 12/12) are the rest.
| Century | Anchor day | Number |
|---|---|---|
| 1800–1899 | Friday | 5 |
| 1900–1999 | Wednesday | 3 |
| 2000–2099 | Tuesday | 2 |
| 2100–2199 | Sunday | 0 |
The Doomsday Algorithm Trainer is a free, open-source game that trains your ability to name the day of the week for any date, using Conway's method. It was designed to feel like a skill-building game rather than a dry exercise.
Seven day buttons arranged in a 2×4 grid. Type as fast as you can. A timer bar ticks down — miss it and you lose your streak. Correct answers are rewarded with an animated flash and your streak counter grows.
A circular layout with the seven days arranged as a heptagon — inspired by the natural 7-fold structure of the week. Tap the correct position on the ring to answer.
A reference panel inside the game with the full Doomsday formula, century anchors, all monthly reference dates, and the "9-to-5 at 7-Eleven" mnemonic — everything you need without leaving the app.
The time limit shortens as your streak grows — 10 second budget at start, dropping progressively to 2 seconds at streak 40+.
A day-of-week calculator tells you the answer instantly. The Doomsday Algorithm Trainer teaches you to produce the answer yourself — from memory, in your head, in seconds.
These are complementary tools. Use a calculator when you need a quick lookup. Use the trainer when you want to develop the mental skill of computing dates without any tools at all.
What is the Doomsday Algorithm?
Conway's Doomsday Algorithm is a mental math technique for calculating the day of the week for any date. It relies on certain dates within a year — called doomsdays — always falling on the same weekday. Learn the year's doomsday, count from the nearest anchor date, and you have your answer.
What are doomsday dates?
Doomsday dates are calendar dates that always fall on the doomsday for any given year: 4/4, 6/6, 8/8, 10/10, 12/12 (even-month doubles); 5/9, 9/5, 7/11, 11/7 (the "9-to-5 at 7-Eleven" set); the last day of February; and January 3 or 4 depending on whether it's a leap year.
How do I calculate the year's doomsday for 2026?
Year 2026: century anchor = Tuesday (2). YY = 26. a = 26 ÷ 12 = 2, b = 26 mod 12 = 2, c = 2 ÷ 4 = 0. Doomsday = (2 + 2 + 0 + 2) mod 7 = 6 = Saturday. So every doomsday date in 2026 falls on a Saturday.
What day of the week was I born? (without a calculator)
Use the Doomsday Algorithm: find your birth year's doomsday, then count from the nearest doomsday reference date to your birthday. With a little practice this takes under 30 seconds to do in your head. Or just practice with the Doomsday Trainer until you can do it in seconds.
Is the Doomsday Algorithm hard to learn?
The basics can be learned in an afternoon. The full method — including leap year edge cases and non-2000s centuries — takes longer to make automatic. The algorithm has three distinct parts: century anchor (4 values to memorise), year formula (a short arithmetic procedure), and monthly reference dates (12 anchor dates). The trainer makes practice fast and addictive.
What is the "9-to-5 at 7-Eleven" mnemonic?
"I work 9-to-5 at 7-Eleven" encodes four odd-month doomsday dates: May 9, September 5, July 11, November 7. Pair this with the even-month doubles (4/4, 6/6, 8/8, 10/10, 12/12) and you have all 12 months covered.
What is the difference between the Doomsday Algorithm and Zeller's congruence?
Both methods calculate the day of the week. Zeller's congruence (1882) is a direct algebraic formula, better suited to computer implementation. Conway's Doomsday Algorithm (1973) is designed for mental calculation — it breaks the problem into memorisable sub-tasks (century anchors, reference dates) that are much easier to run in your head.
Does the trainer handle leap years correctly?
Yes. The trainer can optionally show a leap year hint for January and February dates, since the doomsday for those months shifts by one day in a leap year (January doomsday = 4 instead of 3; February doomsday = 29 instead of 28).
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