Doomsday Calculator

The Doomsday Wheel

Famous Years to Doomsday-Check

Click a year to compute its doomsday and see the algorithm steps.

Doomsdays 2020-2031

For just the weekday of a specific date, see Day of Week.

Conway's 1973 Formula

Standard Doomsday Dates (Conway Memory Aids)

No saved years yet. Tap "Save Year" to remember up to eight doomsdays in your browser's localStorage.

How to Read the Doomsday Wheel

1. Type a Gregorian year in the picker. The wheel rotates so that its pointer lands on the year's doomsday weekday.
2. Read the algorithm-steps box. The four numbers (a, b, c, anchor) sum mod 7 to the weekday index; this is exactly what Conway computed in his head.
3. Browse the 'all 12 doomsdays' grid. Each listed date (4/4, 6/6, … 12/12) falls on that weekday, plus Mar 14, May 9, Jul 11, Sep 5, Nov 7 (the '9-to-5 at the 7-Eleven' mnemonic).
4. Walk from a doomsday to any target date in your head: count forward or back in the same month. For cross-month walks, use the standard doomsday in the target month as a stepping stone.
5. Save the year. The last eight doomsdays you compute persist in browser localStorage for revision.

How Conway Made Calendar Math Mental

In 1973, mathematician John Horton Conway — already famous for the Game of Life (1970) and on his way to surreal numbers (1976) — published a short note titled 'Tomorrow is the day after Doomsday' in Eureka, the Cambridge University journal of mathematics. In it he presented a five-second mental algorithm for computing the day of the week of any Gregorian date. The trick: every year has an 'anchor weekday' (the doomsday) on which 4/4, 6/6, 8/8, 10/10, and 12/12 all fall. Walking from a doomsday to any other date in the same month is then a small arithmetic step.

Conway's doomsday rule was a refinement of the Lewis Carroll method (1887) and Zeller's congruence (Christian Zeller, 1882), but built for mental arithmetic. The algorithm has three layers: identify the century anchor (1800s = Friday, 1900s = Wednesday, 2000s = Tuesday, 2100s = Sunday, repeating in a 400-year cycle that mirrors the Gregorian leap rule), compute the year's doomsday from the year's last two digits, and step from the nearest standard doomsday to the target date. With practice, the entire chain takes under five seconds.

The century-anchor cycle reflects the Gregorian leap exception. Pope Gregory XIII's 1582 reform (Inter gravissimas) excluded century years from being leap unless divisible by 400. So 1700, 1800, 1900 were not leap; 2000 was. Each non-leap century shifts the calendar by 5 days × 100 + 24 leap days = 525 mod 7 = 0… wait, the correct arithmetic: a non-leap century contains 36,524 days = 5217 weeks × 7 + 5 days, so the doomsday advances 5 weekdays per non-leap century. After four centuries the total shift is 0 mod 7, completing the 400-year cycle.

Within a century, the year's doomsday is computed from the last two digits: let YY = last two digits; compute floor(YY/12) + (YY mod 12) + floor((YY mod 12)/4), then add the century anchor mod 7. The component floor(YY/12) counts whole twelve-year sub-cycles (each shifts the calendar by exactly 16 days = 2 weeks + 2 days), and floor((YY mod 12)/4) accounts for leap years inside the residual. The algorithm is calibrated so that the final mod-7 result lands on the year's doomsday weekday.

Conway claimed he could find any date in his head in under two seconds and held mental arithmetic races against students at Princeton until his death in 2020. The doomsday rule has since become a staple of mental-math curriculum and competitive memory: the World Memory Championship's 'Historic Dates' discipline uses dates from 1000 to 2099 and the doomsday rule is the standard tool. Speed-cubers Feliks Zemdegs and Yusheng Du have publicly demonstrated under-three-second day-of-week calculations using the algorithm.

The rule is closely related to Zeller's congruence (h = (q + floor(13(m+1)/5) + K + floor(K/4) + floor(J/4) − 2J) mod 7), which is the textbook formula for computers, and to the Tomohiko Sakamoto algorithm (used inside the Unix 'cal' utility). The advantage of Conway's rule is exclusively pedagogical and mental — for software, any of those three are equivalent. Modern JavaScript Date objects internally use Sakamoto-style table lookups.

Beyond mental arithmetic, the doomsday rule has practical use for cryptographers verifying timestamps under low-power conditions, archivists dating manuscripts where only the day-of-week is recorded, and chronological puzzle solvers (sudoku-style date puzzles, 'What was the day-of-week on the historical event X?'). This calculator surfaces both the answer (the year's doomsday weekday) and the algorithm steps, so the user learns the rule as a side-effect of using the tool.