The Doomsday Method

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The Doomsday method lets you work out the day of the week for any date in your head. John Conway came up with it. In any given year, a handful of easy dates all fall on the same weekday, the year’s doomsday, and you work out every other date from there.

I first learned it during COVID. It’s a neat trick, there isn’t that much to memorise, and it’s good practice for mental maths. I wanted to get back into it, so I built a small practice tool. It’s free for anyone to use.

The practice tool is at https://wagenfuehrer.com/doomsday/practice.

First: days are numbers

The whole method is one sum. Turn the days into numbers, add up the three steps below, take the total mod 7, and turn the number back into a day only at the very end.

Step 1: The century

Look up the century. That number starts the sum.

They repeat every 400 years, so the 2100s are Sunday again.

Step 2: The year

Count the last two digits in twelves. Each twelve is worth one:

1. Add what the nearest twelve at or below the year is worth.
2. Add the years from that twelve up to your year.
3. Add one for every leap year in that gap (4 years → 1, 8 → 2).
4. Take the total mod 7. Keep it as a number; there is nothing to convert yet.

Example, 1988: Century Wednesday = 3, Twelve 84 → 7, Years 88 − 84 = 4, Leap years 4 ÷ 4 = 1. 3 + 7 + 4 + 1 = 15, mod 7 = 1.

Step 3: The date

Every month has one date that lands on the doomsday. Take the difference between it and your date, mod 7, and add that to the number from step 2. Mod 7 again, and that is your answer.

Only January and February move: in a leap year they shift up one day, to 4/1 and 29/2. Everything from March on is fixed forever.

Example, 23 April 1988: From step 2 1, April 4/4, Difference 23 − 4 = 19, Mod 7 19 mod 7 = 5. 1 + 5 = 6 → Saturday.