The Doomsday algorithm: the weekday of any date, in your head

1. The one fact behind it

Our calendar has a coincidence built into it. In any year, these five dates fall on the same weekday:

4 April, 6 June, 8 August, 10 October and 12 December. Each one is exactly nine weeks (63 days) after the one before, so they can never drift apart. They read the same in the day/month and month/day conventions, too.

Conway called that shared weekday the year's doomsday. There's one per year, and the whole method comes down to two questions: what is this year's doomsday, and how far is my date from a doomsday date?

2. Weekdays as numbers

The arithmetic is easier if each weekday is a number. Sunday is 0, and the rest follow:

Conway's mnemonic: Noneday, Oneday, Twosday, Treblesday, Foursday, Fiveday, Six-a-day.

The other habit is that sevens don't matter. Seven days later is the same weekday, so you can add or take away 7, 14, 21 or 28 whenever it helps. Going 6 days forward is the same as 1 day back.

3. The twelve doomsday dates

Every month has a date that lands on the year's doomsday. You have five already. The rest come with hooks:

The odd months pair up and swap: 5/9 and 9/5, 7/11 and 11/7. That's the 7-Eleven sentence. A leap year is any year divisible by 4, except century years, which must be divisible by 400: 2000 was a leap year, 1900 was not.

Practise the month dates in the trainer →

4. Any date this year

For a date in the current year you can skip straight here, because you only need to know this year's doomsday. It's Saturday in 2026.

Take 18 September 2024, whose year has Thursday as its doomsday:

1. Month doomsday

   September's doomsday date is the 5th (9/5), so 5 September 2024 is a Thursday.

2. Jump in sevens

   5 + 14 = 19, so 19 September is a Thursday too.

3. Count the rest

   The 18th is one day earlier: Wednesday.

That's already a party trick: once you've looked up this year's doomsday, anyone's birthday this year is a few seconds away. Try it with this year's dates →

5. Century anchors

For other years, you build the doomsday yourself from two parts. The first is the century's anchor, the doomsday of its year 00. There are only four, and they repeat every 400 years:

Almost every date you'll be asked about is in the 1900s or 2000s, so start with two: 1900 is "We-in-dis-day" (Wednesday), and 2000 is "Y-Tue-K" (Tuesday).

6. The year offset

The second part is how far the year has moved the doomsday since its century began. Each ordinary year moves it one weekday on, and each leap year two. The classic way to count that is simple and always works:

1. Take the last two digits of the year, y.
2. Divide y by 4 and drop the remainder. That's the number of leap days so far.
3. Add the two.
4. Take away sevens until you're left with 0 to 6. That's the offset.

Add the offset to the century anchor, and you have the year's doomsday.

Practise year doomsdays →

7. All four steps

Put together, every date goes the same way: century anchor → year offset → month doomsday → count.

The moon landing: 20 July 1969

The US Declaration of Independence: 4 July 1776

New Year's Day 2050

8. Try any date

Enter a date and see the same four steps worked out for it.

9. Cheat sheet

Everything on one card. Print it, or keep it open while you use the trainer.

Print the cheat sheet

10. Faster year offsets

The classic offset is the easiest to understand, but it makes you hold three numbers at once. With practice, most people switch to a method that keeps only one in their head. The best known is Odd + 11, published by Chamberlain Fong and Michael K. Walters in 2010:

1. If y is odd, add 11.
2. Halve it.
3. If the result is odd, add 11.
4. Take away sevens, then subtract what's left from 7.

The Doomsday app teaches several faster routes, from the dozens method Conway used to memorising all hundred offsets outright, and helps you pick the one that suits you.

11. Where it comes from

John Horton Conway, the mathematician best known for the Game of Life, introduced the method in 1973 in a paper called Tomorrow is the Day After Doomsday, in the Cambridge student journal Eureka. He built it on a rule Lewis Carroll had sent to Nature in 1887 and said so himself; his own addition was the doomsday dates for each month. Conway practised constantly: his computer is said to have quizzed him with random dates every time he logged in.

It works for any date in the Gregorian calendar, which began in 1582. Dates kept in the older Julian calendar, as in Britain until 1752, need a small adjustment.

Turn this into a habit

Reading the method takes ten minutes. Making it fast takes practice. The Doomsday app has a 48-lesson course built from this method, drills for each step, a Daily Challenge and a rating that tracks your speed. The first 16 lessons are free.

Free trainer

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