How To Work Out The Day Of The Week For Any Date, Past Or Future

There are seven days in a week, for some reason, so none of those questions should be too taxing if you know your seven times table – but what if we were to ask you this: what day of the week was it on July 17, 1973? How about December 1, 1816? Or January 8, 2262?

Now, those questions seem a lot harder – but they are answerable. And if you know the trick, you'd be surprised at how quickly you can do it: the guy who invented the method – John Conway, because of course it was John Conway – got so good at it that he could reportedly work out any date within just a couple of seconds.

All you need is a Doomsday.

Step one: the day of the century

Quick disclaimer: while this algorithm does get rid of the need to just learn all dates in history for a party trick, it does still require some memorization. First up, we need to learn either the “anchor days” – a single day of the week on which to “anchor” an entire century – or else how to work them out.

So, let's go from first principles: the mathematical formula for working out the anchor day is

5 × (c mod 4) mod 7 + Tuesday = anchor,

where c is the floor – that is, the whole part – of the current year divided by 100.

Now, if you're not familiar with mod notation, don't worry: it's like clock counting, where once you get past a certain number you reset to 0 again – hence why “13 o'clock” is more often called “1 o'clock”, because we tell the time “mod 12”. Alternatively, you can think of it as taking the remainder upon division by the modulus: for example, 23 o'clock is 11pm because 23/12 is 1 remainder 11.

So, let's use the current year, 2026, as an example for working out the 2000–2099 anchor day. In this case, 2026/100 = 20.26, so c = 20. 20 mod 4 is 0, which makes everything else especially easy: 0 mod 7 is 0, and then 5 × 0 = 0. Add that to Tuesday to get the anchor day, and we find… yup: it's Tuesday.

Ok, what about last century? Between 1900 and 1999, we have the following: 

5 × (c mod 4) mod 7  + Tuesday = 5 × (19 mod 4) mod 7 + Tuesday             

= 5 × 3 mod 7 + Tuesday                  

= 15 mod 7 + Tuesday                               

= 1 + Tuesday                   

= Wednesday.

Get it? If the answer is no, you can always just memorize them instead: the 19th century's anchor day is Friday; the 20th's is Wednesday; the 21st's is Tuesday – you might remember this as “Y-Tues-K”; the 22nd's is Sunday; the 23rd's is Friday again, and so on. In short: if the year begins with a number divisible by 4, you want Tuesday; if it has a remainder of one upon division by 4, then it's Sunday; a remainder of two means Friday; a remainder of three means Wednesday. 

Step two: the day of the year

Now we've dealt with the century's anchor year, let's get more specific. To find the year's anchor day, or what Conway called the “Doomsday”, first take the last two digits in the year and divide that number by 12, then make a note of the whole part of the answer, the remainder, and the whole part of the remainder divided by 4. Next, add all of those up, and count forward that many from your century's anchor day.

Let's use this year as an example again. We take 26 and divide by 12: that gives us 2 remainder 2. That remainder divided by 4 is 0.5, which gives a whole part of 0. Adding those three results gives 2 + 2 + 0 = 4.

We already found the century's anchor day to be Tuesday, so now it's just a matter of counting 4 days forward, giving a Doomsday of Saturday for 2026.

That was Conway's original formula, but in 2010 a pair of mathematicians presented a different way to compute the same thing. Called the “odd + 11” method for reasons that will become obvious, it runs like this: take your two-digit year and, if it's odd, add 11 – if it's even, leave it as is. Then, divide by two, and if your answer is odd, add 11. Next, take modulo 7, and subtract that from 7.

For 26, the calculation looks like this: 26 is even, so we don't add 11. Dividing by two gives 13, however, so at this point we add 11 to give us 24. 24 = 3 mod 7 (because 24 = 3 × 7 + 3), and 7 – 3 = 4. Add that to the century's anchor day, Tuesday, to once again get Saturday.

Step three: know your Doomsdays

The final part of the algorithm is to relate your given date to a nearby doomsday – and luckily, this part is the easiest and most fun to deal with. The general idea is this: in every month, there are certain days that always fall on the same day of the week – specifically, the doomsday we just worked out for the year. 

Those days are fixed and easy to remember, with one very minor exception. For even-numbered months from April onwards, you can just take the double date: the April 4, June 6, August 8, October 10, and December 12 are all doomsdays. For the odd-numbered months, “I always remember [it] by thinking of having a 9-to-5 job in the 7-Eleven store,” Conway explained back in 2014: it works because 5/9, 9/5, 7/11, and 11/7 are all doomsdays.

That just leaves January, February, and March. The latter two are pretty memorable: you can take the last day of February, regardless of whether it's a leap year or not, and in March, pi day (March 14). It's just January that's a little complicated, because of leap years: you can take January 3 three out of four years, and on leap years, take January 4. 

From there, it's just a matter of taking the closest one to the date you've been given and working it out from there.

Does it work?

Well, let's see. Today's date is May 8, 2026: the nearest doomsday is the 9th, and we already worked out that it's a Saturday. That makes today one day before a Saturday, i.e. Friday – and a look at the calendar confirms that to be the case.

Okay, so how about those examples from the top of the article? July 17, 1973; December 1, 1816; and January 8, 2262? Let's work those out:

First: 1973 gives a century anchor day of Wednesday, which gives a doomsday of… also Wednesday, since the math prescribes that we add 7 to the anchor day. The nearest doomsday is July 11, because of the “9-to-5 job in the 7-Eleven store” rule, which is six days earlier than July 17th – so we add six days to Wednesday, and find that July 17th, 1973 was a Tuesday.

Next: 1816 gives a century anchor day of Friday for a doomsday of Thursday. The nearest Doomsday to December 1 is December 12, because it's an even-number month. Go back 11 days from Thursday – that is, one week and four days – and we find December 1, 1816, to be a Sunday.

Finally: 2262 gives a century anchor day of Friday, and then a doomsday of Friday. 2262 isn't going to be a leap year, because 62 isn't a multiple of 4, so the nearest doomsday is January 3. January 1 is only two days earlier than that, and so January 8, 2262, will be a Wednesday.

Simpler than you thought, huh? Go forth and entertain.