The Doomsday Rule
Ask a friend to give you any date: their date of birth, the date they got married, the date they graduated. Or even a future event: Christmas of 2078, their 99th birthday. With nothing else, you can find the day of the week this event fell or will fall on. How? Using the Doomsday Algorithm.
For the Gregorian Calender, applying the Doomsday algorithm goes as such:
1) Determine the “anchor day” for the century in which the date-in-question falls in.
2) Calculate the doomsday for the year (of the-date-in-question).
3) Choose the closest date from those that always falls on the doomsday (this will make sense in a minute) and count the number of days between that doomsday and the date-in-question to arrive at the day of the week.
A doomsday is a date within a year that always has a certain day of the week. For example, in any given year, April 4th (4/4), June 6th (6/6), August 8th (8/8), October 10th (10/10) and December 12th (12/12) will have the same day of the week. This year, 2026, the doomsday is Saturday. In 2025, the doomsday was Friday.
To find the doomsday of any year, you’ll want to memorise the “anchor day” of the century it falls in:
17th Century (1600 - 1699): Tuesday
18th Century (1700 - 1799): Sunday
19th Century (1800 - 1899): Friday
20th Century (1900 - 1999): Wednesday
The pattern of Tuesday, Sunday, Friday, Wednesday then repeats every 4 centuries, so:
21st Century (2000-2099): Tuesday
22nd Century (2100-2199): Sunday
23rd Century (2200 - 2299): Friday
24th Century (2300 - 2399): Wednesday
and so on…
This is because the Gregorian Calender has 146,097 days, or exactly 20,871 seven-day weeks, every 400 years.
If you want the formula for finding the anchor day itself, take a look at https://en.wikipedia.org/wiki/Doomsday_rule#Finding_a_year's_doomsday . Although you’ll find it’s much easier to just remember these 4 days of the week.
Then to find the doomsday, complete the following:
1) Divide the last 2 digits of the year, we’ll call this “y”, by 12. Truncate your answer to the nearest whole number, and call this “a”. For 2025, y=25, and a=2 (as 25/12 = 2.08 which is 2 once truncated)
2) Find the remainder, we’ll call this “b”. For 2025, b=1 (as 25/12 = 2 remainder 1)
3) Divide “b” by 4. Truncate your answer to the nearest whole number and call it “c”. For 2025, c=0 (as 1/4 = 0.25 which is 0 once truncated).
4) Calculate a+b+c. Call this “d”. For 2025, d= 2 + 1 + 0 = 3.
5) Count d-days (into the future) from that century’s anchor day. For 2025, the 21st Century’s anchor day is Tuesday and d=3. 3 days after Tuesday is Friday. Therefore the doomsday of 2025 is Friday.
SIDE NOTE: An alternative value for ”d” can also be calculated by y* 1.25 (which is the same as y plus y/4) truncated to the nearest whole number. For 2025, that is 25 + (25/4) = 31.25 which is 31 once truncated. 31 days after Tuesday is also Friday. However this calculation is a bit more difficult for larger values of “y”.
If you know the doomsday of a year, you can then easily find the day of the week of any other day. For example, if the 12th of December 2025 (a doomsday) was a Friday, then Christmas of 2025 was 13 days after that, which is a Thursday (Friday + 13 days = Thursday).
To know the doomsday of each month in a year, you can memorise the following:
January: 3rd (common years) and 4th (leap years)
February: 28th (common years) and 29th (leap years)
March: 14th (Pi day)
April: 4th
May: 9th
June: 6th
July: 11th
August: 8th
September: 5th
October: 10th
November: 7th
December: 12th
The mnumonic for “odd” months (besides January/March) is “I work 9 to 5 at the 7-11”, as 5/9, 9/5, 7/11, and 11/7 are all doomsdays. The rule for even months (besides February) is that the date number matches the month number (4/4, 6/6, 8/8, 10/10, 12/12).
You now have a complex skill for solving a problem nobody has anymore, thanks to digital calenders, which will receive a lukewarm reaction from your friends who just witnessed you go silent for 5 minutes to write numbers.