How to use the doomsday rule trainer
- Choose Work out a date and enter a date, or choose Practice dates.
- For one date, read the table of steps from the century anchor to the weekday.
- For practice, pick a set number, how many dates and the range of years.
- Work out each weekday yourself, then tick Show the answers to check.
Formula
Century anchor (Sunday = 0): (5 x (century mod 4) + 2) mod 7
Doomsday of the year = anchor + twelves in the last two digits + the left over + the fours in the left over, mod 7
Doomsday dates: Jan 3 (4 in leap years), Feb 28 (29), Mar 14, Apr 4, May 9, Jun 6, Jul 11, Aug 8, Sep 5, Oct 10, Nov 7, Dec 12
Weekday = doomsday + (date - doomsday date of that month), mod 7
The rule works for the Gregorian calendar, from 1583 on.
Saturday, October 17, 2026
The century is 20, whose anchor day is Tuesday (2). The last two digits are 26, which holds 2 twelves with 2 left over and no fours in the 2. The doomsday of 2026 is (2 + 2 + 2 + 0) mod 7 = 6, a Saturday. In October the doomsday date is the 10th, and 17 is 7 days later, so the weekday is again Saturday.
For February 29, 2024 the doomsday is Thursday, and in a leap year February's doomsday date is the 29th, so the date itself is a Thursday. The anchors for the centuries 1800, 1900, 2000 and 2100 are Friday, Wednesday, Tuesday and Sunday.
How the rule works
John Conway's doomsday rule picks one weekday for the whole year, the doomsday, and then finds a date in every month that falls on it, such as 4/4, 6/6, 8/8, 10/10 and 12/12. The weekday of any date is the number of days from the nearest doomsday date. Because the year's doomsday needs only a little arithmetic with 12s and 4s, it can be done in your head.
The anchor day repeats every four hundred years, because the Gregorian calendar repeats on that cycle. That is why four anchors are all you need for any date from 1600 to 2399.
Practicing
The practice set number always gives the same dates, so you can work through a set and come back to it. Try the month doomsdays first: they are easy to remember, and the rest follows. For plain answers use the Day of Week Calculator, to learn about leap years the Leap Year Calculator, to find every date that falls on a given weekday the Weekday on a Day of the Month Finder, and to turn a date into a day number the Julian Date Calculator.
Assumptions and limits
- Dates are in the Gregorian calendar, from 1583 to 9999.
- Weekdays are numbered from Sunday = 0 to Saturday = 6.
- The dates shown are examples. Use any date you like.
- Practice dates are made from the set number with a fixed method, so they repeat.
Frequently asked questions
Does it work before 1583?
No. Earlier dates in many places were in the Julian calendar, which has different rules, so the tool refuses them.
Why are February and January special?
Their doomsday dates move by one day in a leap year, because the leap day is added at the end of February.
How can I check my answer?
In the work-out mode the tool compares its answer with the calendar. In practice mode, tick Show the answers.
Are the practice dates random?
They look random but depend only on the set number, so the same number always gives the same dates.