Calculate day of week

A small guide on calculating the day of week fairly easily

(Image ‘borrowed’ from here)

All it requires you to remember are 12 dates, (and one day of week each year), the rest is simple calculus that anyone can do without paper.

1) Memorise twelve DATES that got the same weekday, note that it is starting with March, to avoid dealing with Feb 29.

Mar. 1.
Apr. 5.
May 3.
Jun. 7.
Jul. 5.
Aug. 2.
Sep. 6.
Oct. 4.
Nov. 1.
Dec. 6.
Jan. 3. (*)
Feb. 7. (*)

(*) the following year

2) Each year memorise this day of week for current year. E.g. for 2020: Sunday


3) Remember that January and February are handled as previous year. Count the number of days after one of the reference days, While larger than 7 subtract 7 (or: take the remainder of this number by division with 7), and forward the day of week that number of days. (Obviously you can also count days before, and thus step backwards)

Example: what is the weekday of new years eve 2020

Either count this as 3 days before Jan. 3. that we memorised as a Sunday, and thus: Thursday
Or count this as (31-6)=25 days after Dec 6. but 25 4 (Or: 25-7-7-7=4), so 4 days after a Sunday, that is Thursday.


Note that Feb. 28. obviously have the same weekday as Feb. 7 (as 28 7). So as you most likely already knew the day of week of Mar 1. is advanced by one every normal year and by two in leap years.

If you want to calculate for a date somewhere further in the future, you thus need to add 1 per year PLUS an additional 1 per intermediate 29/2 (leap year).
Obviously subtract similar for a date in an earlier year.


(Nerds: You can reduce the calculus slightly by remembering June and February as the zero’th of the month)