How to find the day of the week for any date in your head

Someone names a date, you name the weekday. It looks like memory; it's four small additions and one division by 7. This version works for every date from 1800 to 2199.

The formula

century code + year code + month code + day → remainder after ÷ 7

Remainder	0	1	2	3	4	5	6
Day	Sun	Mon	Tue	Wed	Thu	Fri	Sat

Step 1: the century code

1800s	1900s	2000s	2100s
2	0	6	4

Step 2: the year code

Take the last two digits of the year and add a quarter of them, dropping any remainder. For 1969: 69 + 17 = 86. You can knock 7s off at any point to keep the numbers small — 86 is 2 more than 84, so just carry 2.

Step 3: the month code

Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
0	3	3	6	1	4	6	2	5	0	3	5

Memorise them as three-digit chunks: 033 · 614 · 625 · 035. In a leap year, subtract 1 for January and February only.

Step 4: add the day, divide by 7

Example: 20 July 1969 (the Moon landing)

century 1900s → 0 year 69 + 17 = 86 month July → 6 day → 20 total 112 112 ÷ 7 = 16 remainder 0 → Sunday

Example: 10 September 2026

century 2000s → 6 year 26 + 6 = 32 month Sept → 5 day → 10 total 53 53 ÷ 7 = 7 remainder 4 → Thursday

Example: 29 February 2024 (leap year)

century 2000s → 6 year 24 + 6 = 30 month Feb 3 − 1 (leap) = 2 day → 29 total 67 67 ÷ 7 = 9 remainder 4 → Thursday

Leap years

A year is a leap year if it divides by 4 — except century years, which must divide by 400. So 2000 was a leap year; 1900 and 2100 are not.

Getting fast at it

Once the month codes are automatic, the slow step is the year code. Keep the running total below 7 by casting out 7s as you go, and practise with random dates until you can answer in a few seconds. R3CK0N's Secret mode has a timed Day of Week drill that throws random dates at you and records how long each one takes.

Drill random dates

The calendar trick is a classic of lightning calculation, covered in Arthur Benjamin and Michael Shermer's Secrets of Mental Math.