How to Calculate the Day of the Week!

This always has interested me...

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Happy New Year guys! Sorry for the lack of updates, I had exams and was on vacation. But, I've recently found a fun little formula I found online a while back (I think from the University of Ottawa idk). It's pretty easy to do mentally once you get the hang of it, and a pretty nice way to sharpen your mental math capabilities. I will be using the date, January 8th, 2025

1. Divide the last two digits of a year by 4, and discard any fraction:

25 ÷ 4 = 6.25, so you would use 6

2. Add the day of the month to the quotient:

6 + 8 = 14

3. Add the month's specific key

Month	Key
January	1
February	4
March	4
April	0
May	2
June	5
July	0
August	3
September	6
October	1
November	4
December	4

4. Subtract 1 (only if January of February of Leap Year)
• To check if the year is a leap year, it has to be divisible by 4:

2025 ÷ 4 = 506.25

2025 is not a leap year

5. Add the century

Century	Key
2000's	6
1900's	0
1800's	2
1700's	4

15 + 6 = 21

6. Add the last two digits of the year

   21 + 25 = 46

7. Modulo by 7
• You could use the modulo function on a calculator:

46 mod 7 = 4

• Or do it manually:

46 ÷ 7 = 6.57143...

7 × 6 = 42 (round down)

46 - 42 = 4

8. Match the remaider to the weekday

Weekday	Remainder
Sunday	1
Monday	2
Tuesday	3
Wednesday	4
Thursday	5
Friday	6
Saturday	0

3 = Wednesday, so January 8th, 2025 is a Wednesday!

And there you go! You now know how to find the day of the week a date falls on. Feel free to try this on a date you want!

-ariu, 1/8/2025