How to Calculate the Day of the Week!
This always has interested me...Happy New Year guys! Sorry for the lack of updates, I had exams and was on vacation. 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 perform without a calculator 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
- Divide the last two digits of a year by 4, and discard any fraction:
- Add the day of the month to the quotient:
- Add the month's specific key
- Subtract 1 (only if January of February of Leap Year)
- Add the century
- Add the last two digits of the year
- Modulo by 7
- Match the remaider to the weekday
25 ÷ 4 = 6.25, so you would use 6
6 + 8 = 14
| 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 |
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
| Century | Key |
|---|---|
| 2000's | 6 |
| 1900's | 0 |
| 1800's | 2 |
| 1700's | 4 |
15 + 6 = 21
21 + 25 = 46
You could use the modulo function on a calculator:
46 mod 7 = 4
Or do it manually:
46 รท 7 = 6.57143...
7 × 6 = 42 (round down)
46 - 42 = 4
| 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!
-ariu, 01/08/2025