PSC Study Materials

# Day of the week of any Given Date PSC Problems & Formula

How to Calculate the Day of the week of any given date in no time. By Practicing this formula allows you to take a date and calculate which day of the week it fell on.

### Formula

(Year Code + Month Code + Century Code + Date Number – Leap Year Code) Mod 7
“Mod” means to divide the number and keep only the remainder. For Example if the Total of all codes is 58 mod 7, then divide 58/7 and keep only the reminder i.e. 2

### The Year Code

To calculate the Year Code, use this formula: (YY + (YY Div 4) Mod 7

YY is the last two digits of the year. For the year 2020, it’s 20.
First, divide YY by 4 and discard the remainder: 20 div 4 = 5.
Then add 11 back into the YY number, which is 20 in this case, resulting in 31.
The next step is: 31 mod 7. We’ve divided 31/7 and left with a remainder of 3. That is the Year Code for 2020.

### The Month Code

January – 0, February – 3, March – 3, April – 6, May – 1, June – 4, July – 5, August – 2, September – 5, October – 0, November – 3, December – 5.
This is easy — just memorize the number (033)(614)(525)(035)

### The Century Code

1700 – 4, 1800 – 2, 1900 – 0, 2000 – 6, 2100 – 4, 2200 – 2, 2300 – 0

Just remember the number (420)6(420)

### The Leap Year Code

If the date is from January or February of a leap year, you have to subtract one from your total before the final step and zero for other months.

If you can divide a Gregorian year by 4, it’s a leap year, unless it’s divisible by 100. But it is a leap year if it’s divisible by 400.
1992 is a leap year because you can divide it by four.
1900 is not a leap year because you can divide it by 100.
2000 is a leap year because you can divide it by 400.

### Calculating the Day

Back to the original formula:
(Year Code + Month Code + Century Code + Date Number – Leap Year Code) Mod 7

` For 29 March 2020, here are the results: Year Code: 3 Month Code: 3 Century Code: 6 Date Number: 29 (the 29th of the month) Leap Year Code: 0 (not January or February) So (3 + 3 + 6 + 29 - 0) mod 7 = 41 mod 7 = 0`

Match the resulting number in the list below, and you’ll have the day of the week:

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

29 March 2020 was on a Sunday .