"Everything should be made as simple as possible, but not simpler."

                        -- Albert Einstein

There are three steps to calculating the day of the week from any date.  Each step will result in numbers between 0-6 which will be added together to show us the day of the week. Along the way, you will be reducing any numbers greater than or equal to 7 by subtracting any multiples of 7.  You’ll find that this is not as complex as it looks after you’ve done a few samples later.

Step #1: The Month Value

This is the most difficult step because it requires the memorization of a numeric value for each month.  (Go to the mnemonics section later for assistance with this.)

January = 3                May = 4                 September = 1

February = 6             June = 0                 October = 3

March = 6                  July = 2                  November = 6

April = 2                     August = 5             December = 1

Step #2:  The Day of the Month Value

This is simply the day of the month unless the number is equal to or greater than 7, then you must subtract the greatest multiple of 7 to get a remainder between 0-6.  This is the “reduction by multiples of 7 rule”.

                Examples for days of month = 5^th, 7^th, 8th, 16^th, and 25^th:

                                The 5^th is less than the number 7, so the resulting value would still be 5

                                 The 7^th is equal to 7, so 7 minus 7 leaves a value of 0

                                The 8^th is greater than 7, so 8 minus 7 leaves a value of 1

                                The 16^th is greater than 7x2, so 16 minus 14 leaves a value of 2

                                The 25^th is greater than 7x3, so 25 minus 21 leaves a value of 4

Step #3:  The Year Value

This step has 3 parts.  Yes, it seems a bit more complex than the other steps but once you know the value for a given year, you won’t need to recalculate it in the future. 

A)     The  Year Value (part one) 

Take the last 2 digits of the year and divide by 4, then discard the remainder. If the result is equal to or greater than 7, then you must apply the “reduction by multiples of 7 rule” to get a number between 0-6.

                Example:

For the year 1989, you would divide the 89 by 4 to get an initial result of 22, with a remainder of 1 to discard.  22 is greater than 7x3, so 22 minus 21 = 1.

Important note: If the last 2 digits of the year are divisible by 4 with no remainder, then that is a Leap Year, so you must subtract 1 from the Month Values for January and February.  The other months are not affected.

B)      The Year Value (part two)

 Again, take the last 2 digits of the year.  Apply the “reduction by multiples of 7 rule” to the number to get number between 0-6.

                Example:

For the year 1989, you see that the greatest multiple of 7 that can be subtracted is 84 (7 x 12).  89 minus 84 = 5

C)      The Century Value  (a constant value to be memorized)

1700s = 2

1800s = 0

1900s = 5

2000s = 4

2100s = 2

The total Year Value result is the sum of A+B+C.  If the result is equal to or greater than 7, then you must apply the “reduction by multiples of 7 rule” to get a number between 0-6.

Putting it all together:

Add your Month, Day and Year values together.  If the result is equal to or greater than 7, then you must apply the “reduction by multiples of 7 rule” to get a number between 0-6 where:

1 = Sunday

2 = Monday

3 = Tuesday

4 = Wednesday

5 = Thursday

6 = Friday

0 = Saturday