How to Determine the Day of the Week From the Date

You can find out any day of the week of any given date.

You may have heard of savants who can calculate the day of the week from any date within several seconds. Although this feat seems remarkable, many people could easily do the calculation given just a bit more time and plenty of practice. The method used to make these calculations relies heavily on the fact that certain dates fall out on the same day of the week in any given year. For example, April 4, June 6, Aug. 8 and Oct. 10 all fall on the same day of the week each year. The trick is figuring out what that day is.

Things You'll Need

• Pencil and paper, or computer (optional)

Instructions

1. Divide the last two digits of the year by 12, to get a quotient -- the answer to the division problem -- and a remainder -- what is left over after dividing. Divide the remainder by 4 to get a second remainder. Add together these three numbers -- the quotient, the first remainder and the second remainder. For example, if the last two digits of the year were 25, you would divide that by 12 to get 2, with a remainder of 1. You would then divide that again by 4 to get 0, with a remainder of 1. You would then add 2, 1 and 1 together.

2. Add or subtract 4 to the first two digits of the year until you reach the number 17, 18, 19 or 20. For example, for 1340, you would get 17, which is 13 + 4. If you get 17, use Sunday for the start of the next calculation; if you get 18, use Friday; if you get 19, use Wednesday; if you get 20, use Tuesday.

3. Count the number of days in Step 1 from the day of the week in Step 2. For example, if you got 12 for Step 1 and Sunday for Step 2, count 12 days from Sunday, and you will get Friday. This is "Doomsday," for the purposes of the upcoming steps.

4. Memorize the fact that the following dates fall out on "Doomsday" that year: April 4, June 6, Aug. 8, Oct. 10 and Dec. 12. Then add on May 9, Sept. 5, July 11 and Nov. 7 to the list. You can use the sentence "I have a nine-to-five job at Seven Eleven" to remember these dates. Finally, add the last day of February to the list.

5. Figure out whether the year is a leap year (whether it is divisible by 4, but not the beginning of a century). If it is, add the dates Jan. 4 and Feb. 1 to the list. If it is not, add the dates Jan. 3 and Jan. 31 to the list. All of the dates on the list start on the day of the week you calculated in Step 3.

6. Find the date on the list that is closest to the one that you are calculating. For example, if you are wondering which day of the week April 20 falls out on, you should use the fact that Doomsday falls out on April 4 that year (as well as the Doomsday for that year, calculated in Step 3), to figure it out.

7. Add or subtract seven to the Doomsday date you chose in the previous question, over and over again, until you are less than seven away from the date that you are looking for. Figure out how many days from Doomsday that date must be, and calculate the day of the week that it falls on accordingly.

Tips & Warnings

• Keep in mind that this process will only give you the Gregorian date, not the Julian date. Because Julius Caesar deleted 10 days from the calendar in the 1500s, any date before Oct. 15, 1582, will be three days off of the true day of the week when calculated using this method.

References

• University of Texas at Austin: Doomsday