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The Doomsday Algorithm - Calculating the Weekday of any given Date

In 1970, British mathematician John Conway devised a way to quickly calculate the weekday of any given date without the help of calculators, computers, or calendars

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Calculate the weekday of any date.
Calculating the weekday of any date - it's (nearly) that simple!
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The best thing about the doomsday algorithm: your friends will think you have a superhuman memory, when all you need to do is memorize a set of numbers and do a series of simple calculations.

Conway's algorithm bases on the fact that some dates always fall on the same weekday within any given year. These dates are called doomsdays.

Find out which dates are doomsdays

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Calculating the Weekday for any Date in your Head

There are plenty of scary doomsday formulas out there, but how about those of us who don't hold a degree in mathematics? Here's how to do it in four steps:

Step 1: Memorizing weekdays as numbers

In Conway's concept, each weekday is represented by a number:

Memorize these numbers before moving on. As a mental anchor, it may be helpful to think of Tuesday as “Twosday”.

Step 2: Memorizing the anchor days

Calendars repeat themselves every 400 years, so all you need to do is to remember the anchor days for 4 centuries. As most dates you will come across lie in the time span between 1800 and 2100 it is most practical to remember the anchor days for the 19th, 20th, 21st and 22nd century:

1800 - 1899: Friday

1900 - 1999: Wednesday

2000 - 2099: Tuesday

2100 - 2199: Sunday

For dates outside of this time frame you can simply rely on the 400-year calendar cycle. This means that the anchor day for 1700 - 1799 is again Sunday, in 1600 - 1699 it is Tuesday, and so on.

Note: The rules described here apply only to the Gregorian calendar (“Western calendar”). Different rules apply to the Julian calendar.

Step 3: Calculating the doomsday of any given year

To determine the doomsday of the year in question, you have to follow a series of 6 simple calculations. Before you start, don't forget to memorize the weekday numbers (see step 1) and century anchor days (see step 2).

To illustrate the calculations, an example is given for each - let's say we want to find out which day of the week February 11, 1978 fell on...

  1. How many times does the number 12 fit as a whole into the two last digits of the year number?

    Example date: February 11, 1978. The number 12 fits 6 whole times into 78 (6 x 12 = 72), so the result is 6.
  2. What is the difference between the two last digits of the year number and the product of the multiples of 12 from calculation 1?

    Example: The product of 6 x 12 is 72 (see calculation 1). The difference between 72 and 78 is 6, so the result is 6.
  3. How many times does the number 4 fit into the result of calculation 2?

    Example: The result of calculation 2 was 6. The number 4 fits only once into the number 6, so the result is 1.
  4. What is the century's anchor day?
    Example: The anchor day of the 1900s is Wednesday, which corresponds to number 3 (see step 1), so the result is 3.

  5. Add up all the results.

    Example: 6 + 6 + 1 + 3 = 16, so the result is 16.
  6. Subtract whole multiples of 7 from the result of calculation 5. This will result in a number between 0 and 6, which corresponds to the doomsday of the year.

    Example: 16 - 14 = 2, so the result is 2. This means that the doomsday in 1978 was a Tuesday.

Step 4: Move from the doomsday to the date in question

Now it is only a small step to the final result. You know the doomsday of the year (in 1978, it was Tuesday), and you know which dates of the year are doomsdays. Now you can simply use the doomsday closest to the date in question to find out which weekday it falls on.

In the example date of February 11, 1978, the closest doomsday is the last day of February, which was February 28 because 1978 was not a leap year. Use multiples of 7 to move closer to the date: 28 - 14 = 14. So you know that February 14 was a Tuesday. Now count the days back to February 11, and you will see: February 11, 1978 fell on a Saturday.

Don't give up

This might sound awfully complicated at first, and most of us will need a good minute or three to go through all the steps. But with a little practice things will soon pick up speed. Don't forget: even the inventor of the doomsday rule is said to practice these calculations every day to perfect his speed-calculating skills. According to some sources, Conway can now usually give a correct answer in under two seconds. But then again, he's a math professor.

Don't want to do the math? Use the Weekday Calculator to find out the weekday for any date.

Topics: Time, Calendar

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Dooms Day algorithm

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  2. The Doomsday Algorithm

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