How to Calculate Doomsday

Intro:

For a given year, certain dates like 4/4, 8/8 and 12/12 fall on the same day of the week for that entire year.   So if April 4, 2012 occurs on a Wednesday then so will 8 August 2012 and December 12th 2012.    There are even more days for which this kind of observation is true and it is observations like these that allow constructions such as perpetual calendars.

Step 1:

For some odd reason, the dates that have this property for every calendar year are called doomsdays.  If you want to know the day of the week for some arbitrary date, all you need to do is figure out the nearest doomsday.  For instance, the end of the world is predicted be on 21 December 2012.  Since the nearest doomsday is 19 December 2012, and all doomsday for 2012 fall on a Wednesday, this means that Doomsday falls on a Friday.   One thing to note here is that since the perpetual doomsday fell on 12/12/12.  If you add a week to that you get 12/19/12.  And then you can get to Doomsday.

Step 2:

By the way, Leap Day of a Leap Year is always a doomsday.  Since we are already hooked on Wednesday, and you know all the doomsdays for a given year are related, this means that you can just say Feb 29, 2012 happens on a Wednesday without even thinking about it or looking at a calendar.  As soon as you knew it was a doomsday, its fate was sealed.

Step 3:

The mathematical manipulation involving doomsdays are sometimes called the Doomsday rule or the Doomsday algorithm.

Step 4:

You could do the whole doomsday calculation by hand but most people will just use charts at some point in the calculation.

Step 5:

For instance, if you look up doomsday on Wikipedia you will see that doomsday for 2012 is Wednesday.  So you don’t even have to figure that out if you don’t want to.

Step 6:

Let us say that for some reason you did want to calculate this year’s doomsday.  One formula looks something like this:

(year /12 + year % 12 + (year % 12)/4) % 7 +  anchor day = doomsday

The “year” in this equation is actually just the last two digits of the year.  The percent sign is what is used in the language called C# for modulo.  Modulo means take the remainder of what happens when you divide.  The “anchor day” is a derived from yet another calculation.  Each century has its own anchor day.  The anchor day for our century is Tuesday.

There are other formulas for figuring out doomsday, some are faster and some are more computer oriented.

Step 7:

If you Google techie blogs you will find a computer formula for figuring out doomsday that may remind you of the formula for leap years since it has divisors of both 100 and 400 in it.

The formula looks like this:

Doomsday = 2 + year  + year/4 – year/100 + year/400.

The 2 comes from the anchor day of Tuesday for the century ranging from 2000 to 2099.  Yes we could calculate that particular Tuesday but I would rather take if off a chart.

In this case the year is the full 4 digit year and all divisions use integer arithmetic.  Integer arithmetic means there are no remainders.

So

Doomsday = 2 + 2012 + 2012/4 – 2012/100 + 2012 /400

Doomsday = 2014 + 503 -20 + 5= 2502

In order to figure out what day of the week this is we can use the Excel spreadsheet mod function:

Mod(2502,7) =3

If Monday is the 1st day of the week then Wednesday is the 3rd day of the week so again we get that for 2012 Wednesday is doomsday.  This tells us that for instance 4/4, 8/8 and 12/12 will all be on Wednesdays.  Remember that for Leap Year only, all you had to know is what day Feb 29th falls on and the rest is history!

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