Determinig the Day of the Week in Other Years

The information contained here is a little more difficult to understand but it is worth the time to learn this.  Don't get too bold in front of your friends until you've first had a lot of practice because it's easy to make mistakes when you don't know the material very well.  Please review How to Determermine the Day of the Week for any Date before continuing.

E-mail Craig Ricks, craig@craigricks.com, for specific questions or comments.

Below is a list of years for the 1900's.  Only the leap years are shown here to make the list shorter.  In the long run, you'll really do well if you can memorize the non-leap years as well.

The 1900's:
 00 = 0 20 = 4 40 = 1 60 = 5 80 = 2 04 = 5 24 = 2 44 = 6 64 = 3 84 = 0 08 = 3 28 = 0 48 = 4 68 = 1 88 = 5 12 = 1 32 = 5 52 = 2 72 = 6 92 = 3 16 = 6 36 = 3 56 = 0 76 = 4 96 = 1

Other Years/Centuries After 1900's:
Use this method
to adjust for other centuries after the 1900's:

1900, 2300, 2700, 3100, etc. you use the above year list.
2000, 2400, 2800, 3200, etc. you use the above year list minus 1.
2100, 2500, 2900, 3300, etc. you use the above year list minus 3.
2200, 2600, 3000, 3400, etc. you use the above year list minus 5.

Example:
For the 2000's, 2400's, 2800's, 3200's (and any further number evenly divisible by 400, i.e. even the year 10,400 and beyond), you have to subtract an additional 1.  For example, the year 1904 you would think of a 5, but for 2004 (or 2804, etc.), you would think of a 4.  2000 = 6, 2001 = 0, 2002 = 1, 2003 = 2, 2004 = 4, 2005 = 5, 2006 = 6, 2007 = 0, 2008 = 2, etc.

For 1900, 2300, 2700 (years with first two numbers divisible by 4 minus 1) you do nothing.  They are the same as the 1900 list.

Date Examples:
May 12, 1953 = 1 + 12 + 0 + 3 = Tuesday
March 3, 2805 = 3 + 3 - 1 + 6 = 11 = Thursday
April 7, 3196 = 6 + 7 + 0 + 1 = 14 = Sunday

Years Before 1900's:

Only proceed with this section when you feel you have a good understanding of the other topics.  For calculating the year, there's a special exception for 1800's and earlier.  For the 1800's you subtract 2 from your final result; for 1700's you subtract 4.  Since the Gregorian calendar was adjusted for having too many leap years, there was no September 3 through September 13 in 1752.  For anything before September 3, 1752, you will have to make an adjustment because of the missing days (by adding another 4 to your result).  An easy method for years with 9/2/1752 and earlier is to take 18 minus the first two digits of the year.  1600's would be 18 - 16 = 2.  0700's would be 18 - 07 = 11. The year 0312 would be 18 - 3 (for the 03 part) + 1 (for the 12 part) = 16.

September 2, 1752 is:
September = 5
1752:  52 is 2.  1700 is 18 - 17 = 1.  So 2 + 1 = 3.  1752 = 3
5 + 2 + 3 = 10 = Wednesday

September 14, 1752 is:
5 + 14 + 4 + 2 = 25 = Thursday

Here's the calendar for September 1752.  I've seen some programs on the web and some Windows machines report this wrong (including the leap year for 1700 -- see next section below).  Use Linux or a UNIX operating system for a real calendar.

[root@linux root]# cal 9 1752

`   September 1752Su Mo Tu We Th Fr Sa       1  2 14 15 1617 18 19 20 21 22 2324 25 26 27 28 29 30`

Leap Years:
Leap years are any years evenly divisible by 4... unless divisible by 100 and not 400.  There is an exception to this rule for prior years.  That is, EVERY year that is divisible by 4 is a leap year, including the years divisible by 400 for the years through 1700.  This is because these rules we use didn't change until around 1752.  Don't forget to subtract an extra 1 from your total result for dates containing a leap year in January and February.  Some examples of leap years are: 1400, 1600, 1700, 2000, 2400.  Non-leap years are:  1800, 1900, 2100, 2200, 2300, 2500.  Note that the even though the year 2000 is divisible by 100, it is also divisible by 400 so it is considered a leap year.