# How to calculate the day of the week for a given date.

## © Stu Savory, 2003.

**CAUTION : Theo Zouros, a professor on Crete, tells me (on 24/2/2011) that there is a bug in Gauss's algorithm for some dates.
I shall investigate the problem.**

Let the date be DD/MM/CCYY (european format), where DD is the
day of the month, MM is the month, CC the century-digits and YY the year
within the century. So Wilma's birthday was 23/06/1994. Starting with
the century CC-digits, calculate CC/4 - 2*CC-1 and remember the result. With
all divisions in this exercise, discard any remainder and just keep
the whole part. So, in our example, this is 19/4=4 minus 2*19=38
minus 1, giving minus 35.

Now, using the year YY, calculate 5*YY/4. In this example
that's 5*94 = 470/4 = 117, discarding the remainder. Adding this to
our existing result gives 117-35 = 82.

Using the month MM, calculate 26*(MM+1)/10. In our example this is
26*7 = 182 / 10 = 18, again discarding the remainder. Add this to our
running total giving 82+18 = 100.

Finally just add the day DD. Here 100 + 23 = 123.

Now divide the result by 7, just **keeping the remainder**;
here 123(mod 7) = 4. Counting Sunday as zero, Monday = 1 etc, we get
4 = Thursday. *Easy, when you know how :-) *

The algorithm is attributed
to Gauss. Yes, I do know that Jews and Muslims etc have different
calenders and I do know about the various calender reforms, so this
only applies to the modern Christian-based standardised dates, don't
go using it to check the day of Christ's crucifixion (-fiction?)
or even Chaucer's
birth.

If you can't do this as mental
arithmetic (thus winning beers in the pub) feel free to
use pencil and paper (or a calculator).

Now go visit my blog please, or look at other interesting maths stuff :-)