What's the formula for determing what day of the week any day will be in any year?

Question

You know, so you can be like "What day of the week will April 1, 2007 be?" and then you use the formula to figure it out.

Answer 1

N = d + 2m + [3(m+1)/5] + y + [y/4] - [y/100] + [y/400] + 2

d = day of the month

m = number of the month ( for Jan and Feb use 13, 14 of the previous year, e.g. for feb 18 2003 d=18 m=14 y=2002

y = the year

April 1, 2007

N = 1+2(4)+{3(4+1)/5}+2007+{2007/4}+{2007/100}-{2007/400}+2

For numbers in brackets use the whole number, drop everything after the decimal

N=1+8+{3(5)/5}+2007+501+20+5+2
N=9+15/5+2515
N=9+3+2515
N=2527

now divide N by 7

2527/7=361.0 the number after the decimal is the day of the week. 0 in this case.

0=Sun
1=Mon
2=Tue and so on

Or for an easier way, just look on a digital calander

Answer 2

There are two main ways you can do this.
First, you can memorize the first Sunday of each month for a whole year you wish to know and learn to count up to the date you want to know (adding 7 instead of 1 to speed things up when possible).
The other way (which is much better than the first, if you can do the math in your head) is rather long to explain. This site has the best explanation I've found (although I stopped looking once I knew how to do it) : http://geocities.com/mdetting/day_of_week.html
If you can manage to do it in your head, it's really neat. I've been doing it for years as a parlor trick and it impresses a lot of people. Some people don't seem to care what neat things you can do, and some think you're showing off if you do it. Lots of people refuse to take you seriously at first and just assume that you're BS'ing (which is why I programmed my calculator to check my work a couple of years ago). I suggest you feel out your audience to see if you're going to get a positive reaction from the trick though. Even if you can't do this in your head, it's still useful to be able to do it on paper or with a calculator. Good luck!

Edited to add: There are other methods of doing this calculation, but the ones I've described and linked to are by far the easiest.

Answer 3

It's called Gauss's formula but sorry I can't recall it. Try googling that name. There are only 14 possible calendars; seven for ordinary years (one for each day of the week that January 1 falls on), and similarly 7 for leap years.