date - What is the easiest algorithm to find the day of week of day zero of a given year?

Question

I am trying to figure out what the day of the week of day zero (January 1st) of a given year.

So far I have looked at the Wikipedia page 'Calculating the day of the week' but I was wondering if there is an easiest algorithm if you're just trying to find day zero.

Answer 1

Here's a simple one-liner. I've verified this for all the years 1901-2200 using Excel, and 1582-3000 using Python's datetime.

dayOfWeek = (year*365 + trunc((year-1) / 4) - trunc((year-1) / 100) +
             trunc((year-1) / 400)) % 7

This will give the day of the week as 0 = Sunday, 6 = Saturday. This result can easily be adjusted by adding a constant before or after the modulo 7. For example to match Python's convention of 0 = Monday, add 6 before the modulo.