Determination of The Day of The Week - A Tabular Method To Calculate The Day of The Week

A Tabular Method To Calculate The Day of The Week

This method is valid for the Gregorian calendar as well as the Julian calendar. Britain and its colonies started using the Gregorian calendar on Thursday, September 14, 1752 (the previous day was Wednesday, September 2, 1752 (Old Style)). The areas now forming the United States adopted the calendar at different times depending on the colonial power: Spain and France had been using it since 1582, while Russia was still using the Julian calendar when Alaska was purchased from it in 1867.

The method requires one to know four input parameters to find four numbers to sum. Using modulus to restrict results to 0 through 6, the day of the week can be determined. Since this method uses the "zeroeth" day, we can add the day of the month directly (without subtracting 1). Examples of the evaluation of this method are below. The four inputs and four resulting summands are:

1. Century: Where is the first two digits of the year, the first summand is to be taken from the centuries' table below based on the rule: for Gregorian dates; for Julian dates. With Sunday being day 0, each number represents the day of the week on which March 25th (Lady Day) occurs in year 0 of the century.
2. Year: Because there are 365 days in a common year, which is 52 weeks plus 1 day, each year will start on the day of the week after that starting the preceding year. Each leap year has of course one more day than a common year. Assuming we know on which day a century starts (from above), if we add the number of years elapsed since the start of the century, plus the number of leap years that have elapsed since the start of the century, we get the day of the week on which the year starts. Where is the last two digits of the year, the second summand is to be taken from the years' table. This table makes an exception for 00 years in centuries whose first two digits are evenly divisible by 4, such as the 21st century, where year 00 (2000) was a leap year.
3. Month: The third summand is to be taken from the months' table below. N.B.: each month is taken to start at day "zero."
4. Day of the Month: Use the day number itself as the fourth summand, or use the value from the days' table below, based on the rule: .

Now add the summands and look up the remainder of a division by 7 in the days' table to get the Day of the week: