Footnote references are shaded in yellow. Footnotes are shown below the description.
To calculate the Day-of-Week ("DoW") for any date in the Gregorian calendar, add the values for the Month, Day, and Century/Year using the following three steps:
Step 1 - Add the DAY to the value for the MONTH from the Month Table and subtract from the result the largest multiple of 7 contained in it. Hold this number until step 3. a
Step 2 - Subtract from the last two digits of the YEAR the largest multiple of 28 contained in it, then divideb the result by 4 and round down (i.e., drop the remainder or decimal). Add the two results together and then add the value for the CENTURY from the Century Table. Subtract 1 if the year is a leap yearc AND the month is January or February.d e
Step 3 - Add the results from steps 1 and 2 and then subtract from the result the largest multiple of 7 contained in it. Using the resulting number, look up the Day of the Week in the Day of Week Table.
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Once you have mastered the above basic technique, you can then use the same basic formula with just one more step to find the Month, the Day, the Year and even the Century (if that need ever arises) when you know the other elements of the Date including the Day-of-Week.
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FOOTNOTES: The below footnotes are not needed to master the above technique. They are here for informaiton purposes only. .
a Some people are able to hold this number (between 0 and 6) in their heads while they do step 2. I prefer to "hold" it by subtly using the fingers on my left hand so that I make no mistakes when I return to get it in step 3.
b The reason you divide by 4 is to fund the number of leap years that have occurred since the base year.
c A year is a leap year if it is evenly divisible by 4, that is, there is no remainder when you divide it by 4. The only exception to this is for turn-of century years ('00) not evenly divisible by 400. (1600 and 2000 were leap years, whereas 1700, 1800, and 1900 were not.)
d The reason you subtract 1 here is because in a leap year, the extra day from February 29th is already added in for the full year, and so if February 29th has not occurred yet, you need to take out that extra one day.
e A table with the precomputed full year (CENTURY & YEAR) values can be found by clicking here.
Notice: If computing the year value in step two is too cumbersome for you, there are two alternative methods you might wish to consider. (These are for the year values before the century value is added and the -1 adjustment is made for January/February in leap years. Click here to look at those alternative methods.
a Some people are able to hold this number (between 0 and 6) in their heads while they do step 2. I prefer to "hold" it by subtly using the fingers on my left hand so that I make no mistakes when I return to get it in step 3.
b The reason you divide by 4 is to fund the number of leap years that have occurred since the base year.
c A year is a leap year if it is evenly divisible by 4, that is, there is no remainder when you divide it by 4. The only exception to this is for turn-of century years ('00) not evenly divisible by 400. (1600 and 2000 were leap years, whereas 1700, 1800, and 1900 were not.)
d The reason you subtract 1 here is because in a leap year, the extra day from February 29th is already added in for the full year, and so if February 29th has not occurred yet, you need to take out that extra one day.
e A table with the precomputed full year (CENTURY & YEAR) values can be found by clicking here.
Notice: If computing the year value in step two is too cumbersome for you, there are two alternative methods you might wish to consider. (These are for the year values before the century value is added and the -1 adjustment is made for January/February in leap years. Click here to look at those alternative methods.
