Day of Week Calculator

Your friend's birthday is October 17, 2027 and you want to know what day that falls on so you can start planning whether the weekend works for a party. Your phone calendar will tell you eventually, but tapping through to that exact date is more friction than punching in three numbers and reading the answer.

Enter a date — past, present, or far future. The output is the day of the week. The math uses Zeller's congruence under the hood (the standard algorithm for this) so it's accurate for any date in the Gregorian calendar, which started October 15, 1582 in countries that adopted it then. Earlier dates require Julian-calendar adjustment, which the calculator handles for dates before 1582 but with an asterisk — historical date conversions get hairy because different countries switched calendars at different times.

Zeller's congruence is an arithmetic formula that maps a date to a day-of-week index. The version most commonly used: h = (q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ − 2J) mod 7, where q is the day of the month, m is the month (with January and February counted as months 13 and 14 of the previous year — a quirk of how leap years work), K is the year of the century, and J is the zero-based century. The result h is the day of the week with 0 = Saturday, 1 = Sunday, etc. The algorithm dates to the late 1800s and works for any Gregorian date. The Julian variant has a slightly different constant; the calculator selects automatically based on whether the date is before or after the Gregorian switch.

A worked example: October 17, 2027. q=17, m=10, K=27, J=20. Apply the formula: 17 + ⌊13×11/5⌋ + 27 + ⌊27/4⌋ + ⌊20/4⌋ − 40 = 17 + 28 + 27 + 6 + 5 − 40 = 43. 43 mod 7 = 1. Day index 1 = Sunday. So October 17, 2027 is a Sunday. Now apply the same to your own birthday and you can find out what day you were born without looking it up — many people have never bothered to check.

Where day-of-week calculations get historically thorny: the Gregorian transition wasn't simultaneous. Catholic countries adopted it in October 1582; England didn't until 1752 (when they jumped from September 2 to September 14). Russia waited until 1918. Greece until 1923. So a historical date like September 10, 1752 "didn't exist" in England — that range of 11 days was skipped. The calculator uses Gregorian for all dates after the most common transition date, which is the convention modern history books use. For dates in the gap or in a specific country's transition window, double-check the historical context before relying on the calculation. For dates after 1923, every country is on Gregorian and the calculator is straightforwardly correct.