Day of the Week Calculator

The calculation itself

Zeller's congruence, which computes the weekday arithmetically rather than counting from a reference date.

The formula treats March as the first month of the year, which is why January and February are entered as months 13 and 14 of the preceding year. Shifting the calendar this way moves the leap day to the end, where an irregular February no longer disturbs the pattern the formula depends on.

In practice

The 20th of July 1969 was a Sunday. The 1st of January 2000 was a Saturday. The 29th of February 2024 was a Thursday.

The page also gives the day of the year, which runs to 365 or 366, and the days remaining. The 31st of December 2024 was day 366; the 31st of December 2026 is day 365.

Leap years are those divisible by 4, except centuries not divisible by 400. 2000 qualified on the exception to the exception; 1900 did not.

Why weekdays drift

365 divided by 7 leaves a remainder of one. A given date therefore advances one weekday each ordinary year, and two across a leap year.

The whole cycle repeats every 400 years, which is the length of the Gregorian leap rule. That period contains exactly 146,097 days, and 146,097 divides evenly by 7 — a deliberate feature of the calendar, and the reason the pattern of weekdays is perfectly periodic rather than drifting forever.

A caveat on very old dates

This computes the proleptic Gregorian calendar: the modern calendar extended backwards past its own adoption in 1582.

Historical records from before adoption used the Julian calendar, and countries switched at different times — Britain and its colonies not until 1752. A date from that era can have two legitimate weekdays depending on which calendar the source was using, so historical work needs more care than this page can supply.