Day of the Week Calculator

Why the weekday shifts by one each year

A common year is 365 days, which is 52 weeks plus one day, so any fixed date moves forward one weekday each year — and two across a leap year, because 366 days is 52 weeks plus two. That single fact explains most of what the calendar does: a birthday that fell on a Tuesday falls on a Wednesday next year, unless a 29 February sits between the two, in which case it jumps to Thursday.

The leap year rule has three parts

A year is a leap year if it is divisible by 4, except years divisible by 100, except again years divisible by 400. So 1900 was not a leap year and 2000 was. The correction exists because the solar year is about 365.2422 days rather than 365.25, and the simple four-year rule overshoots by roughly three days every four centuries.

ISO week numbers are not "week of the year"

The ISO 8601 week number counts weeks that start on Monday, and week 1 is the week containing the first Thursday of January. A consequence is that the first days of January frequently belong to week 52 or 53 of the previous year, and the last days of December can belong to week 1 of the next. If a spreadsheet and this page disagree by one, this rule is usually why.

Dates before 1582

The Gregorian calendar was introduced in October 1582, and different countries adopted it over the following three and a half centuries — Britain and its colonies in 1752, Russia not until 1918. A date written in a historical source may therefore be Julian, and converting it naively produces an answer that is confidently wrong by the accumulated difference, which was ten days in 1582 and thirteen by 1900. This page works in the proleptic Gregorian calendar and starts at 1583 rather than pretending the question is simple.

The 400-year repeat

The Gregorian calendar repeats exactly every 400 years, because 400 years contains a whole number of weeks — 20,871 of them. So 1 January 2025 and 1 January 2425 fall on the same weekday, and calendars can be reused on a cycle of 6, 11 or 28 years depending on where the leap years land. An interesting side effect of the same arithmetic: the 13th of the month falls on a Friday slightly more often than on any other weekday.

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