Day of the Week Calculator

Give it a date and it tells you which day of the week that was — or will be — along with the numbers calendars are actually indexed by: the day number within the year, the ISO week, whether the year is a leap year, and the astronomer's Julian day number.

How the weekday is worked out

Not by looking anything up. The date is converted to a count of days since 1 January 1970, which is a small piece of exact integer arithmetic, and then reduced modulo 7. Because 1 January 1970 was a Thursday, weekday = (days + 4) mod 7 with Sunday as 0. The same method underlies Zeller's congruence and the Doomsday rule, which are the pencil-and-paper versions.

Doing it arithmetically rather than through a date object matters: it makes the answer independent of the server's time zone, and it avoids the trap where a two-digit year is silently interpreted as 19-something.

Leap years

Divisible by 4 is a leap year, unless it is a century, unless that century is divisible by 400. So 1996 and 2024 are leap years, 1900 and 2100 are not, and 2000 is — which is why 2000 felt like an exception and was in fact the rule's exception to its own exception. The correction exists because the tropical year is about 365.2422 days, not 365.25; the Gregorian scheme averages 365.2425, leaving an error of roughly one day in 3,200 years.

ISO week numbers

The ISO-8601 week starts on Monday and belongs to whichever year contains its Thursday. Consequently week 1 is the week holding the first Thursday of January, 29, 30 or 31 December can belong to week 1 of the next year, and 1, 2 or 3 January can belong to week 52 or 53 of the previous one. The calculator reports the ISO week-numbering year separately and flags it when it disagrees with the calendar year — a discrepancy that quietly breaks a lot of reporting spreadsheets every January.

The nearby-years table

The same calendar date shifts forward one weekday each ordinary year and two across a leap day, so the whole pattern repeats every 28 years — except around century years that skip their leap day, which is why the table is worth reading rather than the rule.

Dates before 1582

The Gregorian calendar was introduced in October 1582, and Britain and its American colonies did not adopt it until September 1752, when they deleted eleven days. Historic dates here use the proleptic Gregorian calendar — today's rules run backwards — which is the scientific convention and the one ISO-8601 requires. It is not what a contemporary almanac would have printed, and the calculator warns you when the distinction bites. On this convention 4 July 1776 was a Thursday, which matches the historical record because Britain had already switched by then.