Day of the Week Calculator

A calendar year is not a whole number of weeks, and that mismatch is the entire reason a fixed date does not repeat its weekday from one year to the next. A common year runs 365 days — one more than an exact 52 weeks — so whatever weekday a date fell on shifts forward by exactly one day the following year. A leap year adds a second day of shift for any date after February 29, because the extra day inserted that month pushes everything past it one further step around the week. That single mismatch, 365 divided by 7 leaving a remainder of 1, is the whole mechanism behind why a birthday drifts steadily through the days of the week rather than sitting on the same one forever.

The Gregorian calendar’s leap-year rule is more particular than "every fourth year": a year divisible by 100 is not a leap year unless it is also divisible by 400, which is why 1900 was not a leap year but 2000 was. That rule exists to keep the calendar tracking the solar year more precisely, but it has a convenient side effect — across exactly 400 years the calendar contains 146,097 days, and 146,097 divides evenly by 7 into 20,871 whole weeks. Because a whole number of weeks fits inside those four centuries with nothing left over, the entire weekday pattern for every date on the calendar repeats itself exactly, with no drift at all, once every 400 years.

Long before pocket calculators, mathematician John Horton Conway devised a mental shortcut now known as the Doomsday rule for working out a weekday without writing anything down. It leans on the fact that several easy-to-remember dates always share the same weekday within any single year — 4/4, 6/6, 8/8, 10/10 and 12/12 among them, along with the last day of February — a shared weekday Conway called that year’s "doomsday." Once you know a year’s doomsday, you find whichever of those anchor dates sits closest to the date you actually care about and count forward or back in whole weeks to land on the answer. The doomsday itself shifts in a predictable pattern from year to year and century to century — every year in the 2000s, for instance, has its doomsday on a Tuesday — so with a bit of practice the whole calculation can be done in your head.

Zeller’s congruence and the Doomsday rule both assume the Gregorian calendar was already in effect, but it was not adopted everywhere at once. Pope Gregory XIII introduced it in 1582 to correct centuries of accumulated drift in the older Julian calendar, and Catholic countries switched over almost immediately, while Britain and its colonies held out until 1751, when Parliament passed an act mandating the change. Making the switch meant skipping eleven accumulated days outright: Wednesday, September 2, 1752 was directly followed by Thursday, September 14, 1752, with the dates in between simply never occurring in the British calendar. A weekday calculation for a date before a given country’s own switch will not line up with that country’s historical records, since they were still being kept on the Julian system at the time.

Working out the weekday for a date outside living memory, or far enough ahead that nobody has it memorized yet, comes up in a wider range of ordinary and specialized situations than it might seem.