How people compute weekdays in their heads
Mental calculators mostly use the Doomsday rule: in any given year, a family of easy-to-remember dates such as 4/4, 6/6, 8/8, 10/10, 12/12 and the last day of February all share one weekday, the year's "doomsday". Once you know that single anchor for the year, you count forward or back a few days from the nearest easy date. The older, more mechanical approach is Zeller's congruence, a formula that turns a date directly into a weekday number, where q is the day of the month, m the month (with January and February counted as months 13 and 14 of the previous year), K the year within the century, and J the century:
One caution for historical dates: JavaScript, and therefore this calculator, uses the proleptic Gregorian calendar, extending today's calendar rules backward without limit. Before the Gregorian reform of 1582, dates were actually recorded in the Julian calendar, which by then had drifted about ten days out of step, and some countries kept the Julian calendar for centuries afterwards. So the weekday computed here for a medieval date is the Gregorian answer, and it may not match what a contemporary chronicle says.
Frequently asked questions
What is the Doomsday rule?
A mental method popularized by John Conway. In any year, a set of easy dates such as 4/4, 6/6, 8/8, 10/10, 12/12 and the last day of February all fall on the same weekday, the year's doomsday. Learn one anchor per year, then count from the nearest easy date to the date you want. Practiced people can name the weekday of any date in a few seconds.
Do calendars repeat every 28 years?
Only within a stretch that contains no skipped leap year. The 28-year cycle works because 28 is the product of the 4-year leap cycle and the 7-day week, but century years like 1900 and 2100 are not leap years and break the pattern. Between 1901 and 2099 the 28-year rule holds; across 2100 it fails.
Why might very old dates look wrong?
This calculator, like JavaScript itself, projects the modern Gregorian calendar backward indefinitely, which is called the proleptic Gregorian calendar. Before the Gregorian reform of 1582, and later in countries that adopted it late, people actually used the Julian calendar, which had drifted by several days. A weekday recorded in a historical document may therefore differ from the one computed here.