Day of the Week Calculator

How to use the day of the week calculator

1. Enter a date. It starts with today's date.
2. Leave the calendar on Gregorian for modern dates. Choose Julian for old-style dates, such as those in English records before September 1752.
3. Read the weekday, then the Zeller's congruence values, the day of the year, the same date in the other calendar and how far it is from today.

Zeller's congruence formula

Christian Zeller published this method in the 19th century. q is the day of the month, m is the month with March as 3 through to February as 14, K is the year of the century (year mod 100) and J is the zero-based century (⌊year ÷ 100⌋). January and February count as months 13 and 14 of the previous year, so the leap day falls at the end of Zeller's year and doesn't disturb the other months. The ⌊13(m + 1) ÷ 5⌋ term accounts for the uneven month lengths, and the K and J terms add one weekday per year plus one for each leap year, with the Gregorian rule that skips three leap years every four centuries.

The calculator also counts days from a fixed reference date and takes the remainder after dividing by 7. The two methods are independent, and the calculator's tests check Zeller's result against JavaScript's built-in date handling for every 11th day from 1583 to 2600.

Worked examples

July 4, 1776. q = 4, m = 7, K = 76, J = 17. ⌊13 × 8 ÷ 5⌋ = 20, ⌊K ÷ 4⌋ = 19, ⌊J ÷ 4⌋ = 4 and 5J = 85. The sum is 208, and 208 mod 7 = 5, so the day was a Thursday.

January 1, 2000. January becomes month 13 of 1999, so q = 1, K = 99 and J = 19. The terms are 1 + 36 + 99 + 24 + 4 + 95 = 259, and 259 mod 7 = 0: a Saturday.

Holidays by weekday, 2025–2036

A date moves one weekday later each year, or two when a February 29 comes in between, because 365 days is 52 weeks and 1 day.

Old dates and the Julian calendar

The Gregorian calendar replaced the Julian calendar in parts of Europe in October 1582. The days of the week carried on unbroken: Thursday, October 4, 1582 (Julian) was followed by Friday, October 15, 1582 (Gregorian), the very next day. Britain and its colonies, including those in America, switched in 1752, when Wednesday, September 2 was followed by Thursday, September 14. Other countries changed at different times, some in the 20th century.

So for a date taken from an old document, use the calendar it was written in. The Battle of Hastings, October 14, 1066 in the Julian calendar, was a Saturday; the same day is October 20, 1066 in the Gregorian calendar extended backwards.

Tips

• Weekdays repeat every 400 years in the Gregorian calendar, because 400 years contain exactly 146,097 days, which is 20,871 weeks.
• Whole-year calendars repeat, usually after 6, 11 or 28 years depending on where the year falls in the leap-year cycle (century years such as 2100 break the pattern).
• Check the time zone for events near midnight. A calendar date has the same weekday everywhere, but 11 PM in New York is already the next day in London.

To count the days between two dates, use the day counter; to move forward or back from a date, the date calculator; and for your exact age, the age calculator.