What day is a date?

How to find the weekday of any date

The Gregorian calendar has a hidden regularity: it repeats exactly every 400 years. There are 146,097 days in those 400 years, and that number divides exactly by seven, giving 20,871 whole weeks. So every date has a fixed weekday within the cycle, and you can calculate it from its position instead of looking it up. A computer does this by converting the date to a day number and taking the remainder after dividing by seven.

The Doomsday method, by hand

John Conway’s Doomsday method lets you do it in your head. In any given year, a set of easy dates all fall on the same weekday, called the doomsday: 4/4, 6/6, 8/8, 10/10 and 12/12, plus 5/9, 9/5, 7/11 and 11/7, plus the last day of February. For 2027, the dates are January 3, February 28, March 14, April 4, May 9, June 6, July 11, August 8, September 5, October 10, November 7, December 12.

Worked example: what day is July 4, 2027?

1. Start with the century’s anchor. For the 2000s it is Tuesday.
2. Take the last two digits of the year, 27. Divide by 12: 2 with remainder 3. Divide the remainder by 4 to get 0. Add those: 2 + 3 + 0 = 5.
3. Count 5 weekdays on from Tuesday, which is the same as 5 after removing whole weeks. The doomsday for 2027 is a Sunday.
4. July’s easy date is the 11th, so it is a Sunday. July 4 is 7 days earlier, which gives Sunday.

The tool gives the same answer: Sunday, July 4, 2027. Century anchors repeat every 400 years: 1900s Wednesday, 2000s Tuesday, 2100s Sunday, 2200s Friday.

Why a date shifts weekday from year to year

A common year is 52 weeks and one day, so the same date lands one weekday later the following year. A leap year is 52 weeks and two days, so dates after February 29 move two. That is why a date skips a weekday now and then, and why a whole year’s calendar repeats only after 6, 11 or 28 years, with exceptions around century years. The list in the results shows this directly: the same date for the next ten years, including the jump over each leap day. A February 29 appears only in leap years, of course.

Leap years and old dates

Under the Gregorian rule, a year divisible by 4 is a leap year, except century years not divisible by 400. There are 97 leap days per 400 years, giving a mean year of 365.2425 days. The older Julian calendar had a leap year every fourth year without exception, and by the 16th century it had drifted noticeably from the seasons.

The calendar reform of 1582 dropped ten dates: Thursday October 4 was followed by Friday October 15. The weekday sequence was not interrupted, but the day numbers jumped. Britain and its colonies changed in 1752, when September 2 was followed by September 14, and other countries switched as late as the twentieth century. So a date on an English document from before September 1752 was written in the Julian calendar, eleven days behind the Gregorian date by then (and with the year often starting on March 25). This tool uses the Gregorian calendar for all dates, which is called the proleptic Gregorian calendar: ISO 8601 allows it for such dates by agreement, and most software uses it, and it warns you when your date is before the 1582 change.

Weeks near New Year

Under ISO 8601, a week starts on Monday, and week 1 is the week containing the year’s first Thursday. So the first days of January can belong to the last week of the previous year, and the last days of December can belong to week 1 of the next. A year has 53 ISO weeks if January 1 is a Thursday, or if it is a Wednesday in a leap year. These dates show what happens:

Common US usage starts weeks on Sunday and calls the week containing January 1 week 1, so the two systems often differ. More detail is on the week number page.

The other numbers in the results

• Day of the year runs from 1 to 365, or 366 in a leap year. March 1 is day 60 in a common year and day 61 in a leap year. See day of the year.
• ISO ordinal date writes that as YYYY-DDD. This is a standard format.
• “Julian” date (YYDDD) is the informal version used on food packaging, in logistics and on military documents. It has nothing to do with the Julian calendar. See Julian date.
• Julian Day Number is the astronomers’ continuous count. A Julian Date runs from noon to noon, so a calendar date at midnight UT ends in .5, and the whole number shown is the day’s number at noon.
• Modified Julian Date is that count minus 2,400,000.5, and it starts at midnight.
• Unix time counts seconds from January 1, 1970 UTC, and it ignores leap seconds. The value shown is for 00:00 UTC on the date, not local midnight. See Unix time.
• Excel serial number counts days from January 1, 1900 = 1, in the default date system. Excel wrongly treats 1900 as a leap year, kept for compatibility with Lotus 1-2-3, so the serial for March 1, 1900 onward is one higher than a true count.
• Islamic date follows the Umm al-Qura calendar. Local sighting may differ by a day. See Islamic date.

Writing a date so nobody misreads it

All-numeric dates are a common source of error between countries. 03/04/2027 means March 4 in the United States and 3 April across most of Europe, and a date such as 12/11 is impossible to check by inspection. The ISO 8601 format 2027-03-04 runs from largest unit to smallest, sorts correctly as text, and reads the same everywhere. Writing out the month works just as well. Date formats lists the common styles with their standards.

To work with spans instead of single dates, use days between dates and the date calculator.