Day of the Week Calculator

How the Day of the Week Calculator Works

This day of the week calculator tells you which weekday any date falls on, from January 1 of year 1 to December 31, 9999. Pick the month, type the day and the full year, and the answer updates as you type. Use it to find what day of the week you were born, what day a holiday or deadline lands on next year, or which weekday a historical event happened.

The calculator never relies on the browser's date functions for the weekday. It applies Zeller's congruence with whole number arithmetic, then checks the answer two more ways: with John Conway's Doomsday rule and with the Julian Day Number used by astronomers. All three methods appear in the results with your own numbers, so you can repeat the calculation by hand.

• Month, day and year. Enter the full year, such as 1969 rather than 69. Dates that do not exist, such as February 30 or February 29, 2027, show an error instead of a wrong answer.
• Calendar system. The default is the proleptic Gregorian calendar, which extends today's leap year rules backward before 1582. Choose Julian for dates written in the older calendar.
• Results. You get the weekday, which occurrence of that weekday it is in the month (useful for rules like "the fourth Thursday of November"), the month calendar, the day of the year, days left in the year, the ISO 8601 week, the quarter, leap year status, the Julian Day Number and the same date over the next ten years.

Zeller's Congruence: the Day of the Week Formula

Christian Zeller published his calendar formulas in Acta Mathematica in the 1880s. The formula turns a date into a number from 0 to 6. The trick is to treat January and February as months 13 and 14 of the previous year, which moves the leap day to the very end of the counting year.

The term ⌊13(m + 1) ÷ 5⌋ adds the right number of extra days for the months already passed, because months of 30 and 31 days alternate in a regular pattern from March onward. K and ⌊K ÷ 4⌋ add one day per year and one more per leap year in the century. In the Gregorian version, ⌊J ÷ 4⌋ + 5J handles the century rule. Many texts write that term as subtracting 2J; adding 5J gives the same remainder modulo 7 and keeps the sum positive.

Worked example: July 4, 1776

Worked example: January 1, 2027

Worked example: October 4, 1582 in the Julian calendar

The Julian Day Number gives a second route. It counts days continuously from January 1, 4713 BC in the Julian calendar, and the weekday is (JDN + 1) mod 7 with 0 for Sunday. July 4, 2026 has JDN 2,461,226, and 2,461,227 mod 7 = 6, which is Saturday.

How to Calculate the Day of the Week in Your Head: the Doomsday Rule

The mathematician John Horton Conway devised the Doomsday rule as a way to find weekdays mentally. It rests on one fact: in any year, a set of easy dates all share the same weekday, which Conway called the Doomsday. They include 4/4, 6/6, 8/8, 10/10 and 12/12, the pairs 5/9 and 9/5 and 7/11 and 11/7 (the "nine to five at the 7 Eleven" memory aid), and the last day of February.

To find the Doomsday of a year, start from the century anchor: Tuesday for 1600 to 1699, Sunday for 1700 to 1799, Friday for 1800 to 1899, Wednesday for 1900 to 1999, Tuesday for 2000 to 2099 and Sunday for 2100 to 2199. The pattern repeats every 400 years. Then take the last two digits of the year, divide by 12, and add the quotient, the remainder and the remainder divided by 4 (whole part only) to the anchor, counting in days of the week.

For Julian dates the century anchor is Sunday minus one day per century. For 1582 that gives Saturday as the anchor and Wednesday as the Doomsday, so October 10, 1582 in the Julian calendar was a Wednesday and October 4 was a Thursday. The last column of the table also gives the day of the year: add the day of the month to the days before that month, so July 4, 2026 is 181 + 4 = day 185.

What Day of the Week Was I Born?

Enter your birth date with the full year and the hero card shows the weekday, while the calendar card shows the whole month you were born in. Someone born on May 15, 1990 was born on a Tuesday. The "Same date in later years" table then shows how the birthday moved through the week.

A common year has 365 days, which is 52 weeks and 1 day, so a date moves forward one weekday. When a February 29 falls between two birthdays, the date moves two weekdays. Because of those skips, a birthday on May 15, 1990 does not fall on a Tuesday again until 2001, eleven years later.

Gregorian vs Julian Calendar: the 1582 and 1752 Changes

The Julian calendar, set up under Julius Caesar, adds a leap day every fourth year, giving an average year of 365.25 days. The solar year is slightly shorter, so the calendar drifted against the seasons. In 1582 Pope Gregory XIII introduced the Gregorian calendar, which skips the leap day in century years not divisible by 400. Ten dates were dropped to realign the calendar: Thursday, October 4, 1582 was followed by Friday, October 15, 1582. The weekday sequence did not break.

Britain and its colonies, including those in America, kept the Julian calendar until the Calendar (New Style) Act 1750 took effect. By then the gap had grown to 11 days, so Wednesday, September 2, 1752 was followed by Thursday, September 14, 1752. The same act moved the start of the legal year from March 25 to January 1.

The hero card shows the same day in the other calendar. July 4, 2026 in the Gregorian calendar is June 21, 2026 in the Julian calendar, 13 days earlier. A Gregorian date before October 15, 1582 is called proleptic: it applies the modern rules to a time when nobody used them. Software date libraries generally use the proleptic Gregorian calendar, the U.S. Naval Observatory converter switches to the Julian calendar for dates on or before October 4, 1582, and historians usually quote dates in the calendar the source used.

Leap Years, Day of the Year and ISO Week Numbers

In the Gregorian calendar a year is a leap year when it divides by 4, except century years, which must divide by 400. So 2000 was a leap year, 1900 was not, and 2100 will not be. In the Julian calendar every year that divides by 4 is a leap year, including 1900. The calculator applies the rule for the calendar you choose, so February 29, 1900 is rejected in Gregorian mode and accepted in Julian mode.

The day of the year, sometimes called the ordinal date, counts January 1 as day 1 and runs to 365 or 366. Days left is the number of days after the chosen date until December 31.

ISO 8601 numbers weeks from Monday to Sunday. Week 1 is the week that contains the year's first Thursday, so a few days in late December or early January can belong to the neighboring year. January 1, 2026 is a Thursday, so week 2026-W01 starts on Monday, December 29, 2025. January 1, 2027 is a Friday and belongs to week 2026-W53, the last week of 2026. ISO 8601 defines week dates for the Gregorian calendar only, so the ISO week tile shows "Not defined" in Julian mode.

Day of the week in Excel

Excel's WEEKDAY function returns 1 for Sunday through 7 for Saturday by default; WEEKDAY(date, 2) returns 1 for Monday through 7 for Sunday. Excel treats 1900 as a leap year for compatibility with Lotus 1 2 3, so Microsoft notes that WEEKDAY returns wrong values for dates before March 1, 1900. Use this calculator for anything older.

Why Calendars Repeat: the 28 and 400 Year Cycles

Every 400 Gregorian years contain 97 leap years, a total of 146,097 days. That is exactly 20,871 weeks, so the Gregorian calendar repeats every 400 years: January 1, 2426 falls on the same weekday as January 1, 2026. Within one 400 year cycle the 13th of a month falls on a Friday 688 times, slightly more often than on any other weekday.

The Julian calendar repeats every 28 years, because 28 Julian years contain 10,227 days, exactly 1,461 weeks. The Gregorian calendar follows the same 28 year cycle between 1901 and 2099, where no century leap year is skipped. In that span a common year calendar can be reused after 6 or 11 years and a leap year calendar after 28 years. The 2026 calendar returns in 2037 and 2054.

In a leap year, New Year's Day and dates after February 29 sit on different sides of the leap day, which is why 2028 starts on a Saturday while its Christmas lands on a Monday.

Frequently Asked Questions

Sources & References

• Zeller, Chr. Kalender-Formeln, Acta Mathematica 9 (1887), pages 131 to 136 (the weekday congruence for the Julian and Gregorian calendars). doi.org
• Jefferys, W. H., University of Texas at Austin, AST 309. What is the day of the week? (Conway's Doomsday method, century anchors, July 4, 1776 and the October 1582 changeover). utexas.edu
• U.S. Naval Observatory. Julian Date Converter (Julian dates, weekday from the Julian date, and the 1582 and 1752 changeovers). usno.navy.mil
• Royal Museums Greenwich. Which years are leap years? (leap year rules and Britain's 1752 change). rmg.co.uk
• UK Parliament, via legislation.gov.uk. Calendar (New Style) Act 1750 (September 2, 1752 followed by September 14, and the year starting on January 1). legislation.gov.uk
• International Organization for Standardization. ISO 8601-1:2019 Date and time, Part 1: Basic rules, confirmed 2024. iso.org
• Microsoft Support. WEEKDAY function. microsoft.com
• Microsoft Learn. Excel incorrectly assumes that the year 1900 is a leap year. microsoft.com

Every weekday, count and example on this page was recomputed with the same integer formulas the calculator uses and cross checked against an independent date library. Methodology reviewed: 2026.