Day of the Week Calculator,
any date in history.

Calendar guide

How to find any day of the week — algorithms, history, and leap year math.

Calculating the day of the week for an arbitrary date is one of the oldest puzzles in mathematics. Priests needed to calculate when Easter fell; tax collectors needed to know what day a contract expired; astronomers needed to correlate observations across decades. Today, software does it in a nanosecond, but the underlying mathematics is elegant and surprisingly simple.

Zeller's Congruence, the classic formula

In 1882, Christian Zeller, a German mathematician and pastor, published a formula for calculating the day of the week for any Gregorian or Julian date. His formula for the Gregorian calendar:

Worked example: July 4, 1776

Let's verify what day the U.S. Declaration of Independence was signed. July is month 7, so no year adjustment needed.

The U.S. Declaration of Independence was indeed signed on a Thursday.

The Doomsday Algorithm: mental arithmetic trick

In 1973, mathematician John Conway devised the Doomsday Algorithm, a method for calculating the day of the week in your head. It exploits a clever pattern: every year has a set of “anchor” dates that all fall on the same day of the week, called the year's Doomsday.

The Doomsday dates are easy to remember: 4/4, 6/6, 8/8, 10/10, 12/12 all share a day. So does the last day of February, 5/9, 9/5, 7/11, and 11/7 (the “I work 9 to 5 at 7-11” mnemonic). Once you know a year's Doomsday, you can calculate any date in that year by counting forwards or backwards.

• Find the century anchor (e.g. 1900s = Wednesday, 2000s = Tuesday).
• Calculate how many years since the century start, then add ⌊years/12⌋ + (years mod 12) + ⌊(years mod 12)/4⌋ to the anchor.
• Take mod 7 to get the Doomsday for the specific year.
• Count forwards or backwards from a Doomsday date to your target.

Leap year rules, the Gregorian calendar fix

The solar year is approximately 365.2422 days long. Rounding to 365 days creates a cumulative error of about 24 hours every four years. The Julian calendar (introduced by Julius Caesar in 46 BC) corrected this by adding a leap day every four years, but that overcompensates by about 11 minutes per year, which accumulates to one full day every 128 years.

The Gregorian calendar replaced the Julian calendar on October 15, 1582 (a Friday), by papal decree of Pope Gregory XIII. To correct the accumulated 10-day drift, October 4, 1582 (Julian) was immediately followed by October 15, 1582 (Gregorian). Different countries adopted the reform at wildly different times — Britain and its colonies not until 1752, Russia not until 1918.

The Gregorian calendar reform: why historical dates are tricky

Because different countries used different calendars at the same time, historical date records can be ambiguous. When historians say Shakespeare was born on April 23, 1564, that is the Julian date (England hadn't yet adopted the Gregorian calendar). The corresponding Gregorian date would be May 3, 1564.

This calculator uses the proleptic Gregorian calendar, the Gregorian system extended backward through time before 1582. This is the convention used by astronomers and most software, including the international standard ISO 8601. For dates before October 15, 1582, the calculator notes that the result assumes Gregorian rules, not the Julian calendar that was actually in use.

The origin of the day names

English day names blend two traditions: the Roman seven-day week (named after celestial bodies and gods) was adopted into Germanic languages, where Roman gods were replaced with their Norse/Germanic equivalents. Only Saturday retains its purely Roman origin.

ISO week numbers: the international standard

The ISO 8601 standard defines weeks that always start on Monday. Week 1 of a year is defined as the week that contains the first Thursday of January (equivalently, the week containing January 4th). This means:

• January 1st can be in week 52 or 53 of the previous year.
• December 31st can be in week 1 of the next year.
• Each ISO year has either 52 or 53 weeks.

ISO weeks are used in manufacturing, logistics, and European business planning. In the United States, weeks more commonly start on Sunday and week numbering follows the simpler rule of counting from January 1st.