Day of the Week Calculator
Find the exact day of the week for any date in history or the future. Discover Julian day, ISO week number, leap year status, and days elapsed.
The Mathematics Behind Zeller's Congruence
Calculating the day of the week for arbitrary calendar dates is made possible by Zeller's Congruence, an algorithmic formula published by German mathematician Christian Zeller in 1882. It takes into account the irregular lengths of months, leap years, and the century cycle.
For deeper analysis and related planning, you can also explore our Date Difference Calculator and GPA Calculator.
For the Gregorian calendar, the formula is:
Where:
qis the day of the month (1 to 31).mis the month (March = 3, April = 4, ... December = 12). Crucially: January and February are counted as months 13 and 14 of the previous year.Kis the year of the century (Year mod 100).Jis the zero-based century (βYear / 100β).his the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, 3 = Tuesday, 4 = Wednesday, 5 = Thursday, 6 = Friday).
Gregorian Calendar Leap Year Rules
The Gregorian calendar, instituted by Pope Gregory XIII in October 1582, corrected the accumulated 10-day error of the ancient Julian calendar by refining leap year rules. To maintain synchronization with Earth's astronomical orbit (365.2422 solar days per year):
- Every year evenly divisible by 4 is a leap year (366 days).
- Except: Years evenly divisible by 100 are NOT leap years (e.g. 1700, 1800, 1900, 2100).
- Except: Years evenly divisible by 400 ARE leap years (e.g. 1600, 2000, 2400).
Day of the Week in Human History
Frequently Asked Questions
What mathematical formula calculates the day of the week?
The standard algorithm is Zeller's Congruence, invented by Christian Zeller in 1882. It computes the day of the week from the calendar day, month, and year using modular arithmetic.
What day of the week was the Apollo 11 Moon Landing?
The Apollo 11 lunar module landed on the Moon on Sunday, July 20, 1969 at 20:17 UTC.
How does the leap year rule work in the Gregorian calendar?
A year is a leap year if it is evenly divisible by 4, unless it is also divisible by 100. However, if the year is also divisible by 400, it remains a leap year (e.g. 2000 was a leap year, but 1900 was not).
Calendar Note: Dates prior to October 15, 1582 are calculated using the proleptic Gregorian calendar standard. Different European territories adopted the Gregorian calendar at different times (Great Britain and American colonies adopted it in September 1752, Russia in 1918).