Day of the Week
What day is any date?
About This Calculator
The day-of-week calculator tells you what day any historical or future date falls on. This uses Zeller's congruence or the Doomsday algorithm. Useful for historical research, planning events, checking when a birthday falls, or calculating which day of the week a date 100 years ago occurred.
Formula
Zeller's congruence: h = (q + floor(13(m+1)/5) + K + floor(K/4) + floor(J/4) − 2J) mod 7
where q=day, m=month (March=3, Jan/Feb treated as month 13/14 of previous year), K=year%100, J=floor(year/100)
Result: 0=Saturday, 1=Sunday, 2=Monday, ..., 6=Friday
Example Calculation
What day was July 4, 1776?
- Apply Zeller's or use known anchor days
- July 4, 1776 fell on a Thursday
July 4, 1776 was a Thursday
Day of Week for Notable Historical Dates
| Date | Day | Event |
|---|---|---|
| July 4, 1776 | Thursday | US Independence Declaration |
| November 11, 1918 | Monday | WWI Armistice |
| December 7, 1941 | Sunday | Pearl Harbor attack |
| July 20, 1969 | Sunday | Moon landing |
| September 11, 2001 | Tuesday | 9/11 attacks |
| January 1, 2000 | Saturday | Y2K / Year 2000 |
Frequently Asked Questions
How does Zeller's congruence work?
Zeller's formula uses number theory to map any Gregorian or Julian calendar date to a day of the week. It treats January and February as months 13 and 14 of the previous year to simplify leap year handling. The formula gives a number 0-6 mapping to days.
What is the Doomsday algorithm?
Doomsday is a mental arithmetic technique by mathematician John Conway. It identifies 'anchor days' in each year (e.g., the last day of February, 4/4, 6/6, 8/8, 10/10, 12/12 all fall on the same day of the week). Using these anchors you can calculate any day mentally.
Does the day of week repeat on a cycle?
Yes. The Gregorian calendar repeats its day-of-week pattern every 400 years exactly (146,097 days). Within that, common years shift by 1 day and leap years by 2 days. Every 28 years the Julian (but not Gregorian) calendar repeats exactly.
Were calendar dates always the same?
No. In 1582, the Gregorian calendar replaced the Julian calendar, with October 4 followed by October 15 (skipping 10 days). Different countries adopted the Gregorian calendar at different times (Britain in 1752, Russia in 1918). Historical dates before conversion may differ by system.