Day of the Week Calculator - Historical Date Finder
Free online day of the week calculator. Determine the exact weekday for any date in past or future history (e.g. what day was July 4, 1776?). Includes algorithmic mathematical proof via Zeller's Congruence, day of the year, ISO week number, leap year verification, and astrological zodiac sign.
Day of the Week Calculator
Determine the exact day of the week for any date in history with Zeller's Congruence.
Select or Enter Date
Zeller's Congruence Proof
Christian Zeller's algorithm computes day modulo 7:
Calendar Algorithms: Zeller's Congruence & John Conway's Doomsday Rule
Determining what day of the week a historical date occurred relies on modular calendar arithmetic. This guide explains Christian Zeller's 1882 congruence formula and mathematician John Conway's Doomsday mental algorithm.
Zeller's Congruence Mathematical Formula
For the Gregorian calendar, the day of the week h (0 = Saturday, 1 = Sunday, ..., 6 = Friday) is given by:
h = (q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J) mod 7
Where q is the day of the month, m is the month (with January and February counted as months 13 and 14 of the preceding year), K is the year of the century (year mod 100), and J is the zero-based century (⌊year/100⌋).
Step-by-Step Instructions
Enter Any Past or Future Date
Input day, month, and year (e.g. July 20, 1969 or January 1, 2050) into the date selector.
Compute Exact Day of the Week
The tool evaluates Zeller's Congruence and Tomohiko Sakamoto's calendar algorithms to determine the exact weekday (Monday through Sunday).
Inspect Historical Calendar Details
Review astrological sign, day of the year (Day 1 to 365/366), ISO week number, and historical calendar milestones.
Explore Leap Year & Century Diagnostics
See whether the selected year was a leap year and review step-by-step mathematical modulo arithmetic.
Key Features & Capabilities
- Zeller's Congruence algorithmic implementation calculating weekday names across the entire Gregorian calendar (1582 to 9999+)
- Instant output: Day of the Week (Sunday–Saturday), Day of the Year (1–366), and ISO 8601 Week Number
- Historical date verification: discover the day of the week you were born, historic Apollo moon landing weekday, or historical events
- Leap year validator explaining Gregorian quadrennial and quadricentennial rules
- Step-by-step mathematical working illustrating anchor day and doomsday rule algorithms
- 100% private in-browser calculation with zero server logging
Frequently Asked Questions
What is Zeller's Congruence and how does it calculate the day of the week?
Zeller's Congruence is an algorithm devised by Christian Zeller in 1882: `h = (q + floor(13*(m+1)/5) + K + floor(K/4) + floor(J/4) - 2*J) mod 7`, where `q` is the day of the month, `m` is the month (March=3, ..., January/February counted as months 13/14 of previous year), `K` is the year of the century (`year mod 100`), and `J` is the zero-based century (`floor(year / 100)`).
What day of the week was July 20, 1969 (Apollo 11 Moon Landing)?
July 20, 1969 occurred on a Sunday. Neil Armstrong and Buzz Aldrin stepped onto the lunar surface at 02:56 UTC on Monday, July 21 (which was 10:56 PM EDT Sunday evening in the United States).
How does John Conway's Doomsday rule work for mental day-of-week calculation?
Conway's Doomsday rule assigns an 'anchor day' (Doomsday) to every year. Certain memorable dates always fall on the exact same Doomsday each year: 4/4, 6/6, 8/8, 10/10, 12/12, and the last day of February (2/28 or 2/29). Finding the year's Doomsday allows quick mental calculation of any date's weekday.
Why did European countries switch from the Julian to the Gregorian calendar in 1582?
The Julian calendar had an error of 1 day every 128 years because it assumed a year was exactly 365.25 days (instead of the true astronomical 365.2422 days). Pope Gregory XIII introduced the Gregorian calendar in October 1582, dropping 10 days to realign the calendar with the spring equinox.
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