Day of the Week Calculator
A day-of-week calculator determines what day of the week any given date falls on. The Doomsday algorithm (Conway) or modular arithmetic can compute this for any date in the Gregorian calendar.
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Tip: A quick modern shortcut: type any date into Google ("what day was March 15, 1990?") and it will tell you instantly. For mental calculation, the Doomsday algorithm requires memorizing just a few anchor dates.
- 1Use the formula: (d + m + y + y/4 − y/100 + y/400 + c) mod 7
- 2d=day, m=month code, y=year, c=century adjustment
- 3Or simply count forward/backward from a known reference date
- 4JavaScript: new Date("YYYY-MM-DD").getDay() → 0=Sunday, 6=Saturday
July 4, 1776=ThursdayUS Independence Day
January 1, 2000=SaturdayY2K millennium
| Month | Doomsday Date | Easy to remember |
|---|---|---|
| January | 3 (non-leap), 4 (leap) | 3rd or 4th |
| February | Last day (28 or 29) | End of month |
| April, June, Aug, Oct, Dec | 4, 6, 8, 10, 12 | Even months even days |
| May, Sep, Jul, Nov | 9, 5, 11, 7 | "I work 9-5 at 7-11" |
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Fun Fact
John Conway (mathematician, 1937–2020) could calculate the day of any date in his head in under 2 seconds using his Doomsday algorithm. He reportedly practiced by computing the day for random dates on a pocket calculator to check his mental calculations.
References
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