How the weekday is found
The Gregorian calendar repeats every 400 years (146,097 days, exactly 20,871 weeks), so the weekday of any date is fixed by arithmetic. The calculator uses Zeller's congruence, an 1880s formula that maps day, month and year to a number from 0 to 6. The same answer comes from counting days from a known reference date — computers do it that way — but Zeller's version can be done on paper.
Some dates people look up:
| Date | Weekday | Event |
|---|---|---|
| July 4, 1776 | Thursday | US Declaration of Independence |
| July 20, 1969 | Sunday | Apollo 11 moon landing |
| November 9, 1989 | Thursday | Fall of the Berlin Wall |
| January 1, 2000 | Saturday | Y2K |
| September 11, 2001 | Tuesday | |
| February 29, 2024 | Thursday | Leap day |
| January 1, 2030 | Tuesday |
Zeller's congruence, step by step
January and February are treated as months 13 and 14 of the previous year, so that the leap day falls at the end of the 'year' and does not disturb the month offsets. The worked example is July 20, 1969.
| Step | Value |
|---|---|
| q (day) | 20 |
| m (month; Jan/Feb = 13/14 of prior year) | 7 |
| K (year mod 100) | 69 |
| J (century) | 19 |
| h = (q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ − 2J) mod 7 | (20 + 20 + 69 + 17 + 4 − 38) mod 7 = 92 mod 7 = 1 |
| Result (0 = Saturday, 1 = Sunday …) | Sunday |
The doomsday rule: weekdays in your head
John Conway's method for mental calculation: every year has a 'doomsday' weekday shared by a set of easy-to-remember dates — 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7, the last day of February, and 3/14. Learn the year's doomsday (2026: Thursday) and count from the nearest anchor. July 20, 2026: July 11 is a doomsday (Thursday), so July 20 is nine days later — Saturday.
| Month | Anchor day |
|---|---|
| January | 3 (4 in leap years) |
| February | 28 (29 in leap years) |
| March | 14 (Pi Day) |
| April | 4 |
| May | 9 |
| June | 6 |
| July | 11 |
| August | 8 |
| September | 5 |
| October | 10 |
| November | 7 |
| December | 12 |
Same date, other years
A date moves forward one weekday each year, or two when a February 29 falls in between. That is why birthdays cycle through the week and why the calendar repeats after 6, 11 or 28 years. The result table shows the same date in nearby years; the row below shows how January 1 moves.
| Year | Weekday | |
|---|---|---|
| 2024 | Monday | Leap |
| 2025 | Wednesday | |
| 2026 | Thursday | |
| 2027 | Friday | |
| 2028 | Saturday | Leap |
| 2029 | Monday | |
| 2030 | Tuesday |
Day of year and ISO week
The result also gives the day number within the year (July 20 is day 201, or 202 in a leap year) and the ISO 8601 week number, used in European business calendars: weeks start on Monday and week 1 is the week containing the year's first Thursday, so December 29–31 can belong to week 1 of the next year and January 1–3 to week 52 or 53 of the previous one.
Historical dates and calendar changes
The calculator applies the Gregorian calendar to all dates. Britain and its colonies switched from the Julian calendar in September 1752 (skipping 11 days), Catholic Europe in 1582, Russia in 1918. A weekday for a date before a country's switch is the 'proleptic Gregorian' answer and may differ from the day people at the time experienced. For dates after 1752 in the English-speaking world it is exact.