Finding the Weekday for Any Date
The Gregorian calendar repeats on a 400-year cycle containing exactly 146,097 days — a number divisible by seven. That means the whole pattern of weekdays repeats every 400 years, and any date's weekday can be computed rather than looked up.
Computers do it by counting days from a fixed reference and taking the remainder modulo 7. People can do it with a mental algorithm.
The Doomsday Rule
John Conway's method, which a practised person can run in a few seconds. It rests on the observation that several dates in every year always fall on the same weekday — that year's "doomsday".
| Month | Doomsday date | Mnemonic |
|---|---|---|
| January | 3rd (4th in leap years) | 3 years in 4, 4 years in 400 |
| February | 28th (29th in leap years) | The last day |
| March | 14th | Pi day |
| April | 4th | 4/4 |
| May | 9th | 9 to 5 at 7-11 |
| June | 6th | 6/6 |
| July | 11th | 9 to 5 at 7-11 |
| August | 8th | 8/8 |
| September | 5th | 9 to 5 at 7-11 |
| October | 10th | 10/10 |
| November | 7th | 9 to 5 at 7-11 |
| December | 12th | 12/12 |
The anchor day for the 2000s is Tuesday. Find the year's doomsday, then count forward or back from the nearest doomsday date in the month you want.
ISO Week Numbers
ISO 8601 defines week 1 as the week containing the first Thursday of January — equivalently, the week containing 4 January. Weeks start on Monday.
The consequence is that early January dates sometimes belong to week 52 or 53 of the previous year, and late December dates sometimes belong to week 1 of the next. Most European business systems use ISO weeks; North American systems more often start weeks on Sunday and number them differently.
The 400-Year Cycle
| Period | Days | Divisible by 7? |
|---|---|---|
| 1 common year | 365 | No — shifts 1 day |
| 1 leap year | 366 | No — shifts 2 days |
| 4 years | 1,461 | No |
| 28 years | 10,227 | Yes, within a century |
| 400 years | 146,097 | Yes — the full cycle |
A curious consequence of the 400-year cycle: the 13th of the month falls on a Friday slightly more often than on any other weekday — 688 times in 4,800 months, against 684 or 687 for the others.
Calendar Repeats
Because of the shifting pattern, a given year's calendar repeats at irregular intervals of 6, 11 or 28 years. A common year following a leap year repeats after 6 years; leap years repeat every 28 years within a century, though century rules can disrupt this.
The 1582 Discontinuity
The Gregorian calendar replaced the Julian one in October 1582, and ten days were deleted: 4 October was followed directly by 15 October in Catholic countries. Britain and its colonies did not adopt it until 1752, by which time eleven days had to be dropped, and Russia waited until 1918.
This means weekday calculations before a country's adoption date depend on which calendar the source used. This calculator uses the proleptic Gregorian calendar and declines dates before 1583 for that reason.
Frequently Asked Questions
What day was I born on?
Enter your date of birth above. The result also shows which occurrence of that weekday it was in the month.
Why does my week number differ from my calendar app?
Because of the week-numbering standard. ISO weeks start on Monday and week 1 contains the first Thursday; many U.S. applications start weeks on Sunday and call the week containing 1 January week 1.
How often is Friday the 13th?
At least once a year and at most three times. Over the full 400-year cycle it is marginally the most common weekday for the 13th.
Can I check a date in the far future?
Yes, up to the year 4000. The Gregorian rules are deterministic, so the answer is exact — assuming the calendar is not reformed again.