How the Day Of The Week Calculator Works
Every date falls on one of seven days, and they repeat in the same order without a break. Because of this, there is a way to work out the day of any date, in the past or the future, with only some arithmetic. The Day of the Week Calculator does this for you, for any date from the year 1 to the year 9999.
The calendar
The calculator uses the Gregorian calendar, the calendar that is used in almost every country. Its rules for a leap year are:
- A year that can be divided by 4 is a leap year (2024).
- But a year that can be divided by 100 is not (1900, 2100).
- Except that a year that can be divided by 400 is (2000, 2400).
A leap year has 366 days, with the extra day on 29 February. This gives a year of 365.2425 days on average, which is close to the real length of the solar year. The Gregorian calendar was introduced in 1582 and adopted at different times in different countries. For earlier dates, the calculator extends the same rules backward (the proleptic Gregorian calendar), so the weekday of a date before the change may not agree with the records of that time.
How the weekday is found
The days of the week repeat every 7 days, so the calculator only needs the number of days between your date and a date whose weekday is known, and then the remainder after dividing by 7. A short formula that does this is the one of Tomohiko Sakamoto:
if the month is January or February, take 1 off the year weekday = (year + year/4 - year/100 + year/400 + offset[month] + day) mod 7 offset = 0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4 (January to December) 0 = Sunday, 1 = Monday, ... 6 = Saturday
Here the divisions are whole numbers (the fraction is dropped). Example, 15 March 2024:
| Step | Calculation | Result |
|---|---|---|
| Years and leap days | 2024 + 506 - 20 + 5 | 2,515 |
| Add the month offset for March | 2,515 + 2 | 2,517 |
| Add the day | 2,517 + 15 | 2,532 |
| Remainder after dividing by 7 | 2,532 - 361 x 7 | 5 = Friday |
Other checks: 20 July 1969 (the first Moon landing) was a Sunday, and 29 February 2000 was a Tuesday.
What else you get
- Day of the year: 1 for 1 January, up to 365 or 366 for 31 December. For 15 March 2024 it is 75 of 366.
- ISO week: the week number used by many businesses and countries. Weeks start on Monday, and week 1 is the week with the first Thursday of the year. So the first days of January can be in week 52 or 53 of the year before, and the last days of December can be in week 1 of the next year. For example, 30 December 2024 is in week 1 of 2025.
- Quarter: Q1 for January to March, Q2 for April to June, Q3 for July to September, and Q4 for October to December.
- Days from today: how many days the date is in the past or in the future, counted in whole calendar days.
- The same date in the next years: for example, a birthday moves forward one weekday each year, and two in a leap year.
Chart: the length of each month
Each block is about 0.8 days. Green months have 31 days, amber months have 30, and February (red) has 28, or 29 in a leap year.
Jan ████████████████████████████████████████ 31 Feb ████████████████████████████████████ 28 Mar ████████████████████████████████████████ 31 Apr ███████████████████████████████████████ 30 May ████████████████████████████████████████ 31 Jun ███████████████████████████████████████ 30 Jul ████████████████████████████████████████ 31 Aug ████████████████████████████████████████ 31 Sep ███████████████████████████████████████ 30 Oct ████████████████████████████████████████ 31 Nov ███████████████████████████████████████ 30 Dec ████████████████████████████████████████ 31
Table: the weekday of 1 January
| Year | 1 January | Leap year |
|---|---|---|
| 2026 | Thursday | No |
| 2027 | Friday | No |
| 2028 | Saturday | Yes |
| 2029 | Monday | No |
| 2030 | Tuesday | No |
| 2031 | Wednesday | No |
| 2032 | Thursday | Yes |
The weekday of a date moves forward one day each year (because 365 = 52 x 7 + 1), and two days after a leap day (because 366 = 52 x 7 + 2).
Chart: Friday the 13th
The calendar repeats exactly every 400 years, and in this time the 13th of the month falls on a Friday more often than on any other day. Counting all 4,800 months of one cycle, the number of times is below. The bars start at 670 so that the small differences can be seen, and each block is about 0.5 of a day.
Sunday ██████████████████████████████████████ 687 Monday █████████████████████████████████ 685 Tuesday █████████████████████████████████ 685 Wednesday ██████████████████████████████████████ 687 Thursday ███████████████████████████████ 684 Friday ████████████████████████████████████████ 688 Saturday ███████████████████████████████ 684
Chart: the days of 29 February
There are 97 leap days in the 400-year cycle. They also fall on every day of the week, and the difference is small. Each block is about 0.4 of a day.
Sunday ███████████████████████████████████ 13 Monday ████████████████████████████████████████ 15 Tuesday ███████████████████████████████████ 13 Wednesday ████████████████████████████████████████ 15 Thursday ███████████████████████████████████ 13 Friday █████████████████████████████████████ 14 Saturday █████████████████████████████████████ 14
Why the time zone does not change the answer
A date does not have a time zone. The calculator works out the weekday from the year, the month and the day that you choose, and not from a moment in time, so you get the same answer anywhere. Only the number of days from today uses your own date.
What this calculator does not include
- Other calendars, such as the Julian, the Hebrew, the Islamic and the Chinese calendars.
- The date of a holiday or an event. You give it the date.
- Years before 1 or after 9999.
This tool is for general information. For dates before 1582, the weekday is worked out with the Gregorian rules.