What this calculates
Enter any date from 1583 to 2400 and this tells you the day of the week it falls on, which day of the year it is, its ISO week number, whether its year is a leap year, and how many days are left in that year.
The formula
Zeller's congruence
h = (q + ⌊13(m + 1) ÷ 5⌋ + K + ⌊K ÷ 4⌋ + ⌊J ÷ 4⌋ + 5J) mod 7
Reading h
0 Saturday · 1 Sunday · 2 Monday · 3 Tuesday · 4 Wednesday · 5 Thursday · 6 Friday
Leap year
divisible by 4, and not by 100 unless also by 400q is the day of the month and m the month, with January and February counted as months 13 and 14 of the previous year. K is the year within its century (47 for 1947) and J is the century (19). ⌊ ⌋ means round down.
Worked example
For 1 January 2000, January counts as month 13 of 1999, giving h = 0: a Saturday.
When to use it, and the mistakes to avoid
Use it to find the day you were born, the weekday of a historic event, whether a future date lands on a weekend, or a week number for planning and payroll.
The mistakes that cost the most:
- Forgetting the January–February shift. In Zeller's method they belong to the year before, as months 13 and 14.
- Counting 1900 as a leap year. Century years must divide by 400; 1900 did not.
- Confusing week numbering systems. ISO weeks start on Monday; some calendars start weeks on Sunday and number them differently.
- Rounding up in the formula. Every ⌊ ⌋ rounds down.
- Using it before 1583. Earlier dates were in the Julian calendar.
FAQ
What day of the week was 15 August 1947?
A Friday. India's first Independence Day fell on the 227th day of 1947, in ISO week 33.
How do I find the day I was born?
Enter your date of birth and the calculator gives the weekday straight away. It works for any date from 1583, when the Gregorian calendar was in use, to 2400.
How can I work out the day of the week by hand?
Use Zeller's congruence: h = (q + ⌊13(m + 1) ÷ 5⌋ + K + ⌊K ÷ 4⌋ + ⌊J ÷ 4⌋ + 5J) mod 7, where q is the day, m the month (with January and February as months 13 and 14 of the year before), K the year within the century and J the century. h = 0 is Saturday, 1 Sunday and so on to 6, Friday.
What is the ISO week number?
The week of the year by the ISO 8601 standard, used in business and much of Europe. Weeks start on Monday, and week 1 is the one containing the year's first Thursday - so 1 January can belong to week 52 or 53 of the year before. 1 January 2000 was in week 52 of 1999.
Which years are leap years?
Years divisible by 4, except century years, which must be divisible by 400. So 2024 and 2000 were leap years, but 1900 was not and 2100 will not be.
Why does the calculator start at 1583?
The Gregorian calendar began in October 1582, when ten days were dropped to correct the old Julian calendar. Dates before it were recorded differently, and the same weekday rules do not apply to them.