Day of the Week

Find the day of the week for any date from year 1 to 9999. Solution by Zeller's congruence, day of the year, week number and month calendar.

Any date from year 1 to 9999 works.

Test yourself

The day of the week calculator finds the weekday of any date from year 1 to 9999 — a birthday, a historical event or a future holiday. The solution uses Zeller's congruence and also shows the day of the year, the week number, the quarter and a calendar of the month.

Zeller's congruence

h = (q + [13(m + 1)/5] + K + [K/4] + [J/4] + 5J) mod 7

q is the day of the month, m the month (March = 3, …, December = 12; January and February count as months 13 and 14 of the previous year);
K is the last two digits of the year, J the century (leading digits);
[x] is the integer part, mod 7 the remainder after division by 7.

h	0	1	2	3	4	5	6
Day	Sat	Sun	Mon	Tue	Wed	Thu	Fri

Example. July 20, 1969 (Moon landing): q = 20, m = 7, K = 69, J = 19.
h = (20 + [13·8/5] + 69 + [69/4] + [19/4] + 5·19) mod 7 = (20 + 20 + 69 + 17 + 4 + 95) mod 7 = 225 mod 7 = 1 — Sunday.

The formula is for the Gregorian calendar, introduced in 1582 (in Britain and its colonies in 1752).