calc / date & time / DOW

Day of the Week Calculator

The weekday of any date between 1600 and 2400 — the day you were born, a festival, a deadline — plus the same date in nearby years, day-of-year and ISO week number.

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Day of the week

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Day of the year

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Week number

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§1How the weekday is computed

Weekdays repeat in a fixed pattern, so any date's weekday is pure arithmetic — no lookup table of history required. The classic closed form is Zeller's congruence (the party-trick alternative is Conway's doomsday rule, which mentalists use to do this in their heads):

h = ( q + ⌊13(m + 1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J ) mod 7 q = day of month m = month (Mar=3 … Dec=12; Jan=13, Feb=14 of the K = year mod 100 previous year) J = ⌊year/100⌋ h: 0=Sat 1=Sun 2=Mon 3=Tue 4=Wed 5=Thu 6=Fri

The odd-looking ⌊13(m+1)/5⌋ term encodes the 30/31-day month pattern; treating January and February as months 13 and 14 of the previous year pushes the leap day to the end of the counting year so it can't disturb the months before it. JavaScript's Date does the same arithmetic internally (via day counts from an epoch), which is what this page actually calls.

Worked example: 15 August 1947

q = 15, m = 8, year = 1947, so K = 47 and J = 19. Then ⌊13 × 9 ÷ 5⌋ = 23, ⌊47 ÷ 4⌋ = 11, ⌊19 ÷ 4⌋ = 4, and 5J = 95. Sum: 15 + 23 + 47 + 11 + 4 + 95 = 195. 195 mod 7 = 6, and h = 6 means Friday — Independence Day 1947 was indeed the Friday of "tryst with destiny".

§2The gotchas

Before the Gregorian switch, weekdays are ambiguous

The Gregorian calendar started in 1582 (Catholic Europe) but Britain and its colonies — India's records included — switched only in 1752, deleting 11 days. This page uses the proleptic Gregorian calendar throughout, so for dates before the switch the weekday shown may not match what contemporaries wrote in their diaries.

The century leap-year rule

Century years are leap only when divisible by 400: 1900 was not a leap year, 2000 was, 2100 won't be. Any weekday shortcut that assumes "every 4th year" silently breaks across 1900 and 2100 — Zeller's ⌊K/4⌋ + ⌊J/4⌋ + 5J terms exist precisely to get this right.

"Week number" has rival definitions

This page shows the ISO 8601 week: weeks start Monday, and week 1 is the week containing the year's first Thursday — so 29 Dec–3 Jan can belong to the other year's week 52/53 or week 1. The US convention (weeks start Sunday, week 1 contains 1 January) disagrees at exactly those year edges. Check which one your planner uses.

§3Related

Age calculator for exact age from that birth date, day counter for the days between two dates.