Day of the Week Calculator

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Results

Day of the Week

Saturday

for 2000-1-1

Zeller index (h)	0 (0=Sat … 6=Fri)
ISO weekday	6 (1=Mon … 7=Sun)

What is the Day of the Week Calculator?

This tool tells you which day of the week any calendar date falls on — past, present or future. Whether you want to know what day you were born, when a historical event happened, or which weekday a future deadline lands on, enter the year, month and day and get the answer instantly. The calculation uses Zeller's congruence on the proleptic Gregorian calendar.

The weekday is the remainder when dividing by 7, cycling through the seven days.

How to use it

Choose the year, pick the month from the dropdown, and enter the day of the month. Press calculate and the result box shows the weekday name. The table also reports the raw Zeller index (\(h\)) and the ISO weekday number (1 = Monday … 7 = Sunday) for programmers and the curious.

The formula explained

Zeller's congruence computes the weekday with pure arithmetic — no lookup tables. January and February are treated as months 13 and 14 of the previous year, which keeps leap-day handling simple. With \(q = \text{day}\), \(m = \text{adjusted month}\), \(K = Y \bmod 100\) and \(J\) = the century (year ÷ 100), the formula is:

$$h = \left( q + \left\lfloor \frac{13(m+1)}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor + 5J \right) \bmod 7$$

Here \(h = 0\) is Saturday, \(1\) is Sunday, and so on up to \(6\) = Friday.

Zeller's congruence combines the day, month and year terms, then takes the result modulo 7.

Worked example

For 13 March 2020: \(q = 13\), \(m = 3\), \(y = 2020\), so \(K = 20\) and \(J = 20\). Then $$h = \left( 13 + \left\lfloor \frac{52}{5} \right\rfloor + 20 + \left\lfloor \frac{20}{4} \right\rfloor + \left\lfloor \frac{20}{4} \right\rfloor + 100 \right) \bmod 7 = (13 + 10 + 20 + 5 + 5 + 100) \bmod 7 = 153 \bmod 7 = 6 = \text{Friday}.$$ And 13 March 2020 was indeed a Friday.

FAQ

Does it work for old dates before 1582? It uses the proleptic Gregorian calendar, so for very old dates that were originally recorded in the Julian calendar the weekday may differ from the historical record.

Why is Saturday h = 0? That is simply how the classic Zeller formula is defined. The calculator converts it to a readable weekday name for you.

Can I enter any year? Yes, any year from 1 to 9999. Just make sure the day is valid for the chosen month.