ToolNestr

Day of the Week Calculator

Find the exact day of the week for any date in history or the future using Zeller's congruence.

Reviewed by the ToolNestr Editorial Team — July 2026

Day of the week
Calendar grid with highlighted day A calendar month grid showing days of the week with one day highlighted to indicate the calculator result August 1990 Mon Tue Wed Thu Fri Sat Sun 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
August 15, 1990 was a Wednesday

How Zeller's congruence works

Zeller's congruence is an algorithm devised by German mathematician Julius Christian Zeller in 1882. It calculates the day of the week for any date in the Gregorian calendar using modular arithmetic. The formula takes the day, month, and year as inputs and produces a number from 0 to 6, where each number corresponds to a day of the week.

The algorithm treats January and February as months 13 and 14 of the previous year to account for the leap year irregularity. It then performs a series of divisions and modulo operations to account for the year cycle, century cycle, and month offsets. The formula is remarkably compact for how accurately it captures the full Gregorian calendar pattern including leap years.

The formula explained

Treat Jan/Feb as months 13/14 of prior year, then:
h = (q + floor(13(m+1)/5) + K + floor(K/4) + floor(J/4) − 2J) mod 7
Where q = day, m = month, K = year mod 100, J = century

Worked example

August 15, 1990

q (day): 15
m (month): 8
K (year % 100): 90
J (century): 19
h: (15 + floor(13×9/5) + 90 + floor(90/4) + floor(19/4) − 2×19) mod 7
Result: h = 4 → Wednesday (Zeller: 0 = Saturday)
🎂

Birthday Discovery

Find out what day of the week you or someone else was born on. A fun fact for parties or genealogy research.

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Historical Dates

Check what day of the week historical events fell on — the signing of a treaty, a famous battle, or a significant discovery.

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Event Planning

When planning a wedding or event, check what day a specific date falls on in a future year before booking the venue.

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Calendar Creation

Generate accurate calendars for any year. Verify that important dates fall on the expected weekdays before printing.

How to use the day of the week calculator

1

Enter the day

Type the day number (1–31). The calculator validates it against the selected month.

2

Select month and year

Pick the month and type the year. The year can be any Gregorian year from 1752 onwards.

3

Get the result

The calculator shows the day name and full formatted date instantly.

Tips for date calculations

Remember leap years

Years divisible by 4 are leap years, except centuries not divisible by 400. The year 2000 was a leap year; 1900 was not. Zeller's handles this automatically.

Gregorian vs Julian

The Gregorian calendar was adopted at different times across countries. Britain and its colonies adopted it in 1752. Dates before adoption follow the Julian calendar, which is 11 days behind by that time.

January and February adjustment

In Zeller's congruence, January and February are counted as months 13 and 14 of the previous year. This is why the formula treats the year differently for these months.

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Frequently asked questions

How far back does the calculator work?

Zeller's congruence works for the Gregorian calendar, which started in 1752. Dates before that use the Julian calendar and may be off by several days.

What about dates in the distant future?

The formula works for any Gregorian date. However, calendar reforms could theoretically change future reckoning.

Why do I get a different result from some other calculators?

Some tools use the Julian calendar for old dates or treat the year differently. This tool uses the standard Gregorian Zeller's congruence.

Is Zeller's congruence accurate?

Yes — it is a well-known mathematical formula that has been used for over a century. It is accurate for all Gregorian calendar dates.

What day of the week was I born on?

Enter your birth date in the calculator and it will tell you. This is one of the most common uses for this tool.

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