About

Knowing the day of the week for any calendar date is a non-trivial computational problem. The Gregorian calendar's irregular month lengths and leap-year rules make naive lookup impractical for dates spanning centuries. This calculator implements Zeller's Congruence, a modular arithmetic formula published by Christian Zeller in 1882, to map any valid Gregorian date to one of seven weekdays with zero ambiguity. It handles the full Gregorian range from October 15, 1582 (the calendar's adoption date) onward. An incorrect weekday assignment in legal, genealogical, or historical contexts can invalidate documents or misattribute events. The tool also computes your age in days, your zodiac sign, and a countdown to your next birthday.

Limitations: dates before the Gregorian reform (pre-October 15, 1582) used the Julian calendar and will produce historically inaccurate results if entered here. The formula assumes the proleptic Gregorian calendar for earlier dates. Leap-second adjustments do not affect day-of-week calculations.

Formulas

The weekday is computed using Zeller's Congruence for the Gregorian calendar. January and February are treated as months 13 and 14 of the preceding year.

h = ( q + ⌊13(m + 1)5⌋ + K + ⌊K4⌋ + ⌊J4⌋ − 2J ) mod 7

Where: h = day of the week (0 = Saturday, 1 = Sunday, … 6 = Friday). q = day of the month. m = month (3 = March, 4 = April, … 14 = February). K = year of the century (year mod 100). J = zero-based century (⌊year ÷ 100⌋).

Leap year validation follows the Gregorian rule:

{

TRUE if year mod 400 = 0FALSE if year mod 100 = 0TRUE if year mod 4 = 0FALSE otherwise

Reference Data

Day Number	Day Name	ISO 8601 Index	Traditional Index (Sunday=0)	Named After	Historical Significance
0	Saturday	6	6	Saturn (Roman god)	Jewish Sabbath; Zeller's base day
1	Sunday	7	0	Sun (Sol)	Christian day of rest; ISO week ends here
2	Monday	1	1	Moon (Luna)	ISO week starts here
3	Tuesday	2	2	Tiw / Mars	US Election Day (first Tue after first Mon in Nov)
4	Wednesday	3	3	Woden / Mercury	Mid-week; "hump day" colloquially
5	Thursday	4	4	Thor / Jupiter	US Thanksgiving (4th Thu in Nov)
6	Friday	5	5	Frigg / Venus	Islamic holy day; Good Friday
Famous Birth Weekdays
-	Saturday	Albert Einstein - March 14, 1879
-	Tuesday	Isaac Newton - January 4, 1643 (Gregorian)
-	Sunday	Leonardo da Vinci - April 15, 1452
-	Wednesday	Nikola Tesla - July 10, 1856
-	Tuesday	Marie Curie - November 7, 1867
-	Monday	Ada Lovelace - December 10, 1815
-	Friday	Stephen Hawking - January 8, 1942
-	Wednesday	Charles Darwin - February 12, 1809
-	Monday	Mozart - January 27, 1756
-	Sunday	Queen Victoria - May 24, 1819

Frequently Asked Questions

February is the month that gains or loses a day during leap years. By shifting it to the end of the computational year (month 14 of the previous year), the leap day falls at the very end of the cycle, which means the variable-length month never disrupts the floor-division terms in the formula. This avoids the need for a separate leap-year correction branch inside the main equation.

No. The Gregorian calendar was adopted on October 15, 1582, replacing the Julian calendar which had different leap-year rules (every 4 years without the century exception). Dates entered before this reform are computed using the proleptic Gregorian calendar, meaning the weekday is mathematically correct for the Gregorian system but may not match the day historically recorded under the Julian calendar. For Julian dates, a modified form of Zeller's formula with different century correction terms is required.

The tool checks three layers: (1) the month must be between 1 and 12, (2) the day must be between 1 and the maximum days for that month (28, 29, 30, or 31), and (3) February 29 is only accepted if the year passes the Gregorian leap-year test (divisible by 4, not by 100, unless also by 400). Entering February 29, 1900 will correctly be rejected because 1900 is not a Gregorian leap year, while February 29, 2000 is accepted.

A week has exactly 7 days. Any integer mapped through modulo 7 produces a remainder in the range 0-6, which uniquely identifies one of the seven weekdays. The rest of Zeller's formula accumulates the total day offset from a reference point (accounting for days in months, leap years, and century corrections) so that the final mod 7 result corresponds to the correct weekday. The choice of Saturday as 0 is Zeller's original convention.

Yes. Different countries adopted the Gregorian calendar at different times. Britain and its colonies switched in September 1752 (skipping 11 days), while Greece did not adopt it until 1923. A date like February 15, 1712 was a valid date in Sweden (which had a unique calendar anomaly that year) but would map to a different Julian weekday in Russia. This tool assumes universal Gregorian dating regardless of regional adoption history.

The zodiac sign is derived from the same month and day inputs and requires zero additional computation beyond a date-range lookup. It provides context that users commonly seek alongside their birth weekday. The tropical zodiac boundaries used here follow the standard Western astrological convention (Aries begins March 21). These boundaries are fixed date ranges and do not account for precession of the equinoxes.