1. What is Zeller's Congruence?

Zeller's Congruence is an algorithm to calculate the day of the week for any Julian or Gregorian calendar date. It's named after Christian Zeller, the 19th-century German mathematician who developed it.

2. How Does the Formula Work?

The calculator uses Zeller's Congruence formula:

Where:

• \( q \) — Day of the month
• \( m \) — Month (3 = March, 4 = April, ..., 14 = February)
• \( K \) — Year of the century (\( year \mod 100 \))
• \( J \) — Zero-based century (\( \left\lfloor year / 100 \right\rfloor \))

Note: January and February are counted as months 13 and 14 of the previous year.

3. Importance of Day Calculation

Details: Knowing the day of the week for historical dates is important for calendar studies, scheduling applications, and historical research.

4. Using the Calculator

Tips: Enter the day (1-31), month (1-12), and year (any positive integer). The calculator will adjust January and February as needed.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for dates before 1582?
A: The formula works mathematically, but results may not match historical records due to calendar changes during the Gregorian reform.

Q2: What does the result number mean?
A: The formula returns 0=Saturday, 1=Sunday, 2=Monday, ..., 6=Friday.

Q3: Why are January and February treated differently?
A: This adjustment accounts for their position at the beginning of the year in the Gregorian calendar.

Q4: How accurate is this formula?
A: It's mathematically precise for the Gregorian calendar from 1582 onward.

Q5: Can this be used for programming?
A: Yes, it's commonly implemented in programming for day-of-week calculations.