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 particularly useful for determining what day of the week specific dates (like New Year's Day) fell on in past or future years.

2. How Does the Calculator Work?

The calculator uses Zeller's Congruence formula:

Where:

• \( q \) — Day of the month (1 for New Year's Day)
• \( m \) — Month (13 for January treated as previous year)
• \( K \) — Year of the century (\( year \mod 100 \))
• \( J \) — Zero-based century (\( \left\lfloor year/100 \right\rfloor \))

Explanation: The formula accounts for the Gregorian calendar rules, including leap years and century adjustments.

3. Importance of Day Calculation

Details: Knowing the day of the week for New Year's Day helps in historical research, calendar planning, and understanding patterns in annual calendars.

4. Using the Calculator

Tips: Enter any year between 1583 (when Gregorian calendar was introduced) and 9999. The calculator will determine what day of the week January 1st fell on that year.

5. Frequently Asked Questions (FAQ)

Q1: Why does the formula use month 13 for January?
A: Zeller's Congruence treats January and February as months 13 and 14 of the previous year to simplify leap year calculations.

Q2: What calendar does this work for?
A: The calculator works for the Gregorian calendar (years 1583 and later). For earlier dates, the Julian calendar was used.

Q3: How accurate is this calculation?
A: It's mathematically precise for the Gregorian calendar system, accounting for all leap year rules.

Q4: What do the result numbers mean?
A: The result (0-6) corresponds to Saturday (0) through Friday (6). The calculator displays the actual day name.

Q5: Can this be used for any date?
A: While this calculator specifically shows New Year's Day, the formula can be adapted for any date with appropriate parameter adjustments.