Date Calculator Day Of Week

Zeller's Congruence:

\[ Day = (q + \left\lfloor\frac{13(m+1)}{5}\right\rfloor + K + \left\lfloor\frac{K}{4}\right\rfloor + \left\lfloor\frac{J}{4}\right\rfloor - 2J) \mod 7 \]

Day of Week:

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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 German mathematician who developed it in the 19th century.

2. How Does the Calculator Work?

The calculator uses Zeller's congruence formula:

\[ Day = (q + \left\lfloor\frac{13(m+1)}{5}\right\rfloor + K + \left\lfloor\frac{K}{4}\right\rfloor + \left\lfloor\frac{J}{4}\right\rfloor - 2J) \mod 7 \]

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 (floor(year / 100))

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, historical research, and various applications in computer science and business.

4. Using the Calculator

Tips: Enter a valid date (day, month, year). The calculator works for dates in the Gregorian calendar (after October 1582). For Julian calendar dates, different methods are needed.

5. Frequently Asked Questions (FAQ)

Q1: What calendar does this work for?
A: The calculator works for the Gregorian calendar (after October 1582). For Julian calendar dates, a modified formula is needed.

Q2: Why are January and February treated differently?
A: In Zeller's formula, January and February are counted as months 13 and 14 of the previous year to make the formula work correctly.

Q3: What's the range of valid years?
A: The calculator works for years from 1583 to 9999, which covers the entire Gregorian calendar period.

Q4: How accurate is Zeller's congruence?
A: It's 100% accurate for all valid Gregorian calendar dates when implemented correctly.

Q5: Are there alternatives to Zeller's formula?
A: Yes, other algorithms exist like the Doomsday rule or Conway's Doomsday algorithm, but Zeller's is one of the most straightforward for programming implementations.