Day of Week Calculator

How to Use the Day of Week Calculator

1. Select a date using the calendar or enter it manually in YYYY-MM-DD format
2. Click "Find Day of Week" to see the result
3. The calculator will display which day of the week the selected date falls on

Understanding Day of Week Calculations

Determining the day of the week for any date involves complex calculations that account for:

• Calendar System: Our calculator uses the Gregorian calendar, which is the internationally accepted civil calendar in most of the world today.
• Leap Years: The calculation accounts for leap years, which occur every 4 years (with exceptions for century years not divisible by 400).
• Calendar Reforms: For dates before the Gregorian calendar reform (which occurred at different times in different countries), the calculator still uses the Gregorian system retroactively.

The Mathematics Behind Day of Week Calculation

Several algorithms can determine the day of the week for any date. One of the most well-known is Zeller's Congruence, which uses modular arithmetic to calculate the day of the week.

The basic formula for Zeller's Congruence is:

Where:

• h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, etc.)
• q is the day of the month
• m is the month (3 = March, 4 = April, ..., 14 = February)
• K is the year of the century (year mod 100)
• J is the zero-based century (⌊year/100⌋)

Note that in this formula, January and February are counted as months 13 and 14 of the previous year.

Common Applications