Birth Day of the Week Calculator

What is a Birth Day of the Week Calculator?

A Birth Day of the Week Calculator is a tool that determines the specific day of the week on which a person was born. It uses the birth date to calculate and identify which day (Monday, Tuesday, etc.) corresponds to that date in history. This calculator is useful for historical research, personal curiosity, or planning birthday celebrations that align with the original day of the week.

Formula

The formula for calculating the day of the week is based on Zeller's Congruence:

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

Where:

• \(h\) is the day of the week (0 = Saturday, 1 = Sunday, ..., 6 = Friday)
• \(q\) 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 (\(\lfloor year/100 \rfloor\))
• \(\lfloor \cdot \rfloor\) denotes the floor function

Calculation Steps

1. Adjust the month and year:
   • If the month is January or February, subtract 1 from the year and add 12 to the month
   • For other months, use them as is
2. Calculate \(q\), \(m\), \(K\), and \(J\) as defined above
3. Apply the formula: \(h = (q + \lfloor\frac{13(m+1)}{5}\rfloor + K + \lfloor\frac{K}{4}\rfloor + \lfloor\frac{J}{4}\rfloor - 2J) \mod 7\)
4. The result \(h\) corresponds to the day of the week

Example

Let's calculate the day of the week for July 20, 1969 (Moon landing date):

1. July is month 7, so no adjustment needed
2. \(q = 20\), \(m = 7\), \(K = 69\), \(J = 19\)
3. \(h = (20 + \lfloor\frac{13(7+1)}{5}\rfloor + 69 + \lfloor\frac{69}{4}\rfloor + \lfloor\frac{19}{4}\rfloor - 2(19)) \mod 7\)
4. \(h = (20 + 21 + 69 + 17 + 4 - 38) \mod 7 = 93 \mod 7 = 2\)
5. Result: 2 corresponds to Sunday

Visual Representation

This visual representation shows the date July 20, 1969, with the calculated day of the week (Sunday) highlighted in the center of a circular calendar representation. The significance of this date as the Moon Landing Day is noted, demonstrating how the Birth Day of the Week Calculator can be used to find the day of the week for important historical dates.