gen-briefly-explain-the-day-of-the-week-from-a-date-zeller-s-con-2574

Briefly explain the day of the week from a date (Zeller's congruence) and one common misconception about it.

# Zeller's Congruence **What it is:** A mathematical algorithm that calculates the day of the week for any given date. The formula is: **h = (q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ - 2J) mod 7** Where: - h = day of week (0=Saturday, 1=Sunday, etc.) - q = day of month - m = month (3=March, 4=April, ..., 14=February)* - K = year of century (year mod 100) - J = zero-based century (⌊year/100⌋) *Note: January and February are counted as months 13 and 14 of the previous year ## Common Misconception **"Zeller's formula works with January=1 and December=12"** Many people assume they can plug dates in directly with standard month numbering. However, Zeller's congruence requires **January and February to be treated as months 13 and 14 of the *previous* year**. So January 15, 2024 must be entered as month 13, year 2023. This quirk exists because it simplifies the leap year calculations within the formula, but forgetting this adjustment is the #1 reason people get incorrect results.