Zeller's Congruence Calculator

About this calculator

Zeller's congruence is a formula devised by German mathematician Christian Zeller in the 19th century that computes the day of the week for any Gregorian (or Julian) calendar date using only arithmetic on the day, month and year. The calculation treats January and February as months 13 and 14 of the previous year, then combines the day, an adjusted month term, and terms for the year and century to produce a raw value called h, which is then taken modulo 7 to give a number representing a specific weekday (the exact mapping depends on the formula's convention).

Because it needs no lookup tables or calendar libraries, Zeller's congruence has long been used to teach modular arithmetic, to verify that a historical date fell on the weekday a document claims, and to implement day-of-week logic in embedded or resource-constrained systems where importing a full calendar library isn't practical.

This calculator takes any date, walks through Zeller's formula, and shows both the resulting weekday and the intermediate raw h value.