Easter Date Calculator

The computus is a calendar algorithm, not an astronomy engine. It locates Easter as the first Sunday following the paschal full moon that falls on or after March 21, where March 21 is a fixed ecclesiastical equinox rather than the true astronomical one, and the paschal full moon comes from a tabular lunar model rather than an observation. The variables in the anonymous Gregorian algorithm each carry a distinct job: a = year mod 19 is the position in the 19-year Metonic cycle, b and c split the year into century and year-within-century, d through g apply the Gregorian solar and lunar corrections for century years, and h fixes the age of the ecclesiastical moon on March 21. The remaining terms l and m convert that lunar age into an offset to the following Sunday. The output range is bounded at March 22 through April 25, a 35-day window, and the full Gregorian Easter pattern only repeats after 5,700,000 years because the solar and lunar century corrections have different periods. The main caveats are that the tabular paschal moon can differ from the true full moon by roughly one to two days, that the algorithm is only defined for Gregorian years from 1583 onward, and that it yields Western Easter only. Eastern Orthodox churches run the same logic on the Julian calendar, currently 13 days offset, so the two dates commonly differ by one, four, or five weeks.

The requirement for a common Easter date came out of the First Council of Nicaea in 325 AD, which affirmed that all churches should celebrate on the same Sunday after the paschal full moon rather than following local Jewish Passover reckoning. Competing 8-year and 84-year lunar cycles circulated for the next two centuries until the Alexandrian 19-year cycle prevailed. Dionysius Exiguus produced Latin Easter tables in 525 AD, and in doing so introduced the Anno Domini year count. The Venerable Bede systematised the whole discipline in De temporum ratione, completed in 725, which taught the computus to medieval Europe and made it the standard subject of clerical mathematics. By the sixteenth century the Julian scheme had drifted about ten days from the observed equinox. The reform designed by Aloysius Lilius and completed by the Jesuit mathematician Christopher Clavius was promulgated by Pope Gregory XIII in the bull Inter gravissimas of February 1582, adding both the century leap-year rule and the separate lunar equation that keeps the tabular moon aligned. Closed-form arithmetic versions followed: Carl Friedrich Gauss published an Easter formula in 1800 and corrected it in 1816, and the compact algorithm used here appeared anonymously in the journal Nature in 1876 and was later printed in Samuel Butcher's Ecclesiastical Calendar of 1877.