Hebrew Calendar Converter

The Hebrew calendar is arithmetic rather than observational, and every conversion reduces to two computations. The first is the molad, the calculated mean new moon of Tishrei, accumulated from a fixed epoch using a mean lunation of 29 days, 12 hours and 793 parts, where one hour is divided into 1080 parts (chalakim). That value equals 29.530594 days, only about half a second longer than the modern measured synodic month of 29.530589 days. The second computation applies the four postponement rules known as dehiyot: Rosh Hashanah is pushed forward if the molad falls at or after noon (18 hours into the day), and it may never fall on Sunday, Wednesday or Friday, with two further rules covering the 9 hours 204 parts case after a common year and the 15 hours 589 parts case following a leap year. Those postponements force the year length to one of six values. Common years run 353, 354 or 355 days and leap years 383, 384 or 385, described as deficient (chaser), regular (kesidran) or complete (shalem), with the slack absorbed entirely by Cheshvan and Kislev, which switch between 29 and 30 days. Leap years carry a thirteenth month, Adar I, in years 3, 6, 8, 11, 14, 17 and 19 of each 19-year Metonic cycle. The main caveat is accumulated drift: the mean lunation runs slightly long, so the calendar gains roughly one day every 216 years against the true moon, and dates are counted from an epoch corresponding to 3761 BCE with days beginning at sunset, not midnight.

Biblical and Second Temple practice was observational. Witnesses reported the first sighting of the crescent to the court in Jerusalem, which sanctified the new month and dispatched signal fires and later messengers to outlying communities. Because messengers could not reach the diaspora in time, a second festival day was added outside the Land of Israel, a practice still followed. Intercalation of the extra Adar was likewise decided case by case, weighing whether the barley would be ripe for the Omer offering and whether the roads and lambs were ready for Passover. Roman persecution and the dispersal of the rabbinic courts made a court-dependent system untenable. Tradition credits Hillel II, patriarch in the Land of Israel, with publishing a fixed calculated calendar around 359 CE, though the scheme in its present form appears to have been settled gradually over the following centuries. Maimonides set out the complete arithmetic, including the molad and the dehiyot, in the Laws of the Sanctification of the New Moon in his Mishneh Torah in the twelfth century, and that treatment remains the standard reference. A notable dispute in 921 to 923 CE between Saadia Gaon of Babylonia and Aaron ben Meir of Palestine over the postponement rules briefly split the two communities onto different festival dates, and its resolution confirmed the Babylonian reckoning still in use.