Hebrew Calendar Converter

The Hebrew calendar is lunisolar. Its months follow the moon, its years follow the sun, and the work of the calendar is reconciling the two. Twelve lunar months are about 354 days, eleven short of a solar year, so seven years in every nineteen add a thirteenth month. Without that, Passover, which the Torah places in the spring, would drift through the seasons the way Ramadan does in the purely lunar Islamic calendar.

The calendar in use today is fixed arithmetic, not observation. Its rules are traditionally attributed to Hillel II in the fourth century, and they can be computed for any year without looking at the sky. That is what this converter does, following the algorithm in Dershowitz and Reingold's Calendrical Calculations, and its output is checked against published dates.

Three pieces make it work.

The molad. Every month begins at a calculated mean new moon, the molad, spaced exactly 29 days, 12 hours and 793 parts apart. A part (chelek) is 1/1,080 of an hour, about 3.3 seconds, so the month is 29.530594 days, within a fraction of a second of the astronomical mean.

The 19-year cycle. Years 3, 6, 8, 11, 14, 17 and 19 of each Metonic cycle are leap years, and a leap year has two Adars: Adar I is the added month, and Adar II is the one that carries Purim. 235 months in 19 years is the reconciliation: 235 lunar months and 19 solar years differ by about two hours.

The postponements (dehiyyot). Rosh Hashanah, 1 Tishrei, is set on the day of the Tishrei molad unless one of four rules moves it. It never falls on a Sunday, Wednesday or Friday, so that Yom Kippur is not on a Friday or Sunday next to Shabbat and Hoshana Rabbah is not on Shabbat. If the molad is at or after noon, Rosh Hashanah moves to the next day. And two rarer rules (known by the mnemonics GaTaRaD and BeTUTaKPaT) stop a year from coming out at an impossible length. The postponements are absorbed by Cheshvan and Kislev, which is why those two months are 29 or 30 days depending on the year and why years come in three lengths: deficient (353 or 383 days), regular (354 or 384) and complete (355 or 385).

One rule matters every time you convert a date: the Hebrew day starts at sunset, not midnight. Monday evening after sunset is already Tuesday's Hebrew date, and Shabbat begins on Friday evening for exactly that reason. A converter that ignores this gives the wrong Hebrew date for everything that happens after dark, such as a birth, a death or a wedding in the evening. The checkbox above handles it; it does not compute the time of sunset, which depends on where you are.

Some practical points. The Hebrew year number turns at Rosh Hashanah in September or October, so a Gregorian year straddles two Hebrew years: add 3,760 before Rosh Hashanah and 3,761 after it. In a leap year, "Adar" on its own is ambiguous; this converter reads it as Adar II, where Purim falls and where a birthday from a common-year Adar is usually kept, but customs for anniversaries differ. And holiday dates are given as the daytime of the first day; each begins at sunset the evening before, and several are kept for an extra day outside Israel.

What this converter does not do: compute sunset, apply local customs, or cover minor fasts and modern commemorations. The holiday list is the seven major festivals, each computed from its fixed Hebrew date.