The Hebrew calendar

Fact sheet

Scientific classification

• Lunisolar: its months are lunar, and its year stays close to the seasons by a leap month, because Passover must fall in spring.
• Arithmetical, not astronomical: it uses neither the true new moon nor the true equinox, but the “molad” — a mean conjunction of fixed length — and a fixed intercalation cycle. That is why Reingold and Dershowitz place it among the arithmetical calendars in Calendrical Calculations; any date in it can be computed with integer operations without any observation.
• It was observational: in the Second Temple and Mishnaic periods the high court (the Sanhedrin) proclaimed the first of the month on the testimony of those who had seen the crescent, and decided intercalation by the state of the crops, the fruit and the equinox. It moved to calculation gradually between the 4th and 10th centuries CE.
• Its standing in scholarship: it is considered one of the most accurate ancient arithmetical calendars in the length of its month (differing from the mean lunar month by less than half a second), but its mean year is about seven minutes longer than the tropical year, so it drifts slowly from the seasons. Historians of science study it as a link between Babylonian astronomy and Islamic and European astronomy, and al-Khwarizmi wrote a treatise on it around 823.

Current rules

1. The day begins at sunset and ends at the next sunset, so the night precedes its day. In calculation the day is counted as 24 hours starting at 6 p.m., and the hour as 1080 “parts” חלקים, so a part is 3⅓ seconds.
2. The molad מולד: the mean conjunction; each molad is separated from the next by 29 days, 12 hours and 793 parts (29.530594 days). The first molad in the reckoning, the “molad of Tohu,” is on Monday night at hour 5 and 204 parts, corresponding to 6 October 3761 BCE in the Julian calendar, and is designated “BaHaRaD” בהר״ד.
3. Intercalation: the leap years are the 3rd, 6th, 8th, 11th, 14th, 17th and 19th of each 19-year cycle. In a leap year “Adar I” (30 days) is added before Adar, and Adar becomes “Adar II.”
4. The New Year (1 Tishrei) falls on the day of the molad of Tishrei, unless one of the four “postponements” requires it to be delayed by one or two days (next section).
5. Month lengths are fixed and alternate (30 then 29), except Heshvan and Kislev: they are 29 and 29 in a “deficient” year, 29 and 30 in a “regular” year, and 30 and 30 in a “complete” year, so the year’s length can accommodate what the postponements impose. This produces 14 possible year types by length and the weekday of the New Year.

The four postponements of the New Year

That is why the Hebrew New Year falls only on Monday, Tuesday, Thursday or Saturday, and Passover (15 Nisan) only on Sunday, Tuesday, Thursday or Saturday.

Months and festivals

The civil year begins with Tishrei, while the Bible counts Nisan as the first month; so Nisan is numbered 1 in the reckoning, and the year number changes on 1 Tishrei. These are the months in the order of the year:

Computed examples

Festivals begin on the evening before their date, because the Hebrew day begins at sunset.

Counting the years

• From the Creation לבריאת העולם: years are counted from the date of creation computed from the ages of the generations in the Torah; its epoch is the year in which the “molad of Tohu” falls (autumn 3761 BCE). This count has prevailed since the 11th century.
• The “Era of Contracts” מניין שטרות, i.e. the Seleucid era (from 312/311 BCE): used by Jews in Iraq and Palestine from the 1st to the 10th century CE, it survived in the East into the 16th century and among Yemenite Jews into the 19th.
• Writing in letters: the year is written with Hebrew letters that have numerical values, usually omitting the thousands: 5787 is written תשפ״ז (400 + 300 + 80 + 7).
• Approximate conversion: add 3760 to the Gregorian year from January until the Hebrew New Year, and 3761 from the New Year to the end of December.

History: from sighting the crescent to fixed calculation

1. Biblical era

   Numbered lunar months

   The Torah mostly names the months by number, makes “the month of Aviv” (the month of ripening ears) the first of the months (Exodus 12:2 and 13:4), and names three other months with names thought to be Canaanite: Ziv, Ethanim and Bul (1 Kings 6:1, 6:38 and 8:2).

2. 6th c. BCE

   The Babylonian exile: the Babylonian names

   In exile the Jews adopted the Babylonian month names — Nisan, Iyar, Tammuz, Av, Elul, Tishrei, Adar and others — which have remained the names of the calendar to the present.

3. Second Temple

   An observational calendar, and rival calendars

   The first of the month was proclaimed on sighting the crescent, and intercalation decided by the state of the crops. Some groups knew a solar calendar of 364 days, as in the Book of Jubilees and the Qumran scrolls.

4. 1st–3rd c. CE

   The Mishnah: witnesses and the Sanhedrin

   The Mishnah and Tosefta describe the proclamation of the month: two witnesses testify before the court that they saw the crescent, and the court proclaims the “sanctification of the month,” then people are informed by beacons and messengers. Intercalation was decided if two of three reasons concurred — late ripening of the barley (aviv), late fruit on the trees, and a late equinox — not for one reason alone. It is related that Gamaliel II (c. 100 CE) showed witnesses pictures of the moon’s phases and compared their testimony with calculation.

5. c. 359 CE

   The tradition of Hillel II

   Hai Gaon (d. 1038) relates that Hillel II issued the fixed calendar “in the year 670 of the Seleucid era” (358/359 CE), so that Jews in the diaspora could do without the court’s proclamation. Historians, however, hold that the rules formed gradually between the 1st and 10th centuries: two dates from the 6th and 8th centuries do not agree with the current rules, and the rules for the New Year reached their final form between 629 and 648.

6. c. 823 CE

   Al-Khwarizmi’s treatise

   Muhammad ibn Musa al-Khwarizmi wrote a treatise on the Jewish calendar: the nineteen-year intercalation cycle, the weekday of the New Year, the computation of the mean positions of the sun and moon, and a worked example for 823/824. It is one of the oldest dated descriptions of the calendar in a form close to its present one.

7. 921–922 CE

   The dispute of Saadia Gaon and Ben Meir

   Aaron ben Meir, head of the academy in Palestine, claimed that the “molad zaken” limit falls 642 parts (about 35 minutes) after noon, so Passover in 922 would have fallen on Sunday for his followers and Tuesday for others. Saadia Gaon answered him in the “Book of Seasons,” supported by the Babylonian academies, and the accepted rule prevailed and a split was averted.

8. 11th c. CE

   Counting from the Creation

   The count from the Creation became the prevailing one, replacing the Seleucid “Era of Contracts.”

9. 1178 CE

   Maimonides: “Laws of the Sanctification of the New Month”

   Maimonides recorded the full rules of the calendar in the Mishneh Torah: the molad, intercalation, the postponements and the year lengths, with an astronomical method for computing the visibility of the crescent; he took as the starting point of his reckoning 3 Nisan of the year 4938 of the Creation (22 March 1178). These rules are in use unchanged to the present.

10. 1948 CE

    The State of Israel

    The Hebrew calendar became one of the state’s two official calendars alongside the Gregorian: public holidays are set by it — such as Independence Day on 5 Iyar — it is written in documents and accepted on cheques.

Drift from the seasons

The mean year of this calendar is 365.2468 days (235 mean months in every 19 years), while the tropical year is 365.2422 days; so the Hebrew year is about 7 minutes longer, one whole day in about 216 years. That is why Passover slowly falls later relative to the spring equinox: its earliest possible date has moved about eight days since the 4th century, so 15 Nisan no longer falls before 26 March, and in about 20% of years it falls a month later than the “after the equinox” rule requires. If the rules stayed as they are, Passover would reach the summer solstice around the year 16652 of the Creation (12892 CE).

The Hebrew calendar shares with The Creator's Calendar the fact that it is lunisolar and adds a month to stay in its seasons; but it adds it by a fixed cycle and a mean month, so it drifts slowly from the seasons, while The Creator's Calendar inserts Al-Nasi according to the actual season from the true new moons.

Current use

• Religious observance: it sets the festivals, fasts, special Sabbaths and Torah readings, the anniversary of a death (“yahrzeit”) and coming of age.
• Israel: an official calendar alongside the Gregorian; both dates are written together in newspapers and documents.
• The Karaites: a Jewish community that does not accept the arithmetical calendar; they begin their months by sighting the crescent in the Land of Israel, intercalate the year according to the ripening of the barley (aviv), and do not apply the four postponements; so their calendar is sometimes a month ahead of the arithmetical one.

The Hebrew calendar on this site

• It is computed by the fixed arithmetical rules as published by Reingold and Dershowitz (which Hebcal implements), and it matched an independent library on every third day from year 1 to 3001, and in the length of every year. As noted above, the computation requires the New Year to fall on Monday, Tuesday, Thursday or Saturday.
• Dates before the rules settled (4th to 10th centuries) are an arithmetical extrapolation, not what the court proclaimed by sighting at the time.
• The civil day is converted; what falls after sunset belongs, by Jewish custom, to the next Hebrew date.
• The Hebrew birthday is computed by the accepted rule (Shulchan Aruch, Orach Chayim 55): someone born in Adar of a common year or in Adar II celebrates in the last month of the year, and someone born on the 30th of a month that has 29 days celebrates on the first of the next month.

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