Hillel II instituted a permanent calendar based on mathematical and astronomical calculations in 358, removing the necessity for eyewitness observations of the new moon, which marks the start of a new month.
- Due to uncertainty about the timing of the new moon, ancient law mandated that people living outside of Israel celebrate two days instead of one for each holiday, with the exception of Yom Kippur, the Day of Atonement.
- This tradition had to be kept even after the calendar was created, according to the Talmud.
- The Jewish period starts with the creation of the world, which is generally dated at 3761 B.C. Hillel's calendar has remained mostly unaltered since the eleventh century, with very minor changes.
- A day is measured from sunset to sunset, a week is seven days long, a month is either twenty-nine or thirty days long, and a year is made up of twelve lunar months plus about eleven days, or 353, 354, or 355 days.
- A thirteenth month of thirty days is intercalated in the third, sixth, eighth, eleventh, fourteenth, seventeenth, and nineteenth years of a nineteen-year cycle to reconcile the calendar with the yearly solar cycle; a leap year may have from 383 to 385 days.
- The civil calendar starts with Tishri, whose first day is Rosh Hashanah, the Jewish New Year. On Nisan 15, Passover, the religious calendar cycle starts (Pesach).
- The Babylonians provided the names for the months of the Jewish calendar.
The months are generally referred to in numerical sequence in the preexilic books of the Bible, starting with Tishri, although there are four months recorded with other names:
Nisan/Abib, Iyyar/Ziv, Tishri/Ethanim, and Heshvan/Bul: Nisan/Abib, Iyyar/Ziv, Tishri/Ethanim, and Heshvan/Bul:
- Nisan is from the middle of March until the middle of April.
- Iyyar: from the middle of April until the middle of May
- Sivan is from the middle of May until the middle of June.
- Tammuz is from the middle of June until the middle of July.
- Av: mid-July to the middle of August
- Elul is from the middle of August until the middle of September.
- Tishri is from the middle of September until the middle of October.
- Heshvan is from the middle of October until the middle of November.
- Kislev is from the middle of November until the middle of December.
- Tevet is from the middle of December until the middle of January.
- Shevat is from the middle of January until the middle of February.
- Adar: from the middle of February until the middle of March
As required, the intercalary month of Adar II is added before Adar.
You may also want to learn more about Global Calendar Systems here.