15.5.78.6 Hebrew Calendar

The Hebrew calendar is a lunisolar calendar. Its current rules were pronounced in the 4th century C.E. by Patriarch Hillel II. New days start at sunset, new months start at a New Moon, and new years start in the northern hemisphere spring.

a Hebrew calendar year has 12 or 13 months, that each have 29 or 30 days. The month names and lengths in days are listed in the following table. Biblical tradition lists Nisan as the first month but has the new year start on the first day of Tishri. The calendar function counts months from the start of the year in Tishri. The month numbers, names, and lengths (in days) are listed in the following table

Number  Month Name    Length
  1          Nisan      30
  2          Iyyar      29
  3          Sivan      30
  4         Tammuz      29
  5             Av      30
  6           Elul      29
  7         Tishri      30
  8        Heshvan   29 or 30
  9         Kislev   29 or 30
 10          Tevet      29
 11         Shevat      30
 12         Adar Ⅰ      30 (only present in leap years)
12/13     Adar (Ⅱ)      29

Leap days may be inserted at the ends of the months of Heshvan and Kislev, and a leap month Adar Ⅰ may be inserted just before month Adar, which in that case is renamed to Adar Ⅱ. This means that any given year may contain six different numbers of days, as listed in the following table

  Days     Designation
   353     deficient ordinary year
   354     regular ordinary year
   355     complete ordinary year
   383     deficient leap year
   384     regular leap year
   385     complete leap year

There are 7 leap years in a fixed cycle of 19 years.

The epoch of the Hebrew calendar is sunset of 6 October -3760 C.E., which was taken to be the date of the creation of the world. The Era of the Hebrew calendar is referred to as A.M. (= Anno Mundi). The first noon after the epoch was the noon of 7 October -3760 C.E., so the calendar function equates 1 Tishri 1 A.M. with 7 October -3760 C.E.

For transforming from Hebrew calendar dates, years from -5879540 through 5878588 provide accurate results.