The Jewish calendar is based on both the lunar and the solar cycles and is used for computing Jewish holidays. Hebrew days begin at sunset when three stars are visible. An ordinary year has 12 months, and a leap year has 13 months. Every month starts approximately on the day of a new moon. There are three year lengths for ordinary years and three for leap years.

In a regular year, months alternate between 29 and 30 days.

The Jewish New Year starts on 1 Tishri, called Rosh Hashana, which celebrates the creation of the world (assumed to be 3761 BC). There is a rather complicated set of 5 rules for determining the date of Rosh Hashana. A formula for computing Rosh Hashana is given by Berlekamp et al. (1982), and a Lisp program for computing the Jewish calendar by Reingold and Dershowitz (1989).