The Jewish calendar (Hebrew: ha-luach ha-Ivri) is the lunisolar dating system traditionally used by Jewish communities to determine the dates of holy days, Torah readings, agricultural cycles referenced in Jewish law, and the count of years since a fixed creation epoch. It combines a lunar month, beginning approximately at the new moon, with periodic intercalation (the insertion of a thirteenth month) to keep its months aligned with the solar year and its associated seasons. Some aspects of the calendar's underlying astronomical and historical claims are contested; see Heliocentrism - Jewish Astronomy Viewpoint for one such dispute.

The calendar in present use is a fixed, calculated system rather than one based on direct observation. Months are reckoned by a mathematical formula (the molad, or mean lunar conjunction) rather than by sighting the new moon, and a predetermined 19-year cycle (the Metonic-style cycle attributed in rabbinic tradition to Hillel II in the 4th century CE) designates seven of every nineteen years as leap years, each receiving an additional month (Adar I). The calendar's epoch begins with year 1 corresponding to 3761/3760 BCE, a date derived from rabbinic chronological calculation rather than astronomical or archaeological dating, and the relationship between this calculated epoch and conventional historical or scientific chronology is a matter of ongoing discussion among traditional and academic scholars alike.

The transition from an observation-based calendar - in which the Sanhedrin received and evaluated witness testimony about the sighting of the new moon each month, and announced leap years by similar deliberation - to the fixed, calculated calendar is treated in more detail at jewish-calendar-history. The medieval scholar Nachmanides (Ramban) is among the rabbinic authorities who wrote on the astronomical underpinnings of the calendar and on the authority by which it was fixed; his views, and those of other commentators, are discussed further in the Viewpoints section below and at jewish-calendar-history.

Contemporary use of the calendar is essentially uniform among observant Jewish communities for the purpose of setting the dates of holidays and the new month (Rosh Chodesh), though communities differ on certain dependent calculations, such as the precise timing used for the start and end of the Sabbath and holidays in different geographic locations.

• Continuity viewpoint - holds that the fixed calendrical system instituted in the talmudic period preserves an unbroken chain of authority and calculation traceable to the Sanhedrin and ultimately to Mosaic tradition, such that the modern calendar's molad and leap-year cycle are not an innovation but a formalization of a process that had operated, in substance, since antiquity. See jewish-calendar-continuity-viewpoint.
• Calculated-innovation viewpoint - holds that the shift from observation-based proclamation by the Sanhedrin to a fixed mathematical formula represented a substantive change in method necessitated by the dispersion of Jewish communities and the loss of a functioning Sanhedrin, rather than a mere formalization of prior practice. See jewish-calendar-calculated-innovation-viewpoint.
• Astronomical-accommodation viewpoint - associated with commentators including Nachmanides, this viewpoint holds that the calendar's underlying astronomical assumptions should be understood, and where necessary reconciled, in light of contemporaneous and later astronomical knowledge, including geocentric and heliocentric models discussed elsewhere on this wiki. See jewish-calendar-astronomical-accommodation-viewpoint and Heliocentrism - Jewish Astronomy Viewpoint.
• Restoration viewpoint - held by a minority of modern authorities and some segments of religious-Zionist thought, this viewpoint holds that a reconstituted Sanhedrin could, and in some interpretations should, resume authority over the calendar, including the calculation of leap years and months, rather than perpetuating reliance on the fixed calendar indefinitely. See jewish-calendar-restoration-viewpoint.

• Fixed versus observed calendar - whether the talmudic-era shift to a fixed, calculated calendar was a legitimate and binding exercise of rabbinic authority or a permanent departure from a Sanhedrin-based observational process remains disputed among traditional and academic scholars. See jewish-calendar-fixed-versus-observed-debate.

• jewish-calendar-history
• jewish-calendar-continuity-viewpoint
• jewish-calendar-calculated-innovation-viewpoint
• jewish-calendar-astronomical-accommodation-viewpoint
• jewish-calendar-restoration-viewpoint
• jewish-calendar-fixed-versus-observed-debate
• Heliocentrism - Jewish Astronomy Viewpoint

1. Sacha Stern, Calendar and Community: A History of the Jewish Calendar, Second Century BCE - Tenth Century CE (Oxford: Oxford University Press, 2001).
2. Nachum Dershowitz and Edward M. Reingold, Calendrical Calculations, 4th ed. (Cambridge: Cambridge University Press, 2018).
3. Maimonides, Mishneh Torah, “Hilkhot Kiddush HaChodesh” (Laws of the Sanctification of the New Month).
4. Nachmanides, commentary on Exodus 12:2, in Ramban (Nachman) on the Torah: Exodus, trans. Charles B. Chavel (New York: Shilo, 1973).