About the Hebrew calendar
The Hebrew calendar is lunisolar: its months follow the moon (29 or 30 days), while a thirteenth month keeps the year in step with the seasons. In a 19-year cycle, seven years (the 3rd, 6th, 8th, 11th, 14th, 17th and 19th) are leap years in which Adar is doubled into Adar I and Adar II. The year number changes on 1 Tishrei (Rosh Hashanah), and years are counted from creation according to Jewish tradition: 5787 began on 12 September 2026.
The month starts are not observed but calculated from the mean conjunction (the molad), with postponement rules that keep Rosh Hashanah off Sunday, Wednesday and Friday. A year therefore has 353, 354 or 355 days — 383, 384 or 385 in a leap year — called deficient, regular or complete according to the lengths of Cheshvan and Kislev.
This converter applies these fixed arithmetic rules (as published by Reingold and Dershowitz in Calendrical Calculations). They have been in use for over a thousand years; earlier dates are computed by extending the same rules backwards. The Hebrew day begins at sunset, so an event after sunset belongs to the next Hebrew date.
Like The Creator's Calendar, the Hebrew calendar keeps its lunar months in their seasons by adding a month — but by a fixed 19-year cycle, whereas The Creator's Calendar inserts Al-Nasi according to the actual season.
For details: The Hebrew calendar — its history from sighting the crescent to fixed calculation, its rules, and the New Year postponements.