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Why does the number of days in a Jewish calendar year vary?

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Circular diagram of the Jewish religious year showing Hebrew months around the outer ring and Gregorian months inside, with major holidays and fasts such as Rosh Hashanah, Yom Kippur, Sukkot, Hanukkah, Passover, and Purim labeled with their dates. — Jewish religious year The months and holidays of the Jewish religious year.

The number of days in a Jewish calendar year varies because it is a lunisolar system that must reconcile lunar months with the solar year to ensure festivals occur in their proper seasons.1

The calendar relies on a schematic structure that only counts complete days, avoiding fractional figures. Common years consist of 12 months and contain 353, 354, or 355 days, while leap years include an additional 30-day month (First Adar) and contain 383, 384, or 385 days.12

Variations in the number of days occur for several reasons:
* Month Lengths: While most months have a fixed length, the months of Ḥeshvan and Kislev vary between 29 and 30 days, resulting in "defective," "normal," or "complete" years.2
* Calendar Rules: The start of the year is often delayed by one or two days—a practice known as deḥiyyot—to prevent certain holidays, such as Yom Kippur, from falling on specific days of the week that would conflict with religious observances.2
* Intercalation: To keep the lunar calendar aligned with the solar year, a 13th month is added seven times during every 19-year Metonic cycle.12