Jewish Leap Year Calculator

Hebrew Calendar Leap Year Formula:

\[ \text{Leap Year} = \begin{cases} \text{true} & \text{if } (7 \times \text{year} + 1) \mod 19 < 7 \\ \text{false} & \text{otherwise} \end{cases} \]

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1. What is a Jewish Leap Year?

In the Hebrew calendar, a leap year occurs 7 times in a 19-year cycle (years 3, 6, 8, 11, 14, 17, and 19). These years have an extra month (Adar I) added to synchronize the lunar calendar with the solar year.

2. How Does the Calculator Work?

The calculator uses the Hebrew calendar leap year formula:

\[ \text{Leap Year} = \begin{cases} \text{true} & \text{if } (7 \times \text{year} + 1) \mod 19 < 7 \\ \text{false} & \text{otherwise} \end{cases} \]

Where:

\( year \) — Hebrew calendar year
\( \mod \) — Modulo operation (remainder after division)

Explanation: The formula checks the position of the year within the 19-year Metonic cycle to determine if it's a leap year.

3. Importance of Leap Years

Details: Leap years ensure that Jewish holidays occur in their proper seasons. Without them, holidays would drift about 11 days earlier each solar year.

4. Using the Calculator

Tips: Enter any valid Hebrew year (1 and above). The calculator will determine if it's a leap year (13 months) or common year (12 months).

5. Frequently Asked Questions (FAQ)

Q1: How often do leap years occur?
A: 7 times in a 19-year cycle, approximately every 2-3 years.

Q2: What's the extra month called?
A: Adar I is added before the regular Adar (which becomes Adar II in leap years).

Q3: When was this cycle established?
A: The 19-year cycle (Metonic cycle) was adopted by Hillel II in the 4th century CE.

Q4: Do leap years affect holiday dates?
A: Yes, Purim and Passover dates are affected by the leap year adjustment.

Q5: Can I convert Gregorian years?
A: This calculator uses Hebrew years. For Gregorian conversion, add 3760/3761 to get approximate Hebrew year.