Unlike the leap year in the Gregorian calendar, which is limited to adding one day at the end of February to compensate for imprecise astronomical and mathematical delineations of time in human calendars, the Jewish leap year has an interesting variation of a whole extra month added. The Jewish calendar tends to be known for its accuracy compared to other calendars.

Where did this concept originate from?

Judaism started with a lunar calendar because of a commandment to track new moons and keep a lunar calendar as specified in Exodus 12:2. The rabbis determined in their studies that a new day was to begin at sundown and desired to keep a seven-day week as outlined in the story of creation. From there, the rabbis extrapolated a seven-day week based on mathematical calculations that likely originated in ancient Babylonia, as many of the greatest astronomers, mathematicians, and philosophers of the time hailed from Babylonia and were educated in its institutions.

Because calendars will round off days, weeks, months, and years for consistency and ease to the average person based on different astronomical cycles and natural occurrences, the need to periodically correct the calendars exists so that seasons and dates do not deviate significantly over time. This is especially true when Judaism aims to bless certain months and observe particular holidays during certain times of the year based on historical, traditional, religious, and/or agricultural reasons. Thus, the occasional addition or subtraction of days or months helps keep such things as the seasonally sensitive holidays on track over the grand scheme of time.

As a result, in the Jewish leap year, there are 13 months rather than 12 in the typical non-leap year in the Hebrew calendar. The additional month in leap years is added after Shevat but before Adar, and thus termed Adar I (or Adar Rishon), whereas the standard Adar then becomes Adar II. In a typical twelve-month cycle, Shevat would merely precede Adar, which is often considered a “lucky” and “happy” month in Jewish traditions.

Judaism desires to maintain Passover in the springtime based on upholding the Torah command, "Guard the month of the spring, and make [then] the Passover offering,” and not having Passover drift off to some other season by failing to adjust the calendar. The spring equinox therefore was of great importance in maintaining the beating drum of time in a calendar format; Israel did not want to have Nissan occurring without observing springtime flowers blossoming throughout the country, the barley maturing for soon harvest, and the trees budding with their springtime fruits.

Furthermore, one did not want rainy conditions and washed-out roads to impede pilgrimages to Jerusalem for the Passover. There needed to be some allotted time for workers to clean up any roads or bridges if needed after the winter rains. Nor would celebrating Passover in the middle of the summer, for instance, be acceptable. Therefore, a leap year to keep Nissan aligned with visible, tangible springtime conditions was of utmost importance in deciding when to implement a thirteenth month.

Maintaining the seasonality of Shavuot and Sukkot is also scripturally important, as those are based on agricultural harvests and cannot occur in potentially any of the seasons if the calendar were left to its own devices and not periodically corrected. Sukkot in late spring or Shavuot silhouetted against a backdrop of autumn leaves, for instance, would simply not uphold the integrity or spirit of the holidays.

The lunar-based Hebrew calendar, in which months begin on the day of a crescent moon after a new moon phase, makes adjustments in an attempt to remain aligned with other solar-based calendars, given that 12 lunar months of approximately 29.5 days each correspond to 354 days, which obviously does not perfectly align with the 365.25 days found in solar-based astronomical calendars.

Such a phenomenon as a Jewish leap year will occur a total of seven times with the 19-year “metonic” cycle, specifically years 3, 6, 8, 11, 14, 17, and 19 of the cycle. For the years for which Adar II is inserted into the calendar, the year is referred to as Shanah Me’uberet, or the pregnant year or enlarged year, due to its “enlarged” time duration compared to non-leap years.

Nineteen solar years are believed to have the same duration of time as 235 lunar months; both expressions of time equate to a duration of 6,940 days, with a slight statistically insignificant difference of a few hours that is seemingly impossible to mathematically rectify. The goal of this exercise is to sync the solar and lunar years. The math has been amazingly perfected so the Jewish calendar ultimately differs from the solar calendar by a grand total of one day every 216 years.

Thus, arguably, the Jewish calendar is a combination of a lunar and solar calendar, given that the months are based on the lunar cycle, but the 19 years are based on a solar cycle. The Jewish calendar is therefore not purely a lunar calendar.

However, other minor adjustments must be made to the calendar to prevent such holidays as Rosh Hashanah from falling on certain days of the week. These minor adjustments are made to the Jewish calendar, whether it is a leap year or not. Therefore, a day might be added to Cheshvan, the eighth month, or subtracted from Kislev, the ninth month.

These possible deviations can result in a Jewish calendar having upwards of six different possible lengths, depending on the adjustments made for the Jewish holidays. In other words, a non-leap year could potentially be 353, 354, or 355 days long, and a Jewish leap year could potentially be 383, 384, or 385 days long. Terminology is assigned to describe the differing lengths of year as deficient (cheserah, referring to 353 or 383 days), regular (kesidrah, referring to 354 of 384 days), or complete (referring to 355 or 385 days).

For the sake of consistency, Purim is consistently celebrated during Adar II during Jewish leap years so as to remain consistent one month prior to Passover. Leap years also have implications for Israeli rental agreements. Year-long rental agreements accommodate the 13th month, if applicable, without extra charge compared to a 12-month year, whereas month-to-month rental contracts, however, require separate payment for the additional month. Thus, renters are generally better served with year-long leases in which their annual rent is unaffected by the leap year.

The concept of a leap year was originally decided by the Sanhedrin; some sages were appointed to discuss the matter of a leap year in a subcommittee essentially, while other sages or judges would join the conversation later in the process to offer additional input into the matter, and then two more sages or judges would join at the end of the conversation prior to the declaration of the calendar for the upcoming year and whether a leap year was to be implemented the following year.

Originally the sages had to get involved in maintaining the integrity of the Jewish calendar because some renegade troublemakers, in a desire to confuse and mislead the Jewish people, intentionally lit fire signals at the wrong times, which made it difficult to accurately determine the new moon. Thus, Rabbi Judah, who was leading the Sanhedrin at the time, decided to eliminate the use of fire signals as a way of determining the new moons and instead attempted to hire messengers who would ride around between towns, announcing the new moon to the townspeople. This was not a very viable method in the long term when it involved walking, riding camels, or other inefficient forms of transportation, and it took so long to get from town to town.

However, Hillel II determined in the 4th century that the matter of determining leap years was best not in the hands of the court, as the Sanhedrin and similar high courts seemed to have limited viability; Hillel II anticipated their dissolution and/or disbandment of such an entity with the changing times. Plus, it was cumbersome and unnecessary for the Sanhedrin to convene each year to establish the upcoming year’s calendar when mathematical extrapolations could establish the calendar without having to meet annually to decide the matter.

Thus, the court he was part of established the nineteen-year cycle to set a permanent calendar that did not need intervention by the Sanhedrin or any other court or governmental body. Calculations were used to determine the months and festivals to eliminate troublemakers from trying to manipulate the system and mislead the Jewish people and to avoid the need for people to travel from town to town to announce the new moon.

The mathematical calculations that go into determining each year’s length are known as sod ha’ibur (literally, "the secret of calendar intercalation"); Maimonides claims this math is not complicated at all, though some of us may disagree with that assessment. As Maimonides once wrote, “the method of the fixed calendar is one which an average school child can master in 3 or 4 days” (Hilkhot Qiddush HaHodesh 11:4).

The sages are known to say, “When Adar enters, we increase in joy.” If this is the case, what a beautiful blessing to have an occasional year with two Adars—Adar I and Adar II.

From all of us at the Shalom Learning Center, may that time and all the months of the year be a blessing and a joy to all of you.