The Jewish Calendar: It’s Complicated

By Jonathan Berkowitz


According to the old joke, early and late are the only two words needed to tell Jewish time, as in, “The holidays sure are early/late this year.” The Jewish calendar can be described in one word: “complicated.” A two-word description would be: “very complicated.” There are uniquely Jewish definitions of a day, its hours, the months, and the year. The Jewish year features a regular cycle of holidays. A full explanation of the intricacies of the history, evolution, and operation of the calendar would fill a book, and indeed, such books have been written. I will endeavour here to introduce you just to the basic principles and share the highlights of how our calendar works.


We’ll begin with the Jewish Calendar Year, which starts on Rosh Hashanah, the “head of the year.” By rabbinical tradition, it commemorates the day when Adam and Eve were created. The year marks how long since the year of creation. To find the corresponding Jewish year for any year on the Gregorian calendar, add 3760 to the Gregorian number, if it is before Rosh Hashanah, or 3761 if it is after Rosh Hashanah.


The length of a Jewish year is not fixed. A standard one has 354 days, comprising six months with twenty-nine days and six with thirty days. Our months follow the lunar orbit (*), which is approximately 29.5 days (12 x 29.5 = 354). But the year could also be 353 or 355 days, or when it is a leap year, 30 days longer (383, 384, or 385 days).


The variation of one day either way from 354 is because the months of Heshvan and Kislev can be both thirty days, both twenty-nine days, or one of each. That prevents certain holidays—Rosh Hashanah and Yom Kippur in particular—from falling on certain days of the week. We’ll discuss this later. The reason for leap years is that, although the months follow the lunar cycle, the lunar months need to align with the seasons of the year, which are based on the solar year, so that the biblical agricultural festivals—Passover, Shavuot, and Sukkot—occur in the proper seasons. This is mandated in the Torah, “Guard the month of the spring, and make [then] the Passover offering.”


In other words, the Jewish calendar is “lunisolar” – a combination of the solar year and the lunar year. This leads to a discrepancy. The solar year has 365 days, 11 more than the lunar year. The difference was resolved by periodically adding a thirteenth month about once every two or three years, what we call a leap year. Without this adjustment Passover would be about 11 days earlier each year, drifting into winter, then fall and summer, and back to spring. The extra month is added after the last month of the standard calendar (remember that Nisan is the first month), so on a leap year—called a pregnant year in Hebrew (shanah meuberet)—we have Adar I and Adar II.


We’re getting ahead of ourselves. Let’s dig a little deeper and look at the problem mathematically. The solar year is 365.24 days (which is why the Gregorian calendar adds one day—February 29—every four years), while the lunar year is 354.37 days. The lunar cycle is 29.53 days in length. The calendar year must have a whole number of months; it can’t have half a month. It must also have a whole number of days, as must each calendar month. A month can’t be twenty-nine and a half days; but as long as the average number of days per month is 29.5, a month of either 29 or 30 days will work. Months of 31 days are not allowed. For religious reasons, the first day of Rosh Hashanah, the first of Tishrei, cannot be on a Sunday, Wednesday, or Friday. And don’t forget that weeks run independently of the monthly and yearly cycles, and a year doesn’t need to have a whole number of weeks, just as the Gregorian calendar year has 52 weeks plus a day or two.


There is a curious pattern between the lunar and solar years that makes a reconciliation possible. The number of days in nineteen solar years equals the number of days in 235 lunar cycles. This nineteen-year period governs the big picture of the Jewish calendar. It explains why we have 12 standard years of 12 months and 7 leap years of 13 months in each period of nineteen years. The years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years.


A Hebrew mnemonic helps in remembering this sequence: GUCHADZaT גוחאדז״ט, where the Hebrew letters gimel-vav-het-aleph-dalet-zayin-tet are used as Hebrew numerals equivalent to 3, 6, 8, 1, 4, 7, 9. (**) Another curiosity is that this cycle is the basis of the Christian ecclesiastical calendar, used to compute the date of Easter each year. That’s why Easter is not on a fixed date in the Gregorian calendar, as Christmas is. To figure out where in the 19-year cycle a year is in, divide the Jewish year by 19 and find the remainder. A remainder of 0 means it is year 19. For example, as we approach the Jewish year 5784, dividing by 19 gives a reminder of 8, so we will enter year 8 of the cycle, which means it will be a leap year.


If you want to show off, you can explain that this pattern is called the Metonic cycle after the fifth century BCE Meton of Athens. If you really want to show off, call the pattern the enneadecaeteris (from Ancient Greek for nineteen). It is remarkably accurate, and, in fact, is the most accurate cycle of time less than 100 years for synchronizing the solar year and the lunar month, whereby a thirteenth lunar month is inserted—the fancier term is intercalated—into a calendar year from time to time. (Three ancient civilizations—Babylonia, China, and Israel—used lunisolar calendars and knew about intercalation from as early as 2000 BCE.)


Is the system perfect? No. No system is. In the Gregorian calendar, adding a day every four years is slightly more than is needed. Generally, a year divisible by four is a leap year, but years ending in two zeroes need to be divisible by 400 (1900 was not a leap year, but 2000 was).


The Metonic cycle of 235 lunar cycles is about two hours longer than 19 solar years (2 hours, 4 minutes and 58 seconds to be more precise). For readers who delight in decimal places, the solar year is 365.2422 days, which is 6,939.602 days every 19 years; the lunar month is 29.53059 days, which is 6,939.689 days every 235 months. Using a whole number of days—6,940, as Meton did—allows for construction of a lunisolar calendar. Don’t worry about the drift of the Jewish calendar in relation to the Gregorian calendar. It will take more than 200 years for the Jewish calendar to be out of sync with the Gregorian calendar by a day.


How did our calendar develop? Originally based on agricultural events, it then shifted gradually to use astronomical data, observation of the moon, and mathematical rules. There was no set calendar when the Sanhedrin (Rabbinical Supreme Court) presided in Jerusalem before the destruction of the Second Temple. Each year they checked the date of the spring equinox. If it fell in the second half of Nisan, the year was declared a leap year. However, that wasn’t the only consideration. If the barley (needed for the omer) had not yet ripened or if the weather was bad enough to hinder travel to Jerusalem for Passover that also triggered the declaration of a leap year. In the fourth century CE, a fixed calendar was finally instituted, based on the Sanhedrin’s methods. That calendar is essentially how new moons and festivals are calculated and celebrated today.


Multiple traditions exist about who created the modern fixed calendar, and why. One posits that it was done by Hillel II, a sage of the fifth generation in Israel and Nasi (chief presiding officer) of the Sanhedrin between 320 and 385 CE. (He is often confused with the better-known Hillel the Elder.) In this tradition, Hillel is also credited with sanctifying Rosh Hodesh. Another tradition contends that the calendar was fixed in response to persecution and oppression that threatened the continued existence of the Sanhedrin. However, both traditions have been questioned.


Maimonides presented a full calendar codification in his twelfth century Mishneh Torah. His work also replaced the counting of years since the destruction of the Temple, with years since creation according to the Genesis story. It is his rules that today are generally used by Jewish communities throughout the world. A little-known fact is that, according to rabbinic reckoning, the beginning of “year 1” is not creation, but about one year before creation.


Back to the present, and the details of the months. Nine months of the year have a fixed number of days, while three are variable: Nisan, Sivan, Av, Tishrei, and Shevat each have 30 days; Iyar, Tammuz, Elul, and Tevet each have 29. Adar has 29 days in a standard year but Adar I has 30 days in a leap year. Heshvan and Kislev have 29 or 30 days. If both are 29 days, the year is deficient or incomplete; if both are 30 days, the year is complete, perfect, or abundant; or if Heshvan has 29 and Kislev has 30, the year is regular or in-order. During leap years Adar I (or Adar Aleph) is added before the regular Adar. In fact, Adar I is considered to be the extra month and has 30 days. Adar II (or Adar Bet) is the “real” Adar and has the usual 29 days. This is why holidays such as Purim are observed in Adar II, not Adar I.


The lengths of Heshvan and Kislev vary because of the so-called Rosh Hashanah postponement rules. The first day of Rosh Hashanah (the first day of Tishrei) can only fall on Monday, Tuesday, Thursday, or Shabbat—the four days are known as the “four gates”. This requirement supersedes a date computed only from the relative positions of the moon, sun, and earth. That, in turn, guarantees that Yom Kippur will not fall on a Friday or Sunday, which would result in two consecutive days when fasting and burying the dead is prohibited. It also ensures that Hoshana Rabbah will not occur on Shabbat, which would interfere with certain customs (such as carrying willows) on this day.


These rules mean there are exactly fourteen different patterns that the Hebrew calendar years may take, distinguished by the length of the year and the day of the week on which Rosh Hashanah falls. The pattern can repeat itself several times in a few years, and then not recur for a long time.


The Jewish calendar is complicated, but also extremely accurate and remarkably precise. So, the next time someone comments about the date of the next Rosh Hashanah, and says it is early (or late) this year, you should respond by saying, “On the contrary, the holidays are exactly on time!”




(*) To be completely accurate in terminology, the lunar cycle in the Jewish calendar is called a synodic month—not to be confused with the sidereal month, the time required for one full orbit of the moon around the earth. The synodic month is longer; after completing its orbit, the moon must travel a little farther to the new position of the earth with respect to the sun.)


(**) There is also a musical mnemonic. The intervals of the major scale, follow the same pattern as the leap years, with do corresponding to year 19 (or 0): a whole tone in the scale corresponds to two standard years between consecutive leap years, and a half tone to one standard year between two leap years. So, counting the tonic as 0, the notes of the major scale divided into 19 intervals of equal temperament, are numbers 0 (or 19), 3, 6, 8, 11, 14, 17, the same numbers as the leap years!