Israel Science and Technology Directory

Jewish studies

Hebrew Calendar

The Hebrew calendar is based on both the lunar and the solar cycles (lunisolar calendar). Months are measured by one revolution of the moon around the earth. According to the Talmud, one complete revolution of the moon around the earth takes 29.53059 days (Masechet Rosh Hashana). This value is very close to the average value measured by NASA: 29.530588. Since the average value is about 29.5 days, months alternate between 29 and 30 days in the Hebrew calendar (see Table below).

The common year in the Hebrew calendar includes 12 months. But there is a difference of about 11 days between 12 lunar cycles and one solar cycle. One complete rotation of the earth around the sun takes 365.25 days. Within a one-year period, 12 lunar cycles are completed in 12 × 29.53059 = 354.36708 days. Therefore the difference between 12 lunar cycles and one solar cycle is precisely 365.25 − 354.36708 = 10.88292 days.

To synchronize the lunar counting of days with the solar cycle, every 19 years a leap year is added wherein the month of Adar is replaced by two months, Adar Alef and Adar Beit ('אדר א' ואדר ב). Thus, a leap year in the Hebrew calendar includes 13 months.

The timing of the leap years is calculated with a periodicity of 19 years. In 19 years, the total difference between the lunar and solar cycles is 19 × 10.88292 = 206.77548 days. This difference amounts to about seven 30 day periods (206.77548 / 7 = 6.892516). The number 19 cannot be divided evenly by 7. So the Hebrew sages decided that leap year will be declared on the following years of a 19 year period: 3, 6, 8, 11, 14, 17, and 19. The addition of seven 30 day months results in a further difference of 3 days (210−207=3) every 19 year cycle. To make up for this difference, 3 days are added on the months of Cheshvan and Kislev at each 19 year period.

The leap year adjustments are not sufficient to prevent continuous drifting of the gap between lunisolar and solar calendars. To halt this drift, Dr. Irv Bromberg has proposed a 353-year cycle composed of 9 repeated 19-year sub-cycles, a sub-cycle truncated to 11 years by omitting 8 years containing 3 leap months, and a further 9 repeated 19-year sub-cycles. Dr. Bromberg has named this proposed revision as the Rectified Hebrew Calendar.

Months of the Hebrew Calendar
MonthNameLeap year monthsDays/MonthחודשCorresponding months
1Tishrei1 Tishrei30תִּשְׁרֵיSept.-Oct.
2Cheshvan2 Cheshvan29/30חֶשְׁוָןOct.-Nov.
3Kislev3 Kislev29/30כִּסְלֵוNov.-Dec.
4Tevet4 Tevet29טֵבֵתDec.-Jan.
5Shevat5 Shevat30שְׁבָטJan.-Feb.
6 Adar Alef30
7 Adar Beit29
7Nissan8 Nissan30נִיסָןMar.-Apr.
8Iyar9 Iyar29אִיָּרApr.-May
9Sivan10 Sivan30סִיוָןMay-June
10Tamuz11 Tamuz29תַּמּוּזJune-July
11Av12 Av30אָבJuly-Aug.
12Elul13 Elul29אֱלוּלAug.-Sept.

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