The Hebrew calendar was adopted from the Babylonians around the time of the [Babylonian exile]?. Previous to that, the Jews used a solar calendar. However, not all Jews accepted this change at the time; Essenes, such as the Qumran? community (authors of the [Dead Sea Scrolls]?) in particular refused to accept the new calendar. However, the opponents of the lunar calendar have long since died out; today all Jews use it.
The Hebrew year 1 started on Monday, September 7, 3761 B.C.. This means that adding 3761 to a Gregorian year number will yield the Hebrew year number (within one year). This actually only works until the gregorian year 22,203, but it's a fairly good rule of thumb.
The Hebrew calendar is tied to the average time taken by the moon to cycle from [lunar conjunction]? to lunar conjunction. The calendar is also tied to a 19 year cycle of 235 lunar months. The average Hebrew year length is 365.2468 days, in contrast to the average tropical solar year which is measured at roughly 365.2422 days. Approximately every 216 years, the Hebrew year is "slower" than the average solar year by a full day. Since the average Gregorian year is 365.2425 days and repeats every 400 years, the average Hebrew year is slower by a day every 231 Gregorian years.
There are exactly 14 different patterns that Hebrew calendar years may take. Each of these patterns is called a "keviyah" (Hebrew for "species"), and is distinguished by the day of the week for [Rosh Hashannah]? of that particular year and by that particular year's length.
A variant of this pattern naming includes another letter which specifies the day of the week for the first day of Pesach (Passover) in the year.
Hebrew time measurement has been strongly influenced by [rabbinic law]?, which divided the hours up into 1080 parts, (a part lasts 3 and 1/3 seconds and each minute has 18 parts). This simplified calculations, as they required only days, hours and parts. The weekdays start with Sunday (day 1) and proceed to Saturday (day 7). Since some calculations use division, a remainder of 0 signifies Saturday. Thus, there are up to 1080 parts per hour, 24 hours per day, and 7 days per week. Since the Hebrew calendar depends on a lunar cycle, the average lunar month is given the name "Molad" (for "birth" of the new moon), and is 29 days, 12 hours, 793 parts long.
The 19 year cycle has 12 non-leap and 7 leap years. There are 235 lunar months in each cycle. This gives a total of 6939 days, 16 hours and 595 parts for each cycle. Due to the vagaries of the Hebrew calendar, 19 Hebrew years can be either 6939, 6940, 6941, or 6942 days each. To start on the same day of the week, the days in the cycle must be divisible by 7, but none of these values can be so divided. This keeps the Hebrew calendar from repeating itself too often. The calendar almost repeats every 247 years, except for an excess of 50 minutes (905 parts). So the calendar actually repeats every 36,288 cycles (every 689,472 Hebrew years).
The leap years of 13 months are the 3rd, 6th, 8th, 11th, 14th, 17th, and the 19th years. Dividing the Hebrew year number by 19, and looking at the remainder will tell you if the year is a leap year (for the 19th year, the remainder is zero). A Hebrew leap year is one that has 13 months in it, a non-leap year has 12 months. A mnemonic word in Hebrew is GUCHADZaT (the Hebrew letters gimel-vav-het aleph-dalet-zayin-tet, i.e. 3, 6, 9, 1, 4, 7, 9. See Hebrew numerals).
A Hebrew non leap-year will only have 353, 354, or 355 days. A leap year will have 383, 384, or 385 days.
Although simple math would calculate 21 patterns for the calendar years, there are other limitations which means that [Rosh Hashannah]? may only occur on Mondays, Tuesdays, Thursdays, and Saturdays, according to the following table:
| Day of Week | Number of Days | ||||
| Monday | 353 | 355 | 383 | 385 | |
| Tuesday | 354 | . | . | 384 | |
| Thursday | 354 | 355 | 383 | 385 | |
| Saturday | 353 | 355 | 383 | 385 |
Basically, the Hebrew months alternate between a short month and a long month, for example: Tishrei (30 days), Cheshvan (29 days), Kislev (30 days), Tevet (29 days), Shevat (30 days), Adar (29 days), Nisan (30 days) Iyar (29 days), Sivan (30 days), Tammuz (29 days), Av (30 days), Elul (29 days).
For leap years, a 30 day month of Adar 1 is added immediately after the month of Shevat, and the 29 day Adar is called Adar 2. This is because the 11.25 days between 12 lunar months and one solar year in just three years adds up to more than a month.
The 265 days from the first day of the 29 day month of Adar (the last one of the year) and ending with the 29th day of Heshvan forms a fixed length period that has all of the festivals specified in the Bible, such as Pesach (Nisan 15), Shavuot (Sivan 6), Rosh Hashannah (Tishrei 1), Yom Kippur (Tishrei 10), Sukkot (Tishrei 15), and Shemini Atzeret (Tishrei 22).
The festival period from Pesach up to, and including Shemini Atzeret, is exactly 185 days long. The time from the [vernal equinox]? up to and including the traditional day of the [autumnal equinox]? is also exactly 185 days long. This has caused some speculation that Pesach should be March 21st, and Shemini Atzeret should be September 21, which are the traditional days for the equinoxes. Just as the Hebrew day starts at sunset, the Hebrew year starts in the Autumn (Rosh Hossannah), although the mismatch of solar and lunar years will eventually move it to another season.
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