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Claus Tøndering –
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The Hebrew Calendar

The current definition of the Hebrew calendar is generally said to have been set down by the Sanhedrin president Hillel II in approximately AD 359. The original details of his calendar are, however, uncertain.

The Hebrew calendar is used for religious purposes by Jews all over the world, and it is one of the official calendars of Israel (the other one being the Gregorian calendar).

The Hebrew calendar is a combined solar/lunar calendar, in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. This is a complicated goal, and the rules for the Hebrew calendar are correspondingly fascinating.

Today’s Hebrew date (until sunset):

What does a Hebrew year look like?

An ordinary (non-leap) year has 353, 354, or 355 days. A leap year has 383, 384, or 385 days. The three lengths of the years are termed, “deficient”, “regular”, and “complete”, respectively.

An ordinary year has 12 months, a leap year has 13 months.

Every month starts (approximately) on the day of a new moon.

The months and their lengths are:

Name Length in a
deficient year
Length in a
regular year
Length in a
complete year
Tishri 303030
Kislev 293030
Tevet 292929
Shevat 303030
Adar I 303030
Adar II292929
Nisan 303030
Iyar 292929
Sivan 303030
Tammuz 292929
Av 303030
Elul 292929
Total: 353 or 383354 or 384355 or 385

A few entries in the table are highligted:

The month Adar I is only present in leap years. In non-leap years Adar II is simply called “Adar”.

In a regular year the numbers 30 and 29 alternate; a complete year is created by adding a day to Heshvan, whereas a deficient year is created by removing a day from Kislev.

The alteration of 30 and 29 ensures that when the year starts with a new moon, so does each month.

What years are leap years?

A year is a leap year if the number “year mod 19” is one of the following: 0, 3, 6, 8, 11, 14, or 17. The value for year in this formula is the “Anno Mundi” described in below.

What years are deficient, regular, and complete?

That is the wrong question to ask. The correct question to ask is: When does a Hebrew year begin? Once you have answered that question, the length of the year is the number of days between 1 Tishri in one year and 1 Tishri in the following year.

When is New Year’s day?

That depends. Jews have several different days to choose from. The most important are:

1 Tishri:
Rosh HaShanah. This day is a celebration of the creation of the world and marks the start of a new calendar year. This will be the day we shall base our calculations on in the following sections.
1 Nisan:
New Year for Kings. This is also the start of the religious year. Nisan is considered the first month, although it occurs 6 or 7 months after the start of the calendar year.

When does a Hebrew day begin?

A Hebrew calendar day does not begin at midnight, but at either sunset or when three medium-sized stars should be visible, depending on the religious circumstance.

Sunset marks the start of the 12 night hours, whereas sunrise marks the start of the 12 day hours. This means that night hours may be longer or shorter than day hours, depending on the season.

When does a Hebrew year begin?

The first day of the calendar year, Rosh HaShanah, on 1 Tishri is determined as follows:

  1. The new year starts on the day of the new moon that occurs about 354 days (or 384 days if the previous year was a leap year) after 1 Tishri of the previous year
  2. If the new moon occurs after noon on that day, delay the new year by one day. (Because in that case the new crescent moon will not be visible until the next day.)
  3. If this would cause the new year to start on a Sunday, Wednesday, or Friday, delay it by one day. (Because we want to avoid that Yom Kippur (10 Tishri) falls on a Friday or Sunday, and that Hoshanah Rabba (21 Tishri) falls on a Sabbath (Saturday)).
  4. If two consecutive years start 356 days apart (an illegal year length), delay the start of the first year by two days.
  5. If two consecutive years start 382 days apart (an illegal year length), delay the start of the second year by one day.

Note: Rule 4 can only come into play if the first year was supposed to start on a Tuesday. Therefore a two day delay is used rather than a one day delay, as the year must not start on a Wednesday as stated in rule 3.

When is the new moon?

A calculated new moon is used. In order to understand the calculations, one must know that an hour is subdivided into 1080 “parts”.

The calculations are as follows:

The new moon that started the year AM 1, occurred 5 hours and 204 parts after sunset (i.e. just before midnight on Julian date 6 October 3761 BC).

The new moon of any particular year is calculated by extrapolating from this time, using a synodic month of 29 days 12 hours and 793 parts.

Note that 18:00 Jerusalem time (15:39 UTC) is used instead of sunset in all these calculations.

How does one count years?

Years are counted since the creation of the world, which is assumed to have taken place in the autumn of 3760 BC. In that year, after less than a week belonging to AM 1, AM 2 started (AM = Anno Mundi = year of the world). In other words, AM 2 started less than a week after the “creation of the world”.

Hebrew year AM 5775 will begin on 25 September 2014.

When was Passover in AD 30?

People who ask this question are normally trying to calculate the exact date of Jesus’ death.

The New Testament states that Jesus died on a Friday at the beginning of the Jewish Passover, and that his resurrection took place on the following Sunday. However, it is not quite clear if Jesus’ death took place immediately before the start of the Jewish Passover or on the first day of Passover. Since Passover starts on 15 Nisan, it is unclear if Jesus died on 14 or 15 Nisan.

This question is important for Christian historians because if you know the date, you may with some degree of confidence also calculate the year; all you have to do is find a year near AD 30 where 14 or 15 Nisan fell on a Friday.

The problem is that we don’t know the exact details of the Hebrew calendar as it was used in the first century. This means that we have to allow for a margin of a day or two in the calculations, and this in turn means that we are left with quite a few possible dates.

Through the centuries several different dates for the crucifixion have been suggested. Currently, the most common theories suggest either 7 April AD 30 or 3 April AD 33.

(I frequently receive e-mail proposing very different approaches to calculating the date for Jesus’ death, including claims that Jesus did not die on a Friday or that he did not die on 14 or 15 Nisan. However, the statements made in this section describe the most commonly held views. A detailed discussion on the dating can be found in Blackburn and Holford-Strevens’ brilliant book[1].)


^ [1] Bonnie Blackburn & Leofranc Holford-Strevens: The Oxford Companion to the Year – An exploration of calendar customs and time-reckoning. Oxford University Press, 1999. ISBN 0-19-214231-3. P. 772 ff.