Computing the Sacred (Biblical/Hebrew/Jewish) Calendar

The familiar Western calendar is the Gregorian calendar, an adjusted Julian calendar promulgated by Pope Gregory XIII in 1582, and adopted in Britain and America in 1752. It is essentially a solar calendar, in which one rotation of the Earth around the Sun is one year. There are 12 months in the year, but they have little to do with the rotation of the Moon around the Earth. Gregorian years are 365 or 366 days long. Months are 30 or 31 days, except February, which is 28 days or 29 days in a leap year.

The Biblical calendar is based on both the rotation of the Moon around the Earth and of the Earth around the Sun. In principle, a month starts when a new moon is observed and lasts till the next new moon occurs. Therefore, months are 29 or 30 days long. Years are 12 or 13 months long and approximately align with the Sun.

In Bible times, when two witnesses saw the new moon, then a new month was declared to start at the next sunset. If they saw it too close to sunset for the New Moon rites to be prepared, then the new month was declared to start at sunset on the following day. The decision as to whether there were to be 12 or 13 months in the year depended on the state of the harvest and whether enough lambs had been born for the sacrifices of the Passover observance. It was this calendar that Jesus followed in the New Testament.

Christian-instigated persecution of Jews forced the Jewish authorities to switch to a computed, rather than observed calendar. This computed calendar matched as closely as possible the decision-making process that had been used previously. It is this computed calendar that is now followed by the vast majority of those who wish to observe the Biblical Holy Days.

Suggestions have been made that the computations should be changed, or that observation should again be used. It is clear that adjustments need to be made to the computed calendar in order to keep it synchronized with the sun and moon. But there is no consensus as to how this should be done, and, in the modern world, this needs to be done years in advance. Returning to observation is idyllic, but totally impractical. The modern world requires plans for religious observances to be made months, or even years, in advance. Only a computed calendar permits this. It is clear that just as "the Sabbath was made for man", so also "the Calendar was made for man." It is a tool to help us worship God. And an essential feature of a tool is that it must be useful and practical.

Month Number Post-Exile Name Pre-Exile Name Computed Days Features
1. Nisan = "Marching" Abib = "Green Ears" 30 days Passover and Days of Unleavened Bread, barley harvest
2. Iyyar, Ijar Zif = blossom 29 days Second Passover
3. Sivan   30 days Pentecost, wheat harvest
4. Tamuz, Tammuz = Babylonian god   29 days Fast of 4th month, "weeping for Tammuz"
5. Av, Ab   30 days Destruction of 1st and 2nd Temple
6. Elul   29 days  
7. Tishrei, Tishri, Tisri Ethanim = flowings 30 days Feast of Trumpets, Atonement, Tabernacles, Last Great Day
8. Cheshvan, Marchesvan Bul = rain 29/30 days "former" rains
9. Kislev, Chisleu   29/30 days Feast of Dedication, Lights = Hannukah
10. Tevet, Tebeth = muddy   29 days  
11. Shvat, Sebat = downpour   30 days "latter" rains
12. Adar = darkened   29 days Purim
Only in leap years:
13. Veadar = "Second Adar"   29 days  

Pre-Exilic names are the months names recorded in the Bible which were used before the Jews went into Exile in Babylon (ca. 600 B.C.). The post-Exilic names are the Babylonian names for the same months, which continued to be used by the Jews after their return to Palestine.

The Rabbis computed that the Jewish calendar started on what would be October 5, 3761 B.C., which is seen as the moment of creation (Elul 25th is the calendar date). Adam was created on the 1st day of the month Tishri (Ethanim), observed by Jews as Rosh HaShana (the Feast of Trumpets).

The difference of 11 1/4 days between 12 lunar months (354 days) and one solar year (365 1/4 days) accumulates in three years to more than a month. If no adjustments are made (as they are not in the Muslim calendar), any month could occur in any season of the year. But the Biblical holydays are closely related to the seasons (for example, the Passover is commanded to occur in the month of "Green Ears" (Abib), i.e., in the spring). So an adjustment to the calendar must be made every few years. Every two or three years, an extra month is added to a year. Such a month is called an "intercalary month." Those years are called leap years. In the computed calendar, the month Adar is added again, and called Veadar, "Second Adar". In earlier times, the thirteenth month could be, instead, "Second Elul".

Jewish traditional holidays that occur in the month of Adar (such as Purim) are celebrated in Veadar in a leap year. The same rule is applied to birthdays, anniversaries and other personal events.

Since the Sun, Earth and Moon repeat their alignments almost exactly every 19 years, the leap years follow a 19 year "Metonic" cycle:

  1. Regular.
  2. Regular.
  3. Leap.
  4. Regular.
  5. Regular.
  6. Leap.
  7. Regular.
  8. Leap.
  9. Regular.
  10. Regular.
  11. Leap.
  12. Regular.
  13. Regular.
  14. Leap.
  15. Regular.
  16. Regular.
  17. Leap.
  18. Regular.
  19. Leap.

In earlier times, there was no fixed cycle. However the "Sabbatical Year", every seventh year, was never a leap year.


In addition to the leap year cycle, the length of each year is slightly adjusted to meet a number of constraints called Dechiot. These small adjustments are made by selecting the length of the two months of Cheshvan and Kislev to be 29 or 30 days. There are four possible combinations, but only three are actually used:

year kind Cheshvan Kislev length of regular year
29 days 29 days 353
("in order")
29 days 30 days 354
---- 30 days 29 days ----
30 days 30 days 355

The four constraints (Dechiot) that determine the exact year length have to do with the exact timing of the holidays in relation to the phase of the moon and with relations to the day of the week.

Dechia 1 - Molad Zaken

The moon goes in orbit around the Earth. Every month, there is one instance in which the moon is exactly between the Earth and the sun and the Earth faces the dark side of the moon. This instance is called Molad ("birth" of a new moon) and it marks the beginning of a new month. The Molad of the first month of the year, Tishrei, marks the Civil New Year or Rosh HaShana = "Head of the Year". This is on Tishri 1. The religious New Year is on Nisan 1.

Since the Earth is facing the dark side of the moon, the moon becomes visible later that day or the next day.

In a year when the Molad of Tishrei occurs after 12:00 noon, Rosh HaShana is postponed until the next day because the moon would not become visible until the next day. This is done by adding one day to the previous year.

Dechia 2 - Sunday, Wednesday, Friday

If the Molad of Tishrei falls on Sunday, Wednesday or Friday, Rosh HaShana is postponed by one day to Monday, Thursday or Saturday, respectively.

The reason is that if Rosh HaShana is on Wednesday or Friday, then Yom Kippur, "The Day of Atonement", would occur on Friday or Sunday. That would make Yom Kippur adjacent to Shabbat, "Sabbath" (Saturday). Yom Kippur is a Fast (no eating) Day, in which we are to afflict ourselves and work is prohibited. The Sabbath is a day of rest and rejoicing, on which work is also prohibited. If they were to occur next to each other, the purpose of one or both days would be compromised.

If Rosh HaShana is on Sunday, Hoshana Raba, the seventh day of the Feast of Tabernacles would fall on Saturday, a rest day, and that would prevent the custom of demolishing the Tabernacles on the last day of that Feast. The eighth day is a solemn assembly on which the demolition cannot take place. So, if the seventh day were a sabbath, the Tabernacles would not be demolished till the ninth day, which is clearly opposed to the command to "dwell in Tabernacles for seven days."

Dechia 3 - Molad of Regular Year on Tuesday

If the Molad of Tishrei of a regular year with 12 months occurs on Tuesday morning, Rosh HaShana would occur on Tuesday. However, this would cause a problem with Rosh HaShana of the following year. It would occur on Friday, Saturday, or Sunday.

To see why, remember that the length of a regular year, in the computed calendar, can be 353, 354 or 355 days. (12 lunar months are approximately 354 days. Only one day deviance is allowed from this.) So Rosh HaShana can only occur 3, 4 or 5 days later in the week next year, compared with this year.

Friday and Sunday are always problems (Dechia 2). Therefore this year must have 354 days and the next Rosh HaShana will fall on Saturday. However, the accurate length of a lunar month is 29 days, 12 hours, 44 minutes and 3 1/3 seconds. The accurate length of a lunar year (12 lunar months) is therefore 354 days, 8 hours, 48 minutes and 40 seconds. This means that if the Molad of this year occurs on Tuesday 6 AM, the Molad of the following year will occur on Saturday 2:48:40 PM, and Rosh HaShana will have to be postponed to Sunday according to constraint number 1 and then postponed again to Monday according to constraint number 2. In order to do that, this year will have to be 356 days long, which is not possible.

The conclusion of the above logic is constraint number 3 which states that if a Molad of a regular year occurs after Tuesday 3:22 AM, Rosh HaShana is postponed to Thursday.

Dechia 4 - Molad of Leap Year on Thursday

This is a similar situation to the one described in contraint number 4. Here the rule is that if a Molad of a leap year occurs after Thursday 12:00 noon, the next Rosh HaShana is postponed from Monday to Tuesday.

All the 4 constraints (Dechiot) can be pre-calculated and represented in tables of short cycles. Hebrew calendar software programs use relatively simple table lookup to determine the exact length of a given year and the date of Rosh HaShana. All the other dates and holidays are calculated by counting from Rosh HaShana.

Understanding the Jewish Calendar by Rabbi Nathan Bushwick. Moznaim Publishing Corporation, 1989.

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