How the Jewish Calculated Calendar Works

The following explanations are based primarily on John Kossey's book (1) which was used as a textbook for "Christian" college students studying the Hebrew calendar. The quotations are from that work unless noted otherwise.

Please note that this explanation is a description of how the calculations work and is not intended as instructions on actually performing the calculations. That is discussed at the end of this article.

1. The calculations involve the following units:

1 part (chalyek) = 76 moments (regaim) or 3.333 seconds
1 hour = 1080 parts (chalakim)
1 day = 24 hours
1 week = 7 days
1 lunar month = 29 days 12 hours 793 parts
1 common year = 12 lunar months
1 intercalary year = 13 lunar months
1 nineteen year cycle = 235 lunar months, or 12 common years plus 7 intercalary years

To perform the calculations requires that one be able to add, subtract, multiply, divide and reduce dates and quantities of time expressed in these units, both in positive and negative terms.

2. Although Gen. 1:5 shows the day beginning at sunset, "6 PM is the arbitrary commencement of a new day for calendar purposes.", regardless of actual sunset.

3. A lunar month varies in length but is given by astronomers as 29 days 12 hours 44 minutes and 2.8 seconds. The "Hebrew calendar incorporates months of 29 and 30 days." The lengths of the individual months are set by calendar rules which ignore the actual length of the months.

"In order, however, to prevent New Year and the day of atonement from falling on Friday or Sunday, a day is sometimes added or subtracted from one of the months. If the day is added, it falls to the month of Heshvan and . . .if the day is subtracted, it is taken from the month of Kislev. . ." (The Universal Jewish Encyclopedia, Vol. 2, p. 632, New York, 1940.).
The actual length of the month is ignored.

4. The solar year is normally measured by our "Roman" calendar of 12 months with 365 or 366 days. The Hebrew calendar uses common years of 353, 354 or 355 days, and leap years of 383, 384 or 355 days. These are "lunar" years expressed in "solar" days.

5. To design a perpetual calendar it was desirable to discover a repeating pattern in the cycles of the sun, moon and earth. Originally the Jews used a Babylonian 8-year cycle but abandoned it for Meton's 19-year cycle.

The Hebrew calendar is based on 19 years or 235 lunar months which is about an hour and a half less than 19 Julian years.

It is now known that this cycle gains 8 days 21 hours 45 minutes 5 seconds in 1900 years. Since this form of the calendar was not used until the 9th cent. AD, the gain so far is only about 5.7 days although some writers say it is over 9 days, perhaps because they use an earlier start date.

6. Although God identified Abib to be the "first month of the year to you (Israel)" (Ex. 12:1-2), the Jews base calendar calculations on establishing Tishri 1 first, and then calculating backwards to determine Abib. Tishri is the 7th month and the first day is when the Jew celebrate "New Year's Day".

7. Jewish historians and scholars say that observation alone was used first, then later, observation with checking by calculation and lastly, calculation only. In spite of Jewish history and traditions, some church of God ministers continue to insist that calculations and postponements date all the way back to (pick one) Christ, Ezra, David, Moses, Abraham, Noah, or Creation.
Prior to Moses, there were no Holy Days aside from the weekly Sabbath. A calendar is not needed to identify the weekly Sabbath, as it is a purely solar event identified by counting to seven.

8. The first step in calculation is to establish the "molad of Tishri". "Molad" is from the Hebrew moled (plural, moledoth). This word means "birth". The molad is "the computed time for the conjunction of the sun, moon, and the earth." In scripture, the term "new moon" is translated from the Hebrew "chodesh" which means the "newness" of the lunar crescent.
A conjunction is an alignment of the moon between the earth and the sun. By definition this occurs only at high noon on the local meridian. The nature of a conjunction means that it cannot ever be observed. The light from the sun at high noon, makes the moon invisible to anyone on earth.
Because of variations in the cycles of the earth, moon and sun, the actual conjunction is not used. The calculations are based on a "mean" conjunction which can be as much as 14 hours before or after the true conjunction.

9. Since Sabbath is the seventh day, Sunday is the first day of the week. God identifies the day as beginning at sunset. However for calculations, "we begin the day at midnight instead of 6 PM so far as calculations are concerned." (Note conflict with #2 above.) For calculations, midnight Sunday night is the beginning of the week. From the 2nd cent. AD until 1925, all astronomers based calculations on the day beginning and ending at noon.

10. For the convenience of calculations, a benchmark was desired. The Jews began in the 3rd cent. AD to use the first molad of Creation as the benchmark for all calculations. That benchmark has been changed several times.
The various benchmarks give the molad as: 4d, 20h, 408p; 2d, 5h, 204p; 6d, 14h, 0p; and 3d, 22h, 876p. ( Calendar ,The Encyclopedia Judaica Jerusalem, Keter Pub. House Ltd. Jerusalem, Israel, 1971, pp. 43-54.)
It is also given as 4d, 9h, 642p. (Encyclopaedia of Religion and Ethics, Edit. by Hastings, 1928, Vol. 3, p. 120.)
The Worldwide Church of God used 1d, 23h, 204p. (The Hebrew Calendar: A Mathematical Introduction, John A. Kossey, Edit. Herman Hoeh, Ambassador College, 1971, 74, pp. 2-2, 2-4, 4-4, 5-8.) It appears that the WCG used a Julian (Roman) calendar date for their calculations of the Jewish calendar as this figure corresponds to the 2d, 5h, 204p shown in the Jewish Encyclopaedia quoted above. It amounts to the same date, but would have to be converted to be accurately used in the Jewish calculations. This conversion is not mentioned in Kossey's text.

11. What happens if the new moon is visible on the 29th day of the calculated month?
"The new moon is sometimes visible on the 29th day. When there needs to be a 30th day [for calculations], it is called new moon as well as the 1st day of the following month". (The Jewish Calendar, Rabbi Ari Cartun, Hillel Foundation, Stanford Univ., http://portfolio-www.stanford.edu/104273).
So, even if the calculated Tishri 1 is obviously incorrect because of the presence of a visible new moon, the rest of the Holy Days are calculated on the incorrect day anyway.

12. To perform the calculations, it is necessary to calculate the advancement of the molad, which is the "excess over the number of full weeks in the elapsed time from the bench mark to the molad Tishri of the desired Roman year." This gives you the day of the week for the molad being calculated.
This requires correctly finding the elapsed time from the bench mark to the required year. It also requires: a) expressing the elapsed time in terms of multiples of 19 year cycles, b) plus common years in the remainder, c) plus leap years in the remainder. Then you must calculate the "advancement" attributable to each of a, b, and c, above. Finally, add the reduced advance of the molad "c" to the bench mark. These are just math problems although they can involve negative numbers and allowance must be made if any dates are BC.

13. For the calculations, the time elapsed must be expressed in 19 year cycles.

14. The remainder of years in excess of 19 must be expressed in common and in leap years.
Before 142 AD, the cycle of leap years used was 2, 5, 7, 10, 13, 16, 18. After 142 AD, the leap years used are 3, 6, 8, 11, 14, 17, 19. Other cycles of leap years were also used prior to 142 AD, which makes any attempt to calculate the Holy Days observed at the time of Christ strictly a matter of speculation. The Essenes, Sadducees and Pharisees all used different calendars in Jerusalem at the same time in addition to other calendars being used by various Jewish groups.

15. Calculating the day of the month involves steps that parallel those of finding the day of the week. A 19-year cycle is shorter than 19 Julian years. An "average" common year is shorter than an "average" Julian year. An "average" leap year is longer than an average Julian year. By using these three differences you can determine by addition and subtraction, the day of the month.

16. Pre-calculated tables can be used to reduce the time required for arithmetic. These are available in some books on the subject and on the Internet.

17. Calculating previous dates in history will require adjustments for the Roman leap year and for the difference between the Julian and Gregorian calendars.
It also requires assumptions as to changes made in the method of calculation used at any time, the cycle of intercalation being used, corrections made due to previous errors, the use of postponements, which postponements were being used, the lengths of the solar and lunar years in use, interference with intercalation by foreign governments (as Rome did) and so on.

18. Orthodox, Conservative and Reform Jewish groups as well as some non-Jewish Christian groups use the postponements in their calculations. After the above calculations are made, the four rules of postponements are applied.
Not all Jewish groups use the postponements and there has never been universal agreement among Jews on the calendar. The Karaites did not accept the calculated calendar until the 14th cent.AD in some areas and not until the17th cent. AD in Egypt. They have never accepted the postponements and consider them un-Biblical. The Essenes observe the feast days but use a solar calendar to schedule them.

19. There are some mathematical shortcuts to determining the day of the week.

20. The calculated calendar uses months of preset lengths regardless of the actual length of the month. Because of this, mathematical shortcuts can be used to determine the festival dates. However, this method ignores the actual phases of the moon, or the actual astronomical date of the month.

21. For leap years the 13th month (Adar II) is added between the 11th and 12th months and is also called the 12th month, but it is never added after the 12th month (Adar).

It can be difficult to find a book that explains the calculations in detail and yet is easy to understand. This author once took a college class which included a requirement that the students be able to calculate any feast date in history using the Jewish calculations. No text was available but we had lecture notes and were given a single page of "rules" and "mathematical shortcuts". It took about six class hours for the majority of the class to understand and successfully do the exercises.
Nothing was presented about the history of the Jewish calendar, its progression of development, its errors, the attempts to correct it, the division it caused among Jews even within the same sects, nor the fact that the Jews plan to abandon it as soon as they can.

If you wish to try calculating dates, most Jewish encyclopedias present a simple explanation but not enough to actually perform the calculations on your own.
One web site that gives a thorough but understandable explanation can be found at: http://roarbush.com/jewcal/index.html
A satirical but accurate explanation is given in the article, "Ram Bam, Bubba And The Molad of Nothing".