Practical Application and Mathematics of the Hebrew Calendar
The purpose of this post is to provide a glimpse into the practical application of the Hebrew Calendar.
Note: The Hebrew year begins on the day of Trumpets, (the first day of the seventh month) and yet the month that Passover falls in is said to be the first. Click here for an explanation.
Converting the dates of the Holy Days to Gregorian.
The Hebrew year 5784 begins on the Gregorian date: Saturday, September 16, 2023. It runs through the winter, spring and summer and concludes on October 2, 2024. This places the Day of Trumpets in 2024 on Thursday, October 3rd.
On the Hebrew calendar the months 1-7 (the month that contains Passover through the month that contains the Fall Holy days) alternate 30, 29, 30, 29 days. This means that the first day of the first month will be 177 days before the feast of Trumpets. 30 + 29 + 30 + 29 + 30 + 29 = 177.
If we wish to find the Gregorian date for the first day of the first month, thereby establishing the Gregorian dates of all the Holy days for the year, we simply subtract 177 days from the day of Trumpets. We will use the Gregorian year 2023 for an example. We can see above that the Feast of Trumpets is on September 16th.
To subtract the 177 days, we can count backwards on the wall calendar, or we can use math.
January 31
February 28, or on a leap year 29
March 31
April 30
May 31
June 30
July 31
August 31
September 30
October 31
November 30
December 31
Subtracting the 16 days in Septmber brings us to the end of August. August has 31 days, so add 16+31, + 31 for July, + 30 for June, + 31 for May + 30 for April = 169. We are still 8 days short of the 177 days, so subtract 8 days from March. This brings us to March 23rd.
March 23, 2023 is the first day of the first month.
15 days later is Passover/ First Day of Unleavened Bread, with the Last Day of Unleavened Bread 7 days after that. We should have begun the count to Pentecost during this time, so that takes care of Pentecost. And we already know the date of Trumpets. 10 days later is Atonement, then 5 days after that begins the Feast of Tabernacles. On the eighth day after Tabernacles begins is the Last Great Day.
All this is pretty simple! So now, how do we know that the day of Trumpets is on September 16th in 2023? I’m glad you asked!
Please note that the Hebrew Calendar does not rely on the Gregorian or any other calendar system. In fact, it is far easier to use if one keeps track of the current Hebrew date on a daily basis, thus making any conversion to the commonly used Gregorian Calendar wholly unnecessary.
Once we have calculated the Hebrew date, the conversion can be made, if necessary, to the Gregorian. However, this requires a known starting point that we know the respective date of using each system. This is because to make the conversion, we count the elapsed number of days from the starting point to the targeted date.
Warning! What follows, seems daunting and intimidating, but is nothing more than basic arithmetic.
To calculate the day of Trumpets that begins the Hebrew year 5784, subtract 1, because we are counting the number of years elapsed.
Divide 5783 by 19 to find the number of 19-year cycles that have elapsed.
5783 ÷ 19 = 304 with a remainder of 7.
304 is the number of cycles that have elapsed, and the remainder of 7 is the number of years that have elapsed.
Apply the leap year pattern to determine the number of months contained in these 7 years.
Year 1 12 months
Year 2 12 months
Year 3 13 months
Year 4 12 months
Year 5 12 months
Year 6 13 months
Year 7 12 months_____= 86 months
Year 8 13 months
Year 9 12 months
Year 10 12 months
Year 11 13 months
Year 12 12 months
Year 13 12 months
Year 14 13 months
Year 15 12 months
Year 16 12 months
Year 17 13 months
Year 18 12 months
Year 19 13 months
There are 235 months in each 19-year cycle, so multiply 304 X 235. The sum is 71,440. Add the 86 for a total of 71,526 months.
Each month contains 29 Days, 12 Hours, 793 Parts
Multiply these by 71,526
71,526 X 29D = 2,074,254D
71,526 X 12H = 858,312H
71,526 X 793P = 56,720,118P
Now we start with Parts. There are 1080P in an hour, so divide 56,720,118 by 1080. the result is 52,518 remainder 678P
Keep track of these 678P
Add the 52,518 to the 858,312H for a total of 910,830H
There are 24 Hours in a day, so divide 910,830 by 24. The result is 37,951 remainder 6H.
Keep track of these 6H
The 37,951 are whole days, so add these to the 2,074,254D for a total of 2,112,205D.
There are 7 days in a week, so divide 2,112,205 by 7.
The result is 301,743 remainder 4D.
The number of weeks elapsed is not important, so disregard this number. The remainder of 4 days is important. If the remainder is 0 or 7 then this represents the seventh day (Saturday).
We now have 4D 6H 678P
Add to these 2D 5H 204P for the “Molad of Creation”
4D + 2D = 6D
6H + 5H = 11H
678P + 204P = 882P
Apply “Postponements” *
If the Molad occurs after noon (12 H) then add one Day to the Molad
If the Molad occurs on Day 1, 4, or 6 add one Day to the Molad
If the Molad occurs on D3 at 9H 204P or later, add one Day to the Molad
If the Molad occurs on D2 between 15 and 18 H on the year following a leap year, add one Day to to Molad.
If any of these apply, check to see if number 2 can be applied again. If it can, then do so.
#2 applies in this case, so the first day of the seventh month (Feast of Trumpets) is on D7 (Saturday)
The next step is to determine the time of the Molad of the following year (in this case the Molad of 5785). There are other ways to calculate what we have just learned, and various shortcuts, but for simplicity's sake the method used previously will suffice.
To avoid unnecessary mental anguish, I will just share that the Molad of 5785 occurs at D5 9H 391P. This will become relevant in a minute.
Because we are trying to determine the Molad of the 8th year of cycle 304, we previously only counted days already elapsed, but now we add the 1 year that we removed at the beginning of the calculations. This brings us to the 8th year, which is a leap year containing 13 months.
A leap year contains a minimum of 383 days, and a maximum of 385 days.
385 days is evenly divided by 7 (55 weeks).
The first year we did the calculations for, places the first day of the seventh month on D7.
The following year’s Molad lands on D5. The difference between the two is 2D, so we subtract 2D from the 385 days.
We now know that the Hebrew year 5784 contains 383 days, or 54 weeks and 5 days.
Possible year lengths for a leap year are 383, 384 or 385 days. The shorter year is said to be “deficient,” the middle length year is said to be “in order,” and the longest year is said to be “full.”
Possible year lengths for a common year containing 12 months are 353, 354 or 355 days. The same labeling applies.
In a “deficient” year, both the 8th and 9th months are 29 days in length.
In an “in order” year, the 8th month has 29 days and the 9th has 30 days.
In a “full” year, both months have 30 days.
The other months always alternate 30, 29, 30, 29 days.
Month 1 30 days
Month 2 29 days
Month 3 30 days
Month 4 29 days
Month 5 30 days
Month 6 29 days
Month 7 30 days
Month 8 29 or 30 days
Month 9 29 or 30 days
Month 10 29 days
Month 11 30 days
Month 12 29 days (30 days in a leap year)
Month 13 29 days (Only exists in a leap year)
With this information it is possible to create a calendar for the entire year 5784.
This year starts on a Saturday, the 8th and 9th months have 29 days, and there is a leap month of 30 days added in between the 11th and 12th months. The year is a total of 383 days long, and concludes on a Wednesday, with Thursday being the start of the next year.
See also Inside the Gearbox of the Hebrew Calendar
* “Postponements” are poorly labeled mathematical rules to adjust the length of the year and keep it in synchrony with the solar and lunar cycles.
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