The Jewish Calendar

Have you ever wondered how the Jewish calendar is composed? I have been curious about this myself for a long time. Jewish holidays occur at times that vary greatly with respect to the Gregorian calendar, the one that I and many others have grown up with.

But what is the Gregorian calendar? Alright, for those of you who don't know, let's do a quick review (don't worry, Jewish calendar fans—I'll come back to that one soon). Chances are overwhelmingly likely that you are already familiar with this solar-based calendar, even if you don't know it by name. It is what one may consider to be "the official calendar" of the modern Western world. This calendar utilizes years that come in only two sizes: 365 days—a regular year—and 366 days—a leap year. Dealing with this calendar is so easy, because a leap year seems to occur "every four years". Actually, it's almost that way. There is an exception to this "every four years" approach, but it's rare. Back when I was about 12 or 13 years old, I learned from a math book how a leap year was determined. The rules were easy for me to remember.

So when is a given year a leap year according to the Gregorian calendar? Okay, here it is! If the year is not evenly divisible by 4 (i.e., if the year, after dividing it by 4, does not result in the remainder being zero), then it is definitely not a leap year! But what if it is evenly divisible by 4? Well, then it is a leap year, unless this same year is also divisible by 100. Then what? In such a case, a larger number, 400, makes the final determination: if the year is evenly divisible by 400, then it is still a leap year. Otherwise, it is not.

So you see, as long as a year is evenly divisible by 4 but not by 100, it is definitely a leap year. But if that year ends in "00", this "threatens" its "leap" status. This is a case of the would-be leap year whose leap status is "vetoed" by the "double-oh" (uh-oh)! The only way to "override" this "veto" is for this such year to be evenly divisible by a number that is four times bigger than that anti-leap 100. This is obviously a rare case when the leap status prevails, thanks to the number 400 (and the number 100 ends up getting defeated in its efforts to stop that year from being a leap year). After all, this only happens every 400 years. "Y2K", the year 2000, is such an example. But 1900 does not get to be a leap year—the number 100 succeeds in stopping it from becoming one.

There are always 12 months in the Gregorian calendar. Seven of these months, January, March, May, July, August, October and December, always have 31 days each. Four of the other months, April, June, September and November, always have 30 days each. But the remaining month, February, always has either 29 or 28 days. It has 28 days in a regular year. But in a leap year, it has 29. The monthly sequence of each year, from start to finish, is: January, February, March, April, May, June, July, August, September, October, November and December.

That sums up the Gregorian calendar. It is based on the assumption that it takes planet earth a little under 365 1/4 days to complete one orbit around the sun. Okay, that's it for this Gregorian detour—it's time to get on with our main feature, the Jewish calendar! So what is this one like, compared to the Gregorian? Well, that's a different story.



SECTION 2: Detailed Molad Tables

SECTION 3: Summarized Molad Tables

SECTION 4: Determining Month Offsets and Leap Years

SECTION 5: Steps to Building a Jewish Calendar

SECTION 6: An Example and some Shortcuts

SECTION 7: More Shortcuts and Parts Usage

SECTION 8: More Examples and Parts Simplification

SECTION 9: Gregorian Issues and Jewish Year Utility

SECTION 10: Gregorian-Jewish 2-Way Date Converter

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