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This article is a reference material for those who wish to have deeper understanding of the theory behind the Online Jewish Calendar Conversion program.
Hebrew Calendar or, as it is alternatively called, Jewish Calendar is a traditional lunisolar calendar used by Jewish people throughout the world. The terms Hebrew Calendar and Jewish Calendar will be used as synonyms in this site.
In all our measurement systems the larger unit consists of several smaller units. Unfortunately we cannot do this with calendar and at the same time preserve the natural calendar units, because the length of lunar month is between 29 and 30 days and the length of a year is between 12 and 13 lunar months. Since we do not want to use fractions in the calendar we have to either completely ignore some of the natural cycles, as purely solar (e.g. Gregorian) or purely lunar (e.g. Muslim) calendars do, or make it more complex as in lunisolar (e.g. Hebrew) calendar.
The lunisolar calendar is based on 2 observations:
1 Two lunar months are practically equal to 59 days
2 235 lunar months are practically equal to 19 solar years.
Therefore, by alternating 29 and 30 day months and interchanging 12 and 13 month years, we can make a lunisolar calendar without using the fractions.
Obviously we can combine 29 and 30 day months and 12 and 13 month years in 19 year cycle in many different ways. The Jewish calendar does it in particular way because of other special considerations, which are explained in detail in this article.