Mathematics of the Jewish Calendar/The lengths of the months
Although the New Year occurs at the start of the month of Tishri (that is the traditional spelling, although increasingly the spelling Tishrei is preferred), the Bible commands that Nissan should be regarded as the first month. ("This month shall be for you the beginning of months: it shall be the first month of the year for you." See Exodus Chapter 12 verse 2.)
As a general rule, the months are alternately 30 and 29 days. As will be explained later, two months (Cheshvan and Kislev) are of variable length. Further, in leap years, an extra month called Adar Rishon (First Adar) is inserted before the month of Adar, which is then renamed Adar Sheni (Second Adar). The months are as follows:
- Nisan, 30 days
- Iyar, 29 days
- Sivan, 30 days
- Tammuz, 29 days
- Av (or Menachem Av), 30 days
- Ellul, 29 days
- Tishri (or Tishrei), 30 days
- Cheshvan (or Marcheshvan), 29 days; sometimes 30 days
- Kislev, 30 days; sometimes 29 days
- Tevet, 29 days
- Shevat, 30 days
- [Adar Rishon (only in leap years), 30 days]
- Adar (called Adar Sheni in leap years), 29 days
In a regular (כסדרן) year, Cheshvan has 29 days and Kislev has 30 — consistent with the pattern of the lengths of the other months, and there are a total of 354 days (384 in a leap year). If Cheshvan and Kislev both have 30 days, the year is called complete (מלא) and there are 355 days (385 in a leap year). If Cheshvan and Kislev both have 29 days, the year is called deficient (חסר)and there are 353 days (383 in a leap year).
Thus an ordinary year can have 353, 354 or 355 days, and a leap year can have 383, 384 or 385 days. No year is allowed to fall outside these limits of length.
Note that 385 days is exactly 55 weeks, so that the Rosh Hashana of a year following an abundant leap year always falls on the same day of the week as the Rosh Hashana of that year. This does not happen with other year types.
It is possible for six consecutive years to contain all six lengths; for example, 5801-5806 does so.