The Hebrew calendar is a lunar calendar based on the 19-year Metonic cycle, where 19 years is almost exactly equal to 235 months. The relationship of the Hebrew year to the Civil year is illustrated by this chart.

The following sections explain the principles of this calendar.

The calculations in the subsequent sections are based on an ancient form
of measuring time. Each day is divided into 24 hours, which are each divided
into 1080 parts (or *halakhim*).

A month is defined as the period from one new moon to the next, corresponding to the astronomical definition of a siderial month. For these calculations the length of a month is taken to be 29 days, 12 hours, and 793 halakhim.

The Biblical date of creation is used as the basis for the Hebrew calendar. Reverse calculation gives the time of the first new moon of Year 1 as 5 hours and 204 halakhim from the beginning of the second day of the week (Sunday evening/Monday). This date corresponds to October 7, 3761 BCE, using the Julian (not Gregorian) calendar. For later arithmetical convenience, we will define the preceding Sabbath as day number 0, so that this date, 1 Tishrei of Year 1, is day number 2.

A year in the Hebrew calendar is normally twelve months:
*Tishrei*, *Cheshvan*, *Kislev*, *Tevet*,
*Sh’vat*, *Adar*, *Nisan*, *Iyar*,
*Sivan*, *Tammuz*, *Av*, and *Elul*. An extra
month (Adar is replaced with Adar I and Adar II) is intercalated
in seven of every nineteen years (years 3, 6, 8, 11, 14, 17, and 19).
Every 19-year cycle thus contains 235 months. These two
cycles of years and months are so close that they diverge at the
rate of only 4.5 days every 1000 years.

Because a lunar month is not a whole number of days, the length of the months can be either 29 or 30 days. A typical year alternates 30- and 29-day months, beginning with Tishrei, which is 30 days. In leap years, Adar I is 30 days and Adar II is 29 days. To further bring the calendar into alignment with the lunar cycle, a year may need to be shortened or lengthened by one day: Kislev may be shortened to 29 days, or Cheshvan may be lengthened to 30 days. Thus, there are six types of years:

- Defective common years, with 353 days
- Regular common years, with 354 days
- Excessive common years, with 355 days
- Defective leap years, with 383 days
- Regular leap years, with 384 days
- Excessive leap years, with 385 days

In the ancient Hebrew calendar, each month began with the first observation
of the first sliver of moon after a new moon. The beginning of each month
is now determined solely by calculation. The first step is to determine
the date and time of the first new moon of the year, the *Molad Tishrei*.

This, and the Molad Tishrei for the following year, determine whether the year needs to be defective, regular, or excessive, and the year’s position in the 19-year cycle determines whether it is a leap year or a common year.

To find the Molad Tishrei for a given year, simply count from year 1 (starting with 2 days, 5 hours, and 204 halakhim as the Molad Tishrei for that year), counting 29 days, 12 hours, and 793 halakhim for each month. This can be done efficiently by first calculating the number of days from Day 0 until the beginning of the current 19-year cycle, counting 235 months (991 weeks, 2 days, 16 hours, and 595 halakhim) for each cycle. Then, for each year from there to the current year, 12 or 13 months should be added. The total can be expressed in weeks, days, hours, and halakhim.

Year: | |
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19-year cycle: | |

Year of cycle: | |

Leap year? | |

Months: | |

Molad Tishrei: |

Hint: Use left and right arrow keys to change year.

Once the date of the Molad Tishrei has been calculated, some additional considerations must be taken into account to determine the actual date of Rosh HaShanah. These considerations may cause the actual date of 1 Tishrei to be postponed from the date of the Molad Tishrei. There are four such postponements:

First, if the time of the Molad Tishrei is later than 18 hours from the beginning of the day, Rosh HaShanah is postponed to the next day. This probably accounts for the fact that the young moon could not have been observed until the next day.

Second, for common years only, if the Molad Tishrei falls on a Tuesday, and is later than 9 hours and 204 halakhim from the start of the day, Rosh HaShanah is postponed to the next day. This rule prevents a situation in which the postponements for the next year would require the year to be 356 days long.

Third, for years following leap years only, if the Molad Tishrei falls on a Monday, and is later than 15 hours and 589 halakhim from the start of the day, Rosh HaShanah is postponed to the next day. This rule prevents a situation that would require the previous year to be only 382 days long.

Finally, if Rosh HaShanah would fall on Sunday, Wednesday, or Friday, it is postponed to the next day. In combination with one of the above postponements, Rosh HaShanah could be postponed by as much as two days. This postponement prevents certain holidays from falling on the Sabbath.

Year: | |
---|---|

Molad Tishrei: | |

1st postponement: | |

2nd postponement: | |

3rd postponement: | |

4th postponement: | |

Rosh HaShanah: | |

Day of week: |

Since we know the Civil date corresponding to Day 0 in the Hebrew calendar (October 5, 3761 BCE — two days before the Molad Tishrei for Year 1), it is a straightforward matter to add the weeks and days to this date to arrive at the corresponding date for any date in the Hebrew calendar.

This conversion is usually done using the astronomical convention of Julian day numbers, where the Hebrew calendar’s Day 0 corresponds to Julian Day 347,996. Given a number of weeks and days from Day 0, we can easily calculate the corresponding Julian Day number.

Year: | |
---|---|

Rosh HaShanah: | |

Days from Day 0: | |

Add Day 0: | + 347996 |

Julian day number: |

Given a Julian day number, it can be converted to the civil calendar as follows.

**Step 1.** Convert it to the number of days since March 3 of Civil
Year 0 (commonly written 1 BCE), by subtracting 1,721,120, which is
the Julian day number for that day (using the Gregorian calendar).
March 3, 1 BCE, in the Julian calendar would have been March 1 had the
Gregorian calendar been in use at the time.
(For the Julian calendar, we use instead a base of March 1, 4713 BCE,
or Julian Day number 60.)

**Step 2.** Compute the number of whole centuries since Civil Year 0
by dividing the result of Step 1 by 36,524.25, the average number of days per century.
Express the result as a whole number of centuries,
then calculate the whole number of days left over.
(For the Julian calendar, skip this step.)

**Step 3.** Compute the number of whole years since the beginning of the
current century by dividing the remainder from Step 2 by 365.25,
the average number of days per year in a century.
Express the result as a whole number of years,
then calculate the whole number of days left over.

**Step 4.** Combine the count of centuries
from Step 2 with the count of years from Step 3 to find the Civil Year,
and use the remainder from Step 3 to find the month and day of the year (count from March 1).
If the month is January or February, the date actually in the following year
(this won’t be a concern in Rosh HaShanah calculations).
September 1 is 184 days after March 1; October 1 is 214 days after March 1.

Julian day number: | |
---|---|

Subtract base: | − 1721120 |

Days since base: | |

Centuries: | |

Years: | |

Days: | |

Date: | |

Calendar: |