I am researching the kings of Judah and Israel and realized that the Hebrew year and the Gregorian year may be different. I know the mean length of the Gregorian year (365.2425 days), but I do not know the length of the Hebrew year. So I come here to find out. What is the mean length (in days) of a Hebrew year, to seven significant digits, like I've shown for the Gregorian year? (In case you don't know, when I say "mean" I am saying "average").
A mean Hebrew month is 29 days + 12 hours + 793/1080 of an hour.
Back then they would add a 13th month into the year whenever the drift appeared to be getting too big, but not on a regular schedule, so it's hard to give an exact estimate of mean year length.
Currently we use a regular schedule of 7 leap years every 19 years, for 235 months in 19 years. Do your math to find a mean year length of 365.2468 days. (No year is actually that long. They are all on the order of ~354 or ~384.)
(In the current fixed calendar, there is also some variance in the lengths of certain months for other reasons (putting holidays on certain days of the week), so the full cycle of the calendar is actually 36288 cycles of 19 year cycles, for a total of 689472 years.)
The Jewish year varies in length, with an extra month some years and with some years having one more or one less day than usual. Ultimately, the main reason for the variation is to keep it from drifting too much from the solar year, such that Passover stays in the Spring time. Therefore, the mean length of the Hebrew year, after all of the variations, ends up, by design, very close to the mean length of the solar year.
According to this WP article, the mean length of the Jewish year is 365.2468 days, or just a smidge longer than the Gregorian year.