How Do I Know If it's a Hebrew Leap Year?

Question

How can I tell if a given year is a Hebrew Leap Year? The simpler, the better.

[Assuming we are using a fixed calendar, not like the "olden days".]

Answer 1

If you have a piano keyboard handy, you can use it as a mnemonic aid:

              Y mod 19 =

│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│    │    │    │    │     │    │    │
│    │    │    │    │     │    │    │
│  0 │  3 │  6 │  8 │  11 │ 14 │ 17 │
└────┴────┴────┴────┴─────┴────┴────┘

• half step = leap years 2 years apart
• whole step = leap years 3 years apart

Answer 2

A Hebrew Leap Year (in modern times) depends on which year of the 19-year cycle we are in. The years of the 19 year cycle that are leap years are: 3, 6, 8, 11, 14, 17, and 19. (to figure out which year of the cycle you're in, find the remainder of the current year when divided by 19).

It turns out there's a simple equation you can use:

(7y+1) mod 19 < 7 

[read, 7 times year, plus 1, divided by 19 & find remainder].

if the remainder is less than 7, it's a leap year. If it's 7 or greater, it's a regular year.

For example, for 5771 (this year):

7 * 5771 = 40397
40397 + 1 = 40398
40398 / 19 = 2126 remainder 4
4 is less than 7, so it's a leap year!

OR, you can use the "old-fashioned," non-mathy method of memorizing גוחאדז"ט - which comes out to: 3, 6, 8, 1, 4, 7, 9. Adding ten to the ones after 8 gets you: 3, 6, 8, 11, 14, 17, and 19 - like we found above.

Answer 3

Simpler is 5771 / 19 = 303 remainder 14 so it is a leap year.

Answer 4

Here's a version that can be done mentally. It works for all years between 5700-5799 (1940-2039):

1) Take the last two digits of the year, and add the second digit to half of the first. If there is a remainder, add 10. If this brings the total to 19 or more, subtract 19. You now know which year in the cycle it is. [Year 19 = 0.]

2) For cycle numbers greater than 7, add 1. Then check if it's evenly divisible by 3 -- if so, it is a leap year.

Example:

The last two digits of 5771 are 71.

1 + 3 (half of 7) = 4

Since there is a remainder: 4 + 10 = 14. --> [It is year #14 in the cycle.]

14 is more than 7, so we add 1, raising it to 15.

Since 15 is divisible by 3, it is a leap year.