Jewish Leap year explained

Hey Rabbi, I was curious why Judaism sometimes adds an extra month to some years? What's the reason behind that?

Thank you for your question.

As you wrote, we are the only religion that adds an extra month to the year, and it is important to know why we do this and the importance this has on the Jewish calendar. I would like to start by introducing two Halachot brought in Tractate Megillah, page 5a:

תלמוד בבלי מסכת מגילה דף ה עמוד א

1. ורבנן דקיסרי משום רבי אבא אמרו: מנין שאין מחשבין שעות לחדשים? שנאמר עד חדש ימים, ימים אתה מחשב לחדשים, ואי אתה מחשב שעות לחדשים.
2. ואמר רבי אבא אמר שמואל: מנין שאין מונין ימים לשנים? שנאמר לחדשי השנה, חדשים אתה מונה לשנים, ואי אתה מונה ימים לשנים.

The Talmud writes:
1. We calculate month, by days not hours. As it is written in the book of Numbers, (Chapter 11, verse 20), “month of days”.
2. We calculate years, by month not days.

To understand these two halachot, we need to realize that the month is calculated by the time it takes the moon to circle the earth, which takes 29 days, 12 hours, and around 44 minutes.

One might say that the new month should begin precisely at the moment the moon completes its cycle, whtch is 12 hours into the 30th day, and this exact time should mark the beginning of the new month. However, from the verse "the month of days," we understand that months are calculated based on the number of days not hours therefore we can only calculate the month by days so how do we do it?

This is why the month of Nissan, which has 30 days, extends 12 hours beyond a complete cycle. The following month, Iyar, has 29 days and ends 12 hours earlier, thus balancing the overage from Nissan. This pattern ensures that the months align correctly throughout the year.

When it comes to calculating the year, then there are three different methods used by three religions, each one calculates it differently. In order to fully appreciate the Jewish method, I would like to first start with the way the Christian and Muslim religions calculate their year.

The Christian way :

The way the Christian religion does it is, that they don’t calculate at all the luner month, they only regard the solar year, so since it takes the sun to circle the earth 365 days, there is no month in a solar year. So, what do they do? They cut the 365 days into 12 corresponding parts in order to make up the 12 months of the year.

The Muslim way:

The Muslim religion’s way of calculating is that they only regard the lunar month, which each month as we said takes 29 days, 12 hours, and 44 minutes to circle the earth. So, the lunar cycle has no year, just an accumulation of months.

Since the Muslim religion follows the lunar month, at the end of twelve cycles, they will have ended the year, so 29.5 multiplied by 12 comes to 354 days for a lunar year, around 11 days less than the solar year. Since that is the way they calculate, it comes out that the lunar year steadily is pushed back 11 days from the solar year, so if, for example, the Muslim holiday called Ramadan falls at the beginning of spring, the next year it will fall 11 days before spring, and the next year it will be 22 days before spring. Eventually, Ramadan will fall in the middle of the winter and continue falling back in the year.

The Jewish Way of Calculating:

The Jewish religion, however, has two calculations, which is that the month is calculated by the lunar month, and the year is calculated by the solar year. This is learned from the verse in Deuteronomy Chapter 16, Verse 1:

דברים פרק טז פסוק א,
שָׁמוֹר אֶת חֹדֶשׁ הָאָבִיב וְעָשִׂיתָ פֶּסַח לַה' אֱלֹהֶיךָ כִּי בְּחֹדֶשׁ הָאָבִיב הוֹצִיאֲךָ ה' אֱלֹהֶיךָ מִמִּצְרַיִם לָיְלָה:

‘Guard the spring month, since it was in the spring that Hashem took you out of Egypt’.

So, if we were to keep only the lunar month, then eventually Passover would not be in the spring; it would be in the middle of winter, as explained above. Therefore, the way we calculate the year is that after 3 years of lunar months, we will be over the 30-day deficit, that is when we add another month of Adar (since, as the Talmud wrote earlier, we cannot add days to the year, only months), and that will sync the lunar year to start again at the beginning of spring, and then Passover will always be in springtime.

Wishing you well.

Tractate Megillah, page 5a:

Deuteronomy Chapter 16, Verse 1