Pesach and the Jewish Calendar

Guest Post from R’ Meir Deutsch (c) [lightly edited by me]

© מאיר דויטש ניסן ה’תשע”ו
את חג המצות תשמור […] למועד חודש האביב
The Hebrew calendar is based on a combination of the lunar and solar calendars, as written in Bereshit:

“יהי מאורות ברקיע השמיים להבדיל בין היום ובין הלילה, והיו לאותות ולמועדים ולימים ושנים.” 

Our calendar is based on the Babylonian one. The names of the months are very similar, and the Babylonian calendar has also a leap year with ADARO SHENI. The Hebrew Calendar, according to Rav Ada (lived in the third century in Pumbedita) has a cycle of 19 years to merge the lunar and solar years. In his calendar we have:

365 days

5 hours

55 minutes

25 seconds.

The length of a year as known today is: 365 days, 5 hours, 48 minutes and 46 seconds, a difference of just 6 minutes and 39 seconds.

For order’s sake, I want to mention, that according to Shmuel  in Eruvin 56a the solar year is 365 days and 6 hours.

ואין בין תקופה לתקופה אלא תשעים ואחד יום ושבע שעות ומחצה.

In HALACHA Shmuel’s calendar was adopted. According to his calendar the ברכת החמה is fixed. Shmuel’s calendar is based on the Julian calendar. As the HALACHA is based on Shmuel’s calendar, the calendar of Rav Ada is not mentioned in the Talmud, but most of the calculations are based on his calendar.         

Today we are in the Jewish year 5776 = ה’תשע”ו, and it is a leap year. When do we add another Adar to our calendar to match the two calendars? According to the formula of the Hebrew calendar the leap years in the 19 year circle are גו”ח אדז”ט, meaning that the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years are leap years.

What do our sages say in that matter? The Talmud in Sanhedrin 12a says:

“תנו רבנן: אין מעברין את השנה לא בשביעית, ולא במוצאי שביעית.”

Don’t we have a problem this year with that? Last year we had a Shmitta year, if so, how come that the current year is a leap year? This problem can be solved by the Yerushalmi:

מסכת פאה פרק ה הלכה א: “ר’ יונתן ברי’ דר’ יצחק בר אחא שמע לה מן הדא אין מעברין את השנה לא בשביעית ולא במוצאי שביעית ואם עברוה הר”ז מעוברת.”

We mentioned earlier which years are leap years according to the formula. Does this formula match the learning of out sages?

Let us have a look at Sanhedrin 11b:

“ת”ר על שלושה דברים מעברין את השנה: על האביב, ועל פירות האילן, ועל התקופה”.

Why do we have to make a year a leap year?

We are ordered to celebrate Passover. We have a date on which we should celebrate it, but we have a condition for fixing the date – the season. The Torah, in Shmot (23, 16) says:

“את חג המצות תשמור […] למועד חודש האביב”

And in Devarim (16, 1) we find written:

“שמור את חודש האביב ועשית פסח לה’ א-לוהיך”

The dates are; for the Pesach sacrifice the 14th of the month (Nissan), and Chag Hamatzot the following day. These dates are according the lunar calendar, but the condition that it should be in the [first] month of spring is determined by the solar calendar. The Rambam writes on this matter:

(רמב”ם הלכות קידוש החודש פרק ד הלכה א): “ולולא הוספת החדש הזה היה הפסח בא פעמים בימות החמה ופעמים בימות הגשמים.”

We have four seasons, Autumn/fall, winter, spring and summer, we call them:

תקופת תשרי, תקופת טבת, תקופת ניסן ותקופת תמוז.

As we are dealing with seasons, they are fixed by the solar calendar.

Tkufat Nissan – 21st March (length of day and night equal)

Tkufat Tamuz – 21st June (the longest day)

Tkufat Tishrei   – 23rd September (length of day and night equal)

Tkufat Tevet – 21st December (the shortest day).

Rashi in Mesechet Rosh Hashana 21a explains the saying of Rav Huna:

“ואביב הוא יום תקופת ניסן, שניסן של חמה נכנס בו, שניסן קרוי אביב על שם בישול התבואה, ובישול התבואה אינו אלא לחשבונה של חמה, שהקיץ והחורף אחר חשבון החמה הם, […] ואילו היה תקופת ניסן ביום חמשה עשר – לא היינו צריכין לעבר את השנה, אלא נעבר אדר ונדחה את ניסן יום אחד, ותפול התקופה ביום ארבעה עשר, אבל כשהיא באה ביום ששה עשר בניסן – לא די לן בעיבורו של אדר, וצריכה השנה להתעבר […].”

And the Rambam writes on this matter:

(רמב”ם הלכות קידוש החודש פרק ד הלכה ב)

“על שלשה סימנין מעברין את השנה, על התקופה ועל האביב ועל פירות האילן, כיצד? בית דין מחשבין ויודעין אם תהיה תקופת ניסן בששה עשר בניסן או אחר זמן זה מעברין אותה השנה, ויעשו אותו ניסן אדר שני כדי שיהיה הפסח בזמן האביב [שהוא 30 יום הראשונים של תקופת ניסן], ועל סימן זה סומכין ומעברין ואין חוששין לסימן אחר.” 

Tkufat Nisan starts on 21st March must start by the 14th of Nisan. If it starts on the 15th we add one day to Adar, and if it starts on the 16th or later we make it a leap year and add the second Adar, otherwise Passover will not be celebrated in the spring, which is the first month of Tkufat Nisan.

Let us take for example this year – 5776. If we did not add the second Adar, the 14th of Nisan, would fall on the 24th of March, which is within the first month of Tkufat Nisan, and Passover would be celebrated in the month of spring. Did we have to add, according to Rashi, the Rambam or the Talmud, the second Adar to the calendar this year? Do we celebrate Passover this year in the first month of spring? 

חג מצות שמח.

Author: pitputim

I've enjoyed being a computer science professor in Melbourne, Australia, as well as band leader/singer for the Schnapps Band. My high schooling was in Chabad and I continued at Yeshivat Kerem B'Yavneh in Israel and later in life at Machon L'Hora'ah, Yeshivas Halichos Olam.

5 thoughts on “Pesach and the Jewish Calendar”

  1. Your error is in your assumption that tekufat nissan is on 21-Mar. That is the date of the sun’s actual tekufah, and if we had a beit din it would use that as its guide, but we follow tekufas Rav Ada, which is on 28-Mar. Therefore if we had not added the month Pesach would fall in the last days of winter, before the tekufah.

    That is why the Catholic Easter, which is based on a 21-Mar tekufah, was on Purim this year, and will catch up to us next year when they have a leap year, while Orthodox Easter, which is based on a 3-Apr tekufah, wihch is a slightly updated version of tekufas Shmuel.

    You also erred in claiming that the halacha follows Shmuel’s cheshbon. In fact for the purpose of the calendar it follows Rav Ada. But for those purposes that are given over to every person to calculate for himself, we use Shmuel’s cheshbon, even though we know it’s incorrect, because it’s simpler.

    Another error is your claim that Pesach must be in the first month after the tekufah. It’s obvious that it can’t be so, because if it were so then the other considerations (the barley, the lambs, the roads) could never be taken into account. The decision whether to make a leap year would be completely inflexible. Bet Din could calculate years in advance when the leap years would have to be, and it could never be a judgment call. However we know that it was a judgment call, and the Sanhedrin had to carefully consider all the factors before deciding when to have a leap year. This proves that it is permitted to have Pesach in the second month of the spring.


    1. @ milhousevh Thank you for your comments.
      Thank you for mentioning the Tkufat Nissan of Rav Ada. About the Beth Din; who knows what a Beth Din in our times would rule?

      I did not write that Halacha follows Shmuel’s chesbon. I wrote “[…] the calendar of Rav Ada is not mentioned in the Talmud, but most of the calculations are based on his calendar.” Where did I err? You see, we are in agreement on this.

      About my “error” that Pesach must be in the first month after the tekufah. Let us see what is written. It says למועד חודש האביב and שמור את חודש האביב Month and not Tkufa. It says month and not months. Is it not so? I did not find anywhere written חודש באביב.
      You are right about the other considerations before the formula for the new calendar. The Sanhedrin had to do the calculations and decide accordingly. They had to have a decision before the end of Adar and decide if these considerations are going to happen in the next months. If because of weather or other conditions the goal was not reached, what then? Maybe that is why the Rambam said: “ועל סימן זה סומכין ומעברין ואין חוששין לסימן אחר.” Was this rule above any of the other rules? One of the reasons of our sages not to add the second Adar in shmita year and the year following it was not to delay the Chadash. We can see in this REGEL that after the Korban Pesach they hurried home to gather the barley crop, and did not stay in Yerushalayim for the reminder of the Regel like in Sukoth.
      לא תוכל לזבוח את הפסח באחת שעריך […] ובישלת ואכלת במקום אשר יבחר ה’ א-לוהיך בו [אבל עולי הרגל לחוצים לצאת לקציר, והפסוק ממשיך] ופנית בבוקר והלכת לאוהליך” (דברים טז). חזור הביתה והחל בקציר.

      As I said you are right about the other considerations. Let us take the barley you mentioned. If the barley is not ripe how could they bring the Omer? Did they use the timing for bringing the Omer as described מהחל חרמש בקמה or LIRTZONCHEM and not Mimacharat Hashabat?
      All well now, but it is hard for me to accept your deduction saying that it is permitted to have Pesach in the second month of the spring.
      Wishing you Chag Sameach and thank you again for your comment.

      It is Passover and I am BECHIPAZON to do the Bdikat Chametz.


  2. You wrote “As the HALACHA is based on Shmuel’s calendar”. In fact it’s based on Rav Ada’s.
    It’s obvious that if a beit din existed nowadays it would look for the tekufah at the actual sun, not at Rav Ada’s cheshbon, with its 2000 years of accumulated error. But since our roshei chodesh were sanctified by Hillel Nesiah’s bet din according to a fixed formula, we are stuck with them until a new bet din is established.
    שמור את חודש האביב simply means to make sure that the month of Nissan is timed so that Pesach falls in the spring. It needn’t be in the first 30 days. It must be so, because if not then how could they ever delay it for any of the reasons listed? The fact that they could and did delay it, and that the decision whether to declare a leap year depended on a subjective judgment weighing many factors, which was entrusted only to the most senior judges of the land, who must not have any personal biases (i.e. the cohen gadol is excluded), proves that Pesach may be any time in the spring. If it were restricted to the first 30 days there would be no flexibility at all, and therefore any five-year-old could decide it, as is the case nowadays.


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