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Calculating the Date of Birkat Hachamah

Calculating the Date of Birkat Hachamah


According to tradition, the sun was created at the moment of the spring equinox1 which coincided with the first moment of the fourth day of creation—the day when G‑d set into orbit the sun, moon and all the heavenly bodies.2 Since, in Jewish tradition, the day begins at the previous nightfall – as we see in the Torah's account of the story of creation, "It was evening, and it was day..." – this actually happened with nightfall on Tuesday evening.

When the sun reaches this starting point again at the exact same time of day and on the same day of the week, we recite the Birkat Hachamah the next morning, shortly after sunrise.3 This occurs once every 28 years—and this year on Nissan 14, 5769 (April 8,4 2009).5

(In other words, the spring equinox occurs every year, but on different days of the week and different times of the day. But once in 28 years it occurs on Wednesday [the fourth day of creation] at the moment of the day's onset.)

Please note, from an astronomic point of view, nothing unusual will happen on this date; the sun, moon, planets and stars will not be aligned in any specific pattern.6

The Calculation

The starting point is the first moment of the (evening preceding the) first Wednesday in history—the fourth day of Creation. Let us use Tuesday evening at 6:00 p.m. as a rounded off time.

According to the astronomical calculations of the 3rd century Babylonian sage Shmuel – regarding whom the Talmud7 says, "He was familiar with the pathways of the heaven as with the streets of his hometown Neharda'a" – the length of a solar year is 365.25 days, or 52 weeks plus 1¼ days.8 It thus follows that precisely one year later, when the sun returned to the original position it occupied at the moment of its creation, it would be 1¼ days (one day and six hours) later in the week: Wednesday at midnight. After two years, it would be 2½ days later in the week: Friday at 6:00 a.m. Only after 28 years, would the sun return to that position on Tuesday at 6:00 p.m.

Birkat Hachamah vs. the Actual Date of the Spring Equinox

Many will undoubtedly take note of the fact that the spring equinox this year will fall on March 20—nineteen days before we will recite the Birkat Hachamah.

To understand the reason for this, let us briefly explain the origins of the Gregorian calendar – the calendar widely used today – which replaced the hitherto used Julian calendar:

The Julian calendar was introduced by Julius Caesar in 46 BCE,9 and – like that of Shmuel – was based on a 365.25 day year. Its structure was as follows:

a. All future years were to consist of 365 days in a normal year, and 366 days in a leap year.

b. A leap year would occur every fourth year.

c. The spring equinox was set as occurring that year on the 25th of March at 6:00 pm. But since the Hebrew day begins at nightfall, the corresponding Hebrew date for the equinox would actually be the 26th March—an important factor as we will soon see.

So, in each Julian millennium there are 365,250 days (750 normal years [750 x 365 = 273,750] and 250 leap years [250 x 366 = 91,500]).

As modern science has established, however, a solar year is 365.24219 days.10 As such, 1000 tropical years is 365,242.19 days.

The Julian millennium – and Shmuel's too – is thus 7.81 days longer than the accurate solar millennium (365,250 - 365,242.19).

By the year 1582, the Julian calendar was about 10 days ahead of the tropical year, and an adjustment was again necessary. Pope Gregory XIII introduced two adjustments to the calendar, and the "Gregorian" calendar was established. These two adjustments were as follows:

a. Ten days were removed from the calendar in 1582.11

b. To prevent the need for any future corrections, a centenary year not divisible by 400 is not a leap year. The years 1700, 1800, and 1900 were therefore not leap years, whereas the years 1600 and 2000 were.

It follows that the Gregorian calendar is currently 13 days ahead of the Julian calendar: 10 days for the initial correction, plus 1 day each for the three 'skipped' leap years in 1700, 1800, and 1900. And the Gregorian calendar is 18 days ahead of Shmuel's year: the extra 5 days due to Caesar having established the spring equinox as occurring on March 26 instead of March 21.12

The Chassidic Angle

So what is the rationale behind saying the Birkat Hachamah on a date predicated on "faulty" calculations?13

The Rebbe posited14 that this is one of those rare conundrums that cannot truly be answered based on the dry facts, rather it requires an explanation culled from the mystical teachings of Torah.15

As mentioned above, the Birkat Hachamah is scheduled for the spring equinox, at the moment when the sun was set into orbit.

Though we celebrate the anniversary of all of creation – including the sun – on Rosh Hashanah,16 approximately six months before the spring equinox, there is actually a debate in the Talmud17 whether the world was created in Tishrei or Nissan. The consensus reached by the Talmud is that with regards to the counting of years we count from Tishrei, but in all areas of Jewish law that pertain to the calculations of "tekufot," seasons (and equinoxes falls under this category), we calculate from Nissan.18

According to mystical teachings,19 both opinions are correct and not contradictory. All agree that the world was created in Tishrei, but that G‑d conceived the idea of creation in the month of Nissan. The Talmudic "debate" is which one of these two dates is more significant.20

The Talmudic ruling quoted above implies that with regards to seasons we ascribe primacy to Nissan—to the conception of the world in G‑d's thought, and the spiritual equinox, as it were: the time when the concept of a spring equinox entered G‑d's mind, rather than the point at which this concept was concretized in physical time. We are actually calculating from a base date that doesn't even exist—the spring equinox that "occurred" in the year before creation!

Accordingly, the timing of this event is set by Shmuel's system, which, according to our Sages, is precisely aligned with the "spiritual" seasons.21

(For more elaboration on this topic, see But the Sun is in the Wrong Place!)


Though Rosh Hashanah, when we celebrate the anniversary of the creation of the world, is on the 1st day of Tishrei – approximately six months before the spring equinox – in all areas of Jewish law that pertain to the calculations of "tekufot," seasons (and equinoxes falls under this category), we calculate from Nissan.
For more on this topic, see last section of this article: "The Chassidic Angle."


Talmud, Berachot 59b. Code of Jewish Law, Orach Chaim 229:2.


As will be explained further on in this article, Birkat Hachamah is based on the solar calendar, calculating a solar year at 365.25 days. The Gregorian calendar that is widely used today also has its origins in a 365.25 day year. It thus follows that the date for Birkat Hachamah will closely correspond to a date on the Gregorian calendar—which explains why the next four Birkat Hachamahs (2009, 2037, 2065 and 2093) will all be on April 8. (See also footnote 12.)


This calculation seems to be problematic because 5769 is not divisible by 28. This Birkat Hachamah, the 206th cycle, should seemingly have been last year, in 5768 (206 x 28 = 5768).
This discrepancy arises because there was no year '0'. The first 12 months after creation were labeled year '1', hence the first Birkat Hachamah was said – by Adam presumably – 28 years later, in the year 29. All subsequent cycles are thus divisible by 28 with a remainder of 1.


In fact, the arrangement of the heavenly bodies will not even resemble the way they were at the time of creation.


Berachot 58b.


Talmud, Eruvin 56a.
Modern astronomy calculates the solar year (also known as a "tropical year") to be 365 days, 5 hours, 48 minutes, and 45 seconds (365.24219 days), 11 minutes and 15 seconds shorter than Shmuel's calculation.
Shmuel, a prominent scholar and astronomer, was no doubt aware of the more accurate duration of a tropical year. Nevertheless, he used the less accurate 365.25 since this figure is much easier to work with, especially for the general populace that for the most part was not proficient in mathematics, and needed to make computations for the performance of various religious precepts (see Sefer Ha'Ibbur by the Ibn Ezra 8a; Responsa Tashbetz vol. 1 s. 108).
Similarly, we find that the Talmud (Eruvin 13b) gives a value of 3 for pi instead of 3.141592. The astronomer Ptolemy acknowledged that he, too, used multiples of 60 in order to avoid dealing with fractions. (Ptolemy, Almagest 1:10).
Another Talmudic sage, Rabbi Adda bar Ahava, computed the tropical year as 365 days, 5 hours, 55 minutes and 25.4 seconds—6 minutes and 40.4 seconds longer than today's calculation, about 5 minutes shorter than Shmuel's year, and the more accurate of the two systems.
Shmuel's year is used for determining when to say Birkat Hachamah and the prayers for Dew and Rain in the daily prayers. Rabbi Adda's year is used for all other halachic calendar calculations.


First, in order to correct previous inaccuracies, the year 46 BCE was made to last 445 days... the so-called "Year of Confusion."


See above, footnote 8.


This was immediately accepted in Spain, Portugal and Italy. Thursday, October 4, of that year was thus followed by Friday, October 15. Germany, Sweden and Denmark accepted the changes in 1700. England accepted the Gregorian calendar in 1752, by which time the Julian calendar was 11 days ahead of the tropical year: September 2 of that year was thus followed by September 14. In Russia, the Gregorian calendar was finally accepted on February 14, 1918, by which time 13 days had to be dropped.


For this reason, in the 22nd century Birkat Hachamah will always occur (in the years 2121, 2149, and 2177) on April 9, rather than April 8. According to the Gregorian calendar a centenary year not divisible by 400 is not a leap year. The year 2100 is not divisible by 400 and will thus not be a leap year; the Gregorian Calendar will fall one day further behind Shmuel's calendar.


The Pachad Yitzchak (entry Chamah b'Tkufatah) explains that "one who recites this blessing, even if not in its proper time, praising G‑d for the works of creation, has not recited a blessing in vain—for it is a blessing of praise that is worthy of being said at any time and moment."


In a talk delivered on the Last Day of Passover 5713 (1953).


Ordinarily, each method of Torah exegesis is self-sufficient, supplying the answers to all the questions it may present, without need to resort to another method to provide resolutions.
Torah, however, is essentially G‑dly wisdom, and there is a need to ensure that we always bear in mind that it – every part of it, even those that seem most logical – is actually Divine wisdom. Therefore G‑d instituted that certain issues would remain unanswerable without an understanding of the concepts as they are elucidated in the mystical texts—those teachings of Torah that are overtly Divine (see Likkutei Sichot vol. 19 p. 209).


Rosh Hashanah actually is the anniversary of the sixth day of creation, the day when Adam and Eve were created. The sun was thus created two days earlier, in the 28th of Elul.


Rosh Hashanah 10b.


Ibid. 12a.


See Nehar Shalom, kavanot for Rosh Hashanah; Likkutei Sichot vol. 16 p. 483-4.


See Our Other Head for more on this topic.


This also explains why we follow Shmuel's calculations for the purposes of computing tekufot, though Rabbi Adda's calculations (see above, footnote 8) more precisely describe the manner in which the seasons play out in physical time (as noted by Maimonides, Laws of the Sanctification of the Moon 10:6, "This [Rabbi Adda's] calculation is more accurate than the first one [Shmuel's]").

Much of the information presented above originally appeared in an article by Dr. Julian Schamroth, on
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Carolina Phx., AZ. via March 12, 2012

Solar Max Isn't this whole subject interesting now in 2012/ 5772, in light of the current scientific facts about the sun's current condition being called The Solar MAX.
Between this year of 2012/ 5772, and 2013/5773 Nasa scientists say the sun will reach a Solar Maximum. Not being sure what that outcome will be for the earth.
Maybe Messiah will come on a day like this! In LIGHT of this news it gives new meaning to Malachi 3:20, in the Neviim.
Maybe it's not about days and dates but cosmic seasons and their implications. Reply

Motti Melbourne, Australia March 11, 2012

Myths and Maths of the Blessing of the Sun I see that this article is still attracting comments 3 years later. (I was sent an automatic email alert of a new comment posted here.)

If anyone is still interested in my article on Birkat Hachama (title is in the subject line of this post), which answers many of the questions posted in the comments, it no longer resides at the web-address given above. It is now at:

The site also contains several other articles on related matters.

Anonymous tomball, tx March 11, 2012

creation I thought the sixth day of creation happened on the 1st of tishrei on Rosh Hashana, when humans were created, how then is the fourth day of creation in nissan?

I'm a little confused because I thought the Messiah will come on a day like this? Reply

mel monsey, ny usa April 12, 2009

birchat hachama the equanox was not on 3-20th in NY, it was on 3-17 SR=SS 7:04. On 3-22 it was on the equator 6:00 am 6:00 pm. Reply

Motti Melbourne, Australia April 12, 2009

Birkat Hachama - the Truth (3) Sorry about the typos in my previous post - and the broken link. Should have been:

The article is called "Myths and Maths of the Blessing of the Sun". It has explains more clearly why this is observed every 28 years, and contains some rational theories about its religious and cultural significance, and the process by which the date was originally set. Reply

Motti Melbourne, Australia April 12, 2009

Birkat Hachama - the Truth (2) There are glaring errors in this article. Firstly, the Julian calendar began in BCE 45 (astronomical nr: -44), NOT 46 BCE. And what is your source for the extraordinary statement that Julius Caesar set the March equinox date at Mar 26 instead of March 21? It makes no sense either logically or astronomically. Firstly, why should it have been March 21? The equinox that year was March 22 Julian, and what is your evidence that Julius put it at March 26?

AND you doesn't understand the Jewish calendar either! The 12 months after creation was year 2 NOT 1. (Footnote 5).
There were two other competing numbering systems, but it is clear you are not using them for you number this year as 5769. And the Shmuelian March tekufa of that year was on THUR Mar 26 Julian at 06:00 (Jewish Time). The first Shmuelian tekufat Nisan of the calendar (Wed at 00:00) was the (mostly theoretical) year 1, in the months BEFORE the creation.

Want the truth? Read this: Reply

Motti Melbourne, Australia April 12, 2009

Birkat Hachama - the Truth David Schreiber, your comment is only correct for a two-body system. It cannot apply to the solar system or even the Sun-Earth-Moon system because a three or multi-body system DOES have an external reference point. And exactly what bearing does Eintein's theory have on this. Just because he used the word "relative" in his theory? Exactly where in Einstein's theories did you read or infer this? (Would you care to quote the relevant passage?)

Are you referring to his general theory of relativity or his special theory of relativity. Reply

David Schreiber Gandelman Jerusalem, Israel April 11, 2009

Re 2: Lindsay But the Sun does not have an orbit That was a big issue in Galileu's times but since Einstein's Relativity there's no diference in saying that the sun orbits earth or the oposite. It's all dependent on where do you set the reference point and how do you choose to calculate it.

It's similar to standing in a moving train with no windows. You are going fowards to a outside observer and not moving at all to a inside observer.

And of you do look out from a window, is the ground going backwards or the train moving fowards? Depends if you fixing the reference on the outside or inside observer. Reply

Yochaon Bogart Sharon, MA/USA via April 7, 2009

Theological, not purely astronomical celebration With arbitrary precision there may never be an EXACT lineup. 365.25 is a great first approximation, hence the celebration.
Use a more accurate 365.24 days/solar year and you get a 175 year cycle. Heres why:
Each yr would then add 1.24 days, or 124/100 days. That fraction reduces to 31/25 days/year. Solve Y * 31/25 = W * 7 for integer numbers of Years and Weeks. First solution is W=31 and Y = 175. Thus, for celebration purposes the Rabbis are right in choosing the first approximation 365 1/4 days per year! Reply

Stephen Weinstein Camarillo, CA April 6, 2009

Re: Lindsay "But the sun does not have an orbit" 1. When we refer to the sun being in the same position, we actually mean that the earth is in the same position (relative to the sun). The earth's position in its orbit (but not its position in its rotation) repeats every approximately 365.2422 days (approximately 1 year). The earth's position in its orbit and the earth's approximate (although not exact) position in its rotation repeat every 1461 days (approximately 4 years). This and the day of the week repeat every 10,227 days (approximately 28 years).

2. You are incorrect in saying that the sun has no orbit. The sun orbits the center of the Milky Way galaxy (the planets stay with the sun, just as the moon stays with the earth during the earth's orbit of the sun). However, the period of this orbit is much longer than the times discussed in this article and is not considered in calculations of the date of Birkat Hachamah. Reply

Lindsay April 6, 2009

But the sun does not HAVE an orbit! I kept reading over and over about how this celebrates the sun being in the same position, and the sun being set into orbit. But we know those are scientific falsehoods! The sun does not HAVE and orbit. It does not circle the earth, as ancients believed. So why is fact being so blatantly ignored here? We are a learned people...celebrating a primitive mistaken belief hardly seems like a good thing! Reply

Anonymous Phoenix, Arizona via April 6, 2009

Timing So, in fact of point would it not hold true that the head of the biblical new year would be at the first of Nissan, and the time of Rosh Hashanah would be the begining of the civil year?
One of men-civil -
One of G-d-perpetual?
Would it not be the new year of
5769 @ Nissan 1,?
In divine providence?
Fall-mens minds and ways
Spring-spiritually G-d's ways? Reply

Dovid Wineberg South Africa April 5, 2009

the best! The best- by far- and the most readable article on this subject. Thank you! Reply

Anonymous April 3, 2009

Shmuel's millenium In Response to Stephen Weinstein, although the article goes through the calculations and that Shumel determined the year to be 365.25 in the year 46, I don't think it was clear that this was the epoch for the current observance. Rather the article implies the epoch was the 4th day of creation and explains the difference from the year 46, but not that this was observed on the equinox itself until that point. Reply

Leon Feldhamer Beit Shemesh, IL via April 3, 2009

The Rebbe's comment How we can ascribe a time to G-d's conception of creation, before time itself was created? Reply

tmimah sm, ca April 2, 2009

When Does the Tekufah Happen? Is it always on the 14th day of the month; hence Yad - related to the "Hand of God"? Is this true for the summer winter and fall tekufah too? Reply

Stephen Weinstein Camarillo, CA April 2, 2009

Shmuel's millenium The equinox occurs every 365.2422 days. The "drift" during 2000 years would be 15.6 days, not 19.

The article states that the Shmuel's calculations were based on the equinox of the year 46 BCE; that was between 2050 and 2060 years before the present time, so the drift would be 16.0 days.

The article states that "The spring equinox was set [by Julius Caesar] as occurring that year [46 BCE] on the 25th of March at 6:00 pm." I calculate the equinox to have actually been on the night of March 23-24 (Julian date) that year. This would account for another 2 days of difference, for a total of 18. (Shmuel may have actually been using the Roman calendar, not the true Julian calendar.)

Finally, although the current equinox is on March 20 (Gregorian) in the U.S., this is not true everywhere in every year. In the last year prior to each civil leap year (in other words, in 2007, 2011, etc.), the equinox occurs in Israel on March 21, which is only 18 days before April 8, not 19 days. Reply

Menachem Posner for April 2, 2009

Shmuel's millenium Shmuel based his calculations on that which he observed at his time. This means that he started out (approximately 2,000 years ago) with a date which is quite similar to (but not the same as) the modern equinox, and things started drifting from there. Reply

Anonymous April 2, 2009

Shmuel's millenium If Shmuel's millenium is nearly 8 days longer than the actual solar millenium, shouldn't Birkas Hachama by now be about 45 days (7.8 X 5.7) after the equinox and not 19? Reply

Stephen Weinstein Camarillo, CA March 29, 2009

Nisan, Tishri, and the seasons We know now that the seasons are reversed in the hemisphere on the other side of the equator. Could the references to creation being either near Tishri 1 or near the spring equinox refer to the same time of year, in light of the fact that Tishri 1 is near to the equinox near to when spring begins in half of the world? Reply

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