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I am trying to figure out mathematically how many people were at a typical Pesach seder in the times of the Temple. I think the number can be approximated from the size, in terms of kosher portions of a typical animal that is suitable for a korban pesach. With that, we could divide by the size of a typical serving of meat. In our times that might be 1/4 pound, but since the korban pesach was to be eaten when satiated, it might be 1/8 pound. So this question boils down to how large is a typical animal that is suitable for a korban pesach. (The weight of kosher portions can be estimated by the weight of dressed meat, which might be found on secular websites related to food.)

Update: Since both a lamb and a kid are valid as a korban peasach, the answer, ideally, would provide information about both. The age of the korban is relevant, since young animals gain weight with time. The korban pesach must be at most one year old (Zevachim pg 25). I do not know the minimum allowable age. So, the question now asks for answers based on species (lamb or kid) the weight at one year and at the minimum acceptable age.

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    When people say dressed meat they mean (I think) without the organs. I assume organs of the pesach were eaten. – msh210 May 16 '16 at 16:53
  • @msh210 Point well taken. I'll update the question. Do you have any idea how much the kosher organs weigh? – Yehuda W May 17 '16 at 12:51
  • No, I don't, sorry. – msh210 May 17 '16 at 13:34
  • All karbanos have a minimum age of eight days. I am not aware of a source that names karban Pesach as an exception. – DonielF Mar 30 '17 at 4:10
  • Also note the Gemara in Kiddushin 41b: "'And all of the congregation of the assembly of Israel shall slaughter it in the late afternoon.' Did the entire congregation slaughter it? Did not only one person slaughter it? Rather, from here we can derive that the agent of a person is like himself." The mechanics of the exegesis aside, the Braisa clearly states that, theoretically, all of Klal Yisrael could partake of a single Karban Pesach. – DonielF Mar 30 '17 at 4:13
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Enlightened by the approaches taken in other answers and encouraged by the large number of views, I suggest this analysis as an answer to my own question.

There is agreement on the web that dressed weight is about 50% (e,g, sites below). There is less agreement on the weight of a lamb of a year of age or under.

This site gives the weight of lambs at 12 months as 20 kg or 44 lbs. http://www.fao.org/wairdocs/ilri/x5522e/x5522e06.htm

This site says the avg weight is 160 lbs at 8 months. https://www.cals.ncsu.edu/an_sci/extension/animal/4hyouth/sheep/sheepfacts.htm

This site gives weights of 33 to 55 kg (73 to 120 lbs) for ages of lamb ranging from 4 to 11 months, with the 33 kg for unweaned 4 months of age. http://www.makingmorefromsheep.com/market-focussed-lamb-and-sheepmeat-production/procedure_3.1.htm

This site says goats gain 1/3 to 1/2 lbs per day and reach 30 to 40 lbs in 66 to 69 days. It says lambs gain .4 to 1 lb per day. http://sheepgoatmarketing.info/education/targetbreeding.php

So 3 of these sites that give lamb weight at a year report: 44, 160, and 120 lbs. The low average seems to be an outlier but I will not throw it out. The average of these 3 estimates is a little over 100 pounds, or dressed weight of 50 lbs. One site said fats and organs are 3% of weight, so I am ignoring them.

Dressed weight includes bone. This site says some 70-75% of a lamb carcass is meat. http://animalscience.psu.edu/extension/meat/pdf/The%20Butcher%20Stole%20My%20Meat.pdf

But raw meat weight is not cooked meat weight. This site says that roasted lamb yields 74%. http://www.ars.usda.gov/SP2UserFiles/Place/80400525/Data/retn/USDA_CookingYields_MeatPoultry.pdf

So, a 100 lb lamb yields 50 pounds of dressed meat, or about 36 lbs of meat to roast, or about 27 pounds after roasting. Assuming a 1/8 pound serving of meat, that comes to 214 people per korban pesach, on average.

A small lamb of 30 lbs would yield a 1/8 lb serving for 64 people.

At lamb at birth weighs about 7 lbs (per one of the above sites). Assuming the above factors apply, that would be 15 people.

What if the participants were really satiated before eating the koran pesach (perhaps due to eating the korban chagiga), and ate only a k'zayis of meat. To find out the impact, we need to estimate the weight of a k'zayis of meat. I tried to do that as follows.

If a k'zayis is a cube 1.2" on edge, or 1.73 cubic inches, and if a cubic foot of water weights 62 lbs, and if meat is mostly water, then one kezayis of meat would weigh 1 oz (if I did the math correctly). If people only ate one k'zayis of meat, the above numbers would have to be multiplied by 2 (since there are 16 oz in a pound or 2 oz in 1/8 lb,)

Perhaps lambs are bigger now than they were in the past. Even so, it seems the seders were large back then.

  • Isn't a k'zayit of wine (like for the four cups) around 3.5-4oz? Wouldn't water be similar? – Monica Cellio Mar 29 at 1:09
  • i think a k'zayis is compressed volume- which means mass/weight as opposed to volum but 1 oz sounds about right – Asher Mar 29 at 3:11
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+100

I am trying to figure out mathematically how many people were at a typical Pesach seder in the times of the Temple.

Not mathematically, but Josephus (Wars book 6 chapter 9 section 3) says:

that feast which is called the Passover, when they slay their sacrifices, from the ninth hour till the eleventh, but so that a company not less than ten belong to every sacrifice… and many of us are twenty in a company

However, it should be noted that Whiston (the translator) had a bias toward this translation. (He notes in a footnote that the number ten-to-twenty matches some Christian belief nicely.) I have not confirmed the accuracy of the translation. (It's apparently from the Ancient Greek "καθ᾽ ἣν θύουσιν μὲν ἀπὸ ἐνάτης ὥρας μέχρις ἑνδεκάτης, ὥσπερ δὲ φατρία περὶ ἑκάστην γίνεται θυσίαν οὐκ ἐλάσσων ἀνδρῶν δέκα, μόνον γὰρ οὐκ ἔξεστιν δαίνυσθαι, πολλοὶ δὲ καὶ συνείκοσιν ἀθροίζονται", but I don't know Ancient Greek.)

  • goo.gl/mTvHBC on Google Translate :) – Shmuel Brin May 16 '16 at 19:20
  • Google translates it as "Prof. HN thyousin hand from the ninth hour until the eleventh, osper Dec faction Perry ekastin sacrifice is quite a minor man ten, only TAP CDR exestin dainysthai, let syneikosin and Accumulate". There seems to be a δέκα in there, which does mean ten) – Shmuel Brin May 16 '16 at 19:21
  • Due to the improvements of Google translate, it is now rendered: in order to bring them back to the age of eleven, then the faction of every one becomes the sacrifice of a few ten-year-old men, only to those who are dignified, many and conscious are summed up – wfb Mar 14 '18 at 0:19
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    10 - 20 probably means heads of households. women and children would probably increase the actual mouth count. – David Kenner Mar 16 '18 at 6:00
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Per this PDF, a lean, shorn lamb will provide about 46lb (20.8kg) of meat. Assuming that the weight given excludes the bones and other inedible portions of the animal (such as chelev), if a 1/8lb serving is used, per the OP, we get 368 servings, or that many places at a seder.

  • Also people only needed to eat a Kezayit. They probably ate more of other things. – Double AA May 16 '16 at 16:10
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    1. I assume it mentions "shorn" just to give the percentage of meat to total weight of the animal. (Obviously, woolly animals have a lower percentage of meat by weight, because more is wool.) The total weight of meat (not as a percentage) would, I assume, not depend on whether the animal is shorn, so you can omit that word from your answer. 2. Its estimate of 46 pounds is based on a 120-pound shorn lamb which is not "very fat". We should choose "very fat" animals for korbanos (citation needed!!), so perhaps the other estimate there (118 pounds) is more accurate. [continued] – msh210 May 16 '16 at 16:24
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    [continued] 3. The estimate there is for "bone-in chops and roasts" only, whereas (I assume) the pesach included also the organ meat etc. 4. The pesach was 8 days to 1 year old; see e.g. cals.ncsu.edu/an_sci/extension/animal/4hyouth/sheep/… , smallfarms.cornell.edu/2014/01/14/… . The PDF is assuming a 120-pound carcass. 5. A pesach could also be a goat. – msh210 May 16 '16 at 16:26
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    6. Its estimate of 118 pounds of meat from a 120-pound carcass makes no sense, so its numbers are highly suspect. (Especially because those 118 pounds of meat supposedly are only "bone-in chops and roasts" and from a long-fleeced animal!) – msh210 May 16 '16 at 16:34
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    @msh210 I wonder -- if I got a fat animal would that mean more fat or more meat? The fat would drip off as I roast it -- would that leave me the same amount of meat? Should I be looking for a more muscular animal? – rosends May 16 '16 at 17:43
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What time of the year are lambs born? California is the same zone, temperatures, growing season, etcetera as Israel and can be used to determine Ancient Israel's Lambing and Wheat harvest, for Passover and First Fruits. Yep, and "First Fruits" is about July 4.

Lambs are born during the winter for various reasons. ... Sheep are short day/long night breeders meaning they breed late summer/early fall and consequently their lambs are born in the winter and spring. Second, during the winter, the pasture that sheep normally eat is dormant. – Carroll County Grown carrollgrown.org/why-are-lambs-born-during-the-winter/

Lambs intended for meat are generally sent for slaughter at five to eight months old. The lambs on our farm were born in March, so, depending on the weather and quality of grass over the summer, they may be ready to sell in August. Year on a Sheep Farm | National Sheep Association https://www.nationalsheep.org.uk/know-your-sheep/year-on-a-sheep-farm/

British lambing season. Spring is a significant time in the farming calendar, as farmers get ready to care for more than 15 million ewes preparing to give birth.Feb 15, 2019 British lambing season | Countryside Online https://www.countrysideonline.co.uk/food-and-farming/...the.../british-lambing-season/

California: While lambing will last for six weeks, most of the lambs (and most of the work) will be concentrated between February 23 and March 23 (indeed, 90 percent of our ewes will lamb in this four week period). sacramentovalley.org/stories/remembering-how/

Field Grazing: The average daily gain of lambs on irrigated pasture will vary from 0.2 to .45 pound per lamb per day. Good feeder lambs on desirable irrigated pasture will usually gain at least 0.3 pound per day. ~ California Sheep Production. William C. Weir and Reuben Albaugh

So, the yearling lambs would have been born in February and March to be the Passover lamb, so their weight would be 7 lbs at birth + In Egypt, they WOULDN'T have made or ate ALL or many of the ADDITIONAL dishes in their hurried situation. The point was a quick, long-energizing, nurishment feast before they rushed out of Egypt and walked for many days. Every family was to have a lamb and only add other people, if they weren't going to be able to eat it all. So, I think it is fair to think in Egypt that they ate an average of 1 lb each person from sundown to sunrise, including babies through elderly. So, let's not skimp at a feast by having only one bite sized cube of lamb. Or as the Chic-fil-a cow would say, "Eat mor Chikin".

The Temple will be Rebuilt on Temple Mount.

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