The biblical narrative in Exodus 11 tells that all firstborn sons of Egypt died in a single night. While maybe there's no historical evidence of that, it would be interesting to know what was the estimated population in Egypt in 1446 BC, so we could deduce the number of (supposedly) killed children.
The exact population is a bit unclear. Estimates for the time period fall in between 2 and 4 million. This area of Egypt was one of the more densely populated areas in the world at that time due to the fertility of the Nile delta.
In the Biblical account, Exodus 12:30 says "for there was not a house without someone dead". Family size is also tough to nail down. Based on typical ancient family structures, we can assume that the average extended family was between 10 and 20 people rather than the lower numbers we see today. So, we can figure that the death toll was probably at least between 100K and 200K, assuming at least one death per extended family (household) with an affected population of about 3 million, give or take.
The Book of Exodus, as near as scholars can tell, was written during the time of the Babylonian Exile (in the 6th Century BC). That means any actual real events depicted would have had to have been part of an oral tradition among the Jewish people for nearly 1,000 years. Expecting such a work to be historically factual is rather unreasonable.
During the Babylonian Exile there would have been a lot of pressure on the Jewish people to assimilate. Such a process had already destroyed the 10 northern tribes during their exile in Assyria. So you can see where a story of how they had persevered as a unified people through a similar enslavement before would have been socially useful (if not outright essential to their continued existence as a separate people).
Thus Exodus was never intended to be a modern-style work of historical event documentation. Exodus is a story about who the Jews were as a people, and what was special about their relationship to their God. Don't miss the forest for the trees.
A number of estimates have been made for the population of ancient Egypt but, as the article The people of ancient Egypt says,
Egyptologists tend to dodge the issue of population numbers, as there are no statistics available and all such numbers are based on more or less educated guesswork.
The British Museum’s Dictionary of Ancient Egypt is among those publications which decline to speculate; there isn’t even an entry for ‘population’. Any figure for a precise year such as 1446 BC really would be a guess so estimates for the New Kingdom (approximately 1550 BC to 1069 BC) will have to suffice.
In Ancient Egypt Population Estimates: Slaves and Citizens, Mark Janzen cites the works of Karl Butzer and David O’Connor. Butzer’s (1976) estimate is around 2.5 to 3 million for the New Kingdom while O’Connor’s (1983) is higher at 2.9 to 4.5 million. On these differences, Janzen says in his footnotes:
Butzer’s attempt remains the best at scientific demography regarding pre-Roman Egypt.
[O’Connor]…these figures seem high, and Butzer’s estimate is far more likely due to it being based on substantial research on geographical and agricultural realities.
Source: The people of ancient Egypt
For the New Kingdom, Janzen also cites F. A Hassan’s (1997) estimate of 2.1 million while The people of ancient Egypt also cites Edward S. Ellis’ estimate of 5 million (Ellis, though, was not a specialist on either Egypt or demography). Of perhaps more interest is this:
According to the Harris papyrus somewhat in excess of 100,000 people belonged to the temple estates during the reign of Ramses III. James Henry Breasted thought that they had been less than 2% of the population, which would give an upper limit of 5,000,000 towards the end of the New Kingdom.
Ramses III ruled from 1186 to 1155 BC so this maximum of 5 million is some 250 to 300 years later than the OP’s date.
Estimates from ancient sources do not seem to cover the New Kingdom specifically; mostly they refer to the Roman period (Diodorus, Josephus Flavius).
Archeologists have extensively surveyed Israel. Archeogist Israel Finkelstein says, that around 2000 BCE 220 settlements, with an estimated population of 40,000. And in the eighth century over 500 sites, with estimated population, of 160,000. That’s the story on the ground folks!
I visited this forum today for the first time, after studying with interest the topic of the firstborn of Israel as recorded in Numbers 3 in a formal population census and wondering if there was any correlation between the number of Israelite firstborn at the time, namely 22,273 (verse 43) and the number of Egyptian firstborn who perished on the night of the exodus in Exodus 12: 29-30 and by projection, the total population of Egypt immediately prior to the exodus; which was a major population depletion event which caused a national crisis (Exodus 14:5). There does seem to be enough data in the exodus account and also in the book of Numbers, to help us project a reasonable population figure for Egypt as follows:
The number of Israelite firstborn males is given as 22,273 while the number of Israelite men in the highly organised and accurate census aged 20 is reported as being 603,550. Accepting the fact that a certain percentage of the males over 20 years were still unmarried, we can still reasonably assume with a 1:1 male:female population ratio that the number of adult men and women was around 1,206,550 although some Hebraic scholars might suggest a higher proportion of males. If we then add an additional one child per household we get 1,810,100 and if more likely two minimum additional children per household, we arrive at a conservatively projected total population for the Israelites of 2,413,100.
How should we then compare this population to that of the non-Hebrew Egyptian population?
One clue to the likely relative population magnitudes is given in Exodus 1:8-10 where a new King ( or Pharoah) came to the throne of Egypt and determined that the highly centralised Hebrew population living in the Nile delta region of Egypt had become "to numerous and powerful for us" and were literally 'swarming' across the land and precipitating a national security crisis.
The question must therefore be asked: "What relative percentage of Hebrew : Egyptian populations would have to be reached to constitute a critical proportion?
My suggested answer is certainly one-half (50%) of the native Egyptians (including all non-Hebrew) and more likely an equal number (100%) or more of the Egyptian population; since an emergency regime for mandatory birth-control was then also immediately forced upon the Hebrews, who were from the Hyksos stock. (Exodus 1: 10-22).
This would then mean that the total population in Egypt at the time, with similar social arrangements and household structures to the Hebrews, can be estimated at between 3,619,400 and 4,826,200, which seems to be confirmed by the other suggested ratios and estimates given in other parts of the various questions to this question.
There is also another possible answer here to the second part of original question posed by Jader Diaz back in 2012, namely "so we could deduce the number of (supposedly) killed children?".
I believe that a possible answer to this can be found in Leviticus 27 and also Numbers 3 and revolves around the topic of dedicating of first-born sons to the Lord and also the process for the redeeming of anything dedicated to the LORD.
This subject was first introduced to Moses by the LORD back in Exodus 11: 4-10 and was in order to make a clear distinction (verse 7) (or a political statement) between the firstborn children of the Hebrews, who were dedicated to the LORD and the firstborn children of the Egyptians, from the King right down to the lowliest subject; who were not dedicated to the LORD and in fact through Pharoah as their Federal leader, were collectively considered by the LORD to be stubborn, proud and resistant to all his words given through Moses and Aaron and steadfastly resistant, despite the many signs and warnings of authenticity which had been given over a period of time.
The actual killing of the Egyptian firstborn makes by the Angel of death is recorded in Exodus 12:29 and is then interestingly followed immediately by God's instruction for the dedication of all future firstborn males of the Hebrews in Exodus 13:1-16.
This is then followed by a brief but important statement of some relevance in Numbers 3:13 which links the taking of Egypt's firstborn with the setting apart of the firstborn of Israel and it seems only logical to assume that the LORD would deal fairly and equally with both of these nations, since as he says, "..for all the firstborn are mine."
This is a complex theological topic which is not relevant to the present answer, excepting that we can assume with some degree of certainly, that if the relative populations of Egypt and the Hebrews at the time of the exodus were substantially equal, then it can also be assumed with a similar degree of certainty, given similar social and family group patterns, that the percentage of firstborn among the Egyptians at the time was likely very similar to or the same as that among the Hebrews.
As already mentioned, this number is 'hidden in plain sight' and is given as 22,273 for the Hebrews (Exodus 3:43), which on the 1:1 ratio basis proposed above, would certainly be far less than the 100,000 or 200,000 proposed elsewhere in this discussion for the number of Egyptian firstborn who died on the night of Passover, preceding the Exodus.
The Wikipedia's World Population Page shows that is estimated that the world population grew from 35 million in 2000 BC to 50 million in 1000 BC. This doesn't answers the question but suggests that Egypt's population could be somewhere between a million to ten million at that time.