The population of Numenor was derived from the Three tribes of the Edain that dwelt in Beleriand before Morgoth overran the continent after the Battle of Unnumbered Tears in 472 FA. These were the Beorians, Hadorians and the Haladin, to whom can be added the somewhat separate Druedain who lived among the Haladin, and presumably survivors of the people of Bor, the Easterlings who remained faithful at the Battle of Unnumbered Tears. In my article on the populations of Beleriand at their height around 450 FA, just before the Dagor Bragollach, I estimated that the Edain numbered around 150,000 at their greatest, divided between the three tribes and a mixed group who remained in Estolad. In the century between this point and Morgoth's destruction their population certainly declined catastrophically through battle losses and their lands being overrun by Morgoth's minions. But a remnant of the Hadorians and Beorians survived as thralls in Dor-Lomin, and some of the Haladin clung on in Brethil, as well as presumably some who fled to the Isle of Balar or the southern forests with the last free Elves. These peoples never accepted Morgoth and when the Valar came in power the surviving Edain alone of the remaining peoples of Beleriand joined their armies and fought against Morgoth's hordes.
If we assume the Edain population declined by about 80% during this period, that leaves a mixed population of around 30,000 remaining at the time of liberation by the Valar and the raising of Numenor, including a tiny community of Druedain. These formed the initial population of Numenor after its raising in 32 of the Second Age. In HoME 12 'The Peoples of Middle Earth' Tolkien states that the first fleet of refugees lead by Elros numbered about 200 ships carrying "between five thousand or at the most ten thousand" people, but also that there was a smaller steady migration of people over the next 50 years. From this we can be reasonably confident that most if not all of the 30,000ish survivors eventually made their way to Numenor.
Numenor's history spanned about 3300 years from its founding and while we can't exactly state its population at specific points we can identify likely trends. Numenorean history hinges around the falling of 'the Shadow' on Numenor: the turning of its people away from loving loyalty towards the Valar and Eru to bitterness towards the Valar and thirsting to escape death. Tolkien repeatedly stated that in this latter period Numenoreans had fewer and fewer children as they focused on preserving themselves from death and brooding on their ancestors, though in the Akallabeth he also states that even before the Shadow they had few children. It seemed characteristic of Tolkien's culturally higher peoples that many chose not to marry in order to pursue arts and crafts, and this may also explain the slow increase of Numenor's population, despite the fact they didn't suffer from disease until after Sauron came to Numenor in 3260 SA.
Numenor's population growth would be affected by the long-life the Numenoreans enjoyed compared to other men. Numenoreans were granted a life three times that of other men, or about 200 years (apart from the Royal Family -The House of Elros- who lived even longer). It makes sense to assume this affected childbirth and I think a length of 50-100 years between generation is reasonable. Tolkien explicitly states (in the Unfinished Tales) that Numenoreans didn't grow much more slowly than other men i.e. at 30 years old they didn't resemble a normal 10 year old, it's just they endured longer as mature adults before old-age set in. We know that there were 25 generations of Kings but we would expect more generations of ordinary citizens than the Royal Family. For my purposes here I assume there were almost twice as many generations of ordinary Numenoreans, reflecting that Elros' House lived twice as long (until the Shadow deepened). This gives about 45 generations.
Numenor's history can be roughly divided into the following periods. Firstly, from 32-600 the period of isolation from Numenor's foundation to re-establishing contact with Middle Earth. Then from 600-1600, the early years of Numenorean contact and settlement on the mainland. From 1600-2020, Numenor goes to war against Sauron and begins building greater settlements or colonies along the shores of Middle Earth. 2020-2900, the Shadow falls on Numenor, the Numenoreans begin to exact tribute from the men of Middle Earth, conquer territory and build a great Empire. 2900-3320, the Shadow deepens on Numenor leading to the eventual confrontation with Sauron, the disastrous assault on Aman itself, and the complete Downfall of Numenor forever.
Estimating Numenor's population presents a very different challenge to my other posts because those were static estimates, screenshots of what the population was at a specific point in time, whereas here we need to estimate Numenor's population dynamically by working out how it grew over 3000 years. It's good Tolkien introduced reasons why Numenor's population growth was comparatively slow because otherwise the huge length of time it existed, over 3000 years, should've produced an astonishingly high population that doesn't seem to fit with the descriptions of its society. We know the starting population, around 30,000 people at Numenor's founding, and then in theory the population at each point is just a simple exponential function of the growth rate, or the average child-birth per woman. However over 45 generations our assumption for Numenorean childbirth rates massively effects the overall population figures we get, particularly at the end.
We have some information to calibrate these with as well after our starting figure. In 600-800 when Numenor first began to make contact again with Middle Earth it was still relatively sparsely populated, as recounted in the tale of 'Aldarian and Erendis', with even large areas of the central mostly inhabited only by sheep. Centuries later in 1700 Numenor's decisive intervention in the 'War of Sauron and the Elves' seems to suggest a much more developed and powerful state. This intensifies over the following centuries as Numenor seems capable of not just exploring across the world but colonising and conquering huge areas of Middle Earth, particularly to the South and East of the lands familiar from LOTR. Presumably by this period Numenor was increasingly crowded and this encouraged the kind of massive emigration familiar from European societies in the industrial 19th and early 20th Centuries. By the time Sauron arrived in the 33rd Century Numenor seems a rather grim and over-developed place, though retaining a certain icy beauty, with violence and strife increasingly breaking out, presumably partly driven by the difficulty of accommodating so many people within its area, though certainly encouraged by Sauron. We can combine these vague images with our knowledge of Numenor's area of 168,000 square miles, twice the size of Britain, and between Germany and France in area, to provide a check on our simple exponential growth model.
For the early period of Numenorean history I estimate an average childbirth rate of 2.4 children per woman. This is obviously just an average, and takes into account Tolkien's statements about Numenoreans having relatively few children, and also that quite a few women would've chosen not to marry at all. For ease I assume this reflects the number of children each woman had that survived into adulthood and bore children, on average, rather than strictly the birth-rate. Numenor was a land without disease or war (for a long time) but Tolkien implies elsewhere child-birth was still painful and potentially deadly, though presumably in proportions more like our modern world than the middle ages.
This model suggests that by 600 SA 8ish generations would've passed and the Numenorean population would be about 130,000. By 800-900 when 'Aldarion and Erendis' is set there would've been around 250,000 people. At this stage we can assume large parts of Numenor outside the central regions would still be basically uninhabited. By the time of Tar-Minastir's great armanent that decisively turned the tide of the 'War of Sauron and the Elves' around 1600-1700 this model gives a now much greater population of around 2.5-3 million people. The difference from Aldarion's time is dramatic, as would be expected over a thousand years. Whereas in 850 it was considered a great voyage for Numenor to send a few ships to Lindon, now Tar-Minastir sends a great fleet and army of, probably, many thousands of soldiers and sailors on scores of ships. Moving further forward we reach the time of Tar-Atanamir the Great, about 2100 SA, the King under whom the Shadow first fell, and Numenor reached "the zenith of its bliss, if not yet of its power". At this point the population reaches about 7 million.
From this time the Numenoreans increasingly establish colonies along the coasts of Middle Earth that grow steadily until they form virtual kingdoms of their own, conquering surrounding territory and including populations of Numenorean colonists and the native men of those areas. These come into continual confrontation with Sauron dominion over most of the inner lands of Middle Earth south and east of Mordor and absorb the excess population as Numenor became more crowded as the centuries pass. My calculations can only give the total Numenorean population descended from the original settlers, and so include both the population of Numenor proper, and the descendant population in the colonies. This whole period can be compared to the rapid imperalist colonisation of the 18th through 20th centuries in our real world. We also have the division in Numenorean society between the King's Men (anti-Valar, Elves) and the Faithful (Pro-Valar, Elves). We are told most people were King's Men, and the Faithful were concentrated in the west where the Eldar visited from Tol Eressa. Both groups steadily emigrated from Numenor, but the Faithful came to the North-West, the lands of LOTR, to Pelargir, and Eriador where Gil-Galad, High-King of the Eldar, held back the influence of Sauron. The King's Men sailed away to the Numenorean colonies and empire in the un-mapped lands of the South and East of Middle Earth that "left many rumours in the legends of Men", but apart from Umbar were anonymous.
I assume around 80% of Numenoreans were King's Men, and about 20% Faithful, though the proportion of Faithful in Numenor itself certainly declined steadily as the divide deepened, persecution grew, and many were driven to emigrate to the Elven lands of the North West, leaving more King's Men on Numenor itself. By the time of Elendil's departure from Numenor we are told he gathered all that remained of the Faithful he could on nine great ships, implying the rest were almost all gone. During this period of the Shadow, covering about a thousand years after Tar-Atanamir, I assume the average population increase over the whole period slowed to only slightly above the replacement rate (for maths purposes I use an average birthrate of 2.05 per woman). This also represents increasing losses in warfare in Middle Earth as well, where it is implied there was continual conflict with Sauron's forces. Still this proportion is enough that by 2500 SA it predicts a population of some 10 million people, mostly on Numenor but also in its colonies, of which about 2 million would've been the Faithful, and by 3000 SA the population has increased again considerably to 15 million.
At this stage the proportion of the Numenorean population that lived outside Numenor would be steadily rising as Numenor itself grew more crowded driving emigration, and natural population increase occurred in the colonies themselves. We have no way of determining exactly what proportion of the Numenorean population dwelt abroad but I think give Tolkien's tendency to discuss the Numenoreans as though they were an aristocracy among wilder men in Middle Earth, it's reasonable to assume even at a late stage it formed a minority of the population. I think it reasonable to suggest that by year 3000 perhaps 5 million Numenoreans were living in kingdoms and colonies scattered across Middle Earth. These would not all be 'pure Numenoreans', many would be of only partial Numenorean blood as over the centuries Numenoreans married men and women of Middle Earth.
From this point around 3000 SA the shadow continued to deepen on Numenor until, after Sauron was brought to the island, civil strife broke out, disease began to plague Numenor and the Faithful were violently persecuted, leading up to the final cataclysmic destruction of Numenor itself. The Faithful increasingly shrank in number as some fell away and others fled to the areas of the North-West that would later form Arnor and Gondor. I assume over this period population growth in Numenor slowed further falling to a complete halt in the period after Sauron's arrival. This suggests a 'final' Numenorean population of around 18 million shortly before the Downfall. We can perhaps sensibly estimate that in this final period there were around 12 million people on Numenor itself and around 6 million spread through its colonies. I think we can justify a continuing assumption that around 25% of the colony population would be Faithful on the basis that while many would've fallen away under persecution, the same persecution would encourage a higher proportion of Faithful to emigrate.
This suggests that in Numenor's final days there were around 1-2 million Faithful of Numenorean and partial descent in the lands around Eriador, Pelargir and the Anduin. There would also have been some 4 million Black Numenoreans spread across Middle Earth, as well as 12 million on Numenor itself, by the end basically entirely Kings Men. According to the Akallabeth at the Downfall Elendil gathered almost all the remaining Faithful who would depart onto this nine ships. We can assume these were enormous vessels, among Numenor's great ships at the height of its power, more like modern Cruise Ships than tiny medieval galleys. But still along with a great store of goods we can't imagine more than around a thousand people fitted on each ship. This means around 9 thousand Dunedain arrived with Elendil, but these figures show they joined a population of Numenorean descent many times larger already in Middle Earth. These people accepted Elendil's right to rule because with the loss of his father, the last Lord of Andunie, he was the hereditary leader of their people, and presumably the most senior surviving descendant of Elros.
These figures are purely illustrative but I think they are in the right ball park, which is as close as we can hope to get. The 1-2 million Faithful of Eriador and Gondor can be compared with my calculation that at the time of LOTR at the end of the 3rd age the population of Gondor was around 2 million, and that of Rohan around 500 thousand. There would've been probably equivalently sized populations (or even more) of native men in Eriador and Gondor as well. These provided the populations of early Gondor and Arnor and the manpower that created the Last Alliance of Men and Elves, that according to Elrond was, with the Elves and others, the greatest host in the history of the 2nd and 3rd Ages of Middle Earth. It also brings into stark clarity the sheer scale of the loss of the Downfall, especially if we assume there were also large losses in the cities of the King's Men spread across the shores of Middle Earth. The result would've been like the destruction of Pompei magnified a thousand times over, combined with the greatest Tsunami the world has ever seen.
A brief word in defence of these estimates. In order to disagree dramatically your first option is that Numenorean fertility was only barely above (but conveniently not below) the replacement rate even before the Shadow and even in the colonies on Middle Earth, such that the population barely increased at all from generation to generation. But this gives ridiculously low population figures for the time of Aldarion and Erendis and even Tar-Minastir. Or you assume fertility must've been higher, but that produces humungous population figures over the extremely long time-frames Tolkien described Numenor as existing, in a blessed land without disease or contraception to control the population.
Nonetheless, I would love to hear your thoughts on these estimates and any suggestions for improving them. They are naturally rough, for we have only the thinnest actual information to go on, but I think they are the best that can be done.