We know that Iron Islands has a huge navy. It is their main strength. We also know that Iron Islands are barren land, very small and even if they fish extensively, it should not support a population as great as the North. In fact, it was one of their motives when they waged war against the North, to obtain Lebensraum for their people.
I am not really shocked with their ship building efficiency. They might steal the wood easily from many unprotected forests in the North or in the Riverlands. The Iron Fleet should already have around 500 ships in total. Building 500 more in one or two years for a seafarer nation should not be the greatest challenge.
However, for such a small nation to man even 500 ships efficiently puzzles me. In a world where the North can muster 20000 men (if they took their time it would at most be 40000), how did Iron Islands man 1000 ships? What would be the crew per ship?
One of the best comparisons I could find is the taking of Deepwood Motte, where Asha Greyjoy commaned 30 longships and about 1000 men, making it about 30 men per ship. Battle for Deepwood Motte is another possible reference point, where it is claimed that Asha Greyjoy had 4 longships and 200 men. This makes 50 men per longship.
So, how can Iron Islands support a fighting population of 30000 while the best North can do is 40000?
Book answers are preferred but TV show answers are also welcome.
Answer
The true answer is we do not know the exact size of the Iron Islands population and so it seems appropriate to use @Aegon's image here:
However, the awoiaf page on the Iron Islands cites that they have 20,000 men and 500 longships which in turn is cited from "A Game of Thrones: d20-based Open Gaming RPG." which is a semi-canon source.
We can also get a figure of 15,000 fighting men from this post on atlasoficeandfireblog which is cited from this video by Elio Garcia:
From there the article extrapolates that the Iron Islands has a population of 1.5 million but that is using a basis that the fighters make up 1% of the population which seems low for a nation such as the Ironborn. Using a figure more around 10% we get 150,000 which seems more reasonable. This isn't exactly unfeasible as in WWII many nations managed to get around 10% fighting population although it isn't sustainable but these are times of war for Westeros.
So using both figures for fighting men and a rough estimate of between 1-10% of the population being fighters we get a population between 150,000 and 2,000,000 though it seems likely to be on the lower side of things.
However, in my opinion (especially as they rely on raiding), the percentage of fighting men is likely around 3-5% maybe a bit higher which gives a total population of between 450,000 and 1,000,000.
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