This link puts the land area of Westeros as follows:

1. The North: 1,132,154 miles²
2. The Reach: 479,135 miles²
3. Dorne: 328,472 miles²
4. The Riverlands: 268,881 miles²
5. The Vale: 255,016 miles²
6. The Stormlands: 201,967 miles²
7. The Westerlands: 192,720 miles²
8. The Crownlands: 130,148 miles²
9. The Gift: 63,347 miles²
10. The Iron Islands: 11,136 miles²

One way to estimate population is to identify a comparable location in high medieval Europe (around 1400) and its population density.

This could work as follows:

1. The North = European Russia, 6 people per square mile
2. The Reach = France, 66 people per square mile
3. Dorne = Spain, 25 people per square mile
4. The Riverlands = Germany, 45 people per square mile
5. The Vale = Scotland, 13 people per square mile
6. The Stormlands = Ireland, 25 people per square mile
7. The Westerlands = Italy, 85 people per square mile
8. The Crownlands = England, 51 people per square mile
9. The Gift = Empty
10. The Iron Islands = Iceland, population 80,000

(Source for the populations, which I have then divided by land area to reach pop density)

This in turn gives populations as follows:

1. The Reach: 31,622,910
2. The Westerlands: 16,381,200
3. The Riverlands: 12,099,645
   
4. Dorne: 8,211,800
   
5. The North: 6,792,924
   
6. The Crownlands: 6,637,548
7. The Stormlands: 5,049,175
   
8. The Vale: 3,315,208
   
9. The Iron Islands: 80,000
   
10. The Gift: 0

Army size

Half the population is women, who can't be raised as levees.

Of the remaining male half, fighting age is probably 16-40.

If you say life expectancy of around 50 years, then that's around 48% of the male population are fighting age.

So in total, around 24% of the population are probably men of fighting age who are, in principle, able to be militarised.

However, in medieval times, around 90% of the population was engaged in agriculture. Raise too many and you disrupt your food supply.

Let's say, purely as a finger in the air number, you can raise 1 in 20 (5%) fighting age men without overly disrupting your food supply.

This would mean population size to army size is:

Population size * 0.50 (women) * 0.48 (fighting age) *0.05 (available)

Or, army size is 1.2% of the population. This would give you army sizes of:

1. The Reach: 379,475
2. The Westerlands: 196,574
3. The Riverlands: 145,196
4. Dorne: 98,542
5. The North: 81,515
6. The Crownlands: 79,651
7. The Stormlands: 60,590
   
8. The Vale: 39,782

Rather higher than we see in the books. Also this would put Robert's rebellion as:

Rebels: 327,083
Crown: 557,668
Neutral (Tywin): 196,574

 

Cool math, but at the end of the day, supplies and logistics limit the size of armies, not recruitable pop (recruitable pop matters little in pre-industrial warfare, as a general rule). According to your own numbers, high-medieval France, being half the size of the Reach and with the same pop-density, should have been able to muster 180k armies on the regular, but the baguettes could only bring around 20k to Agincourt. Even the whole of Christendom in the crusades only managed to field and sustain 30k armies as an absolute max. If anything, given the level of technology and gov. administration present in Westeros, Martin's armies are hideously oversized.

 

Niez is right. The figures we see in canon are absurd, though if you assume that the Reach army of "100 000" to include the entirety of it (servants, camp followers, levies, men-at-arms, knights, nobles, etc) and not just the fighters, it becomes a bit more reasonable. Further, while assuming that (circa) 1% of the population is the expected army size, this is generally the entire fighting force, which includes men garrisoned across the kingdom.

We also can't use real world figures to reckon with, as King's Landing has a population of 500 000 (ish), which I believe is completely out of the norm for comparable medieval cities.

 

King's Landing is not entirely without precedent; it largely matches medieval Constantinople at its peak. And of course Rome itself was around 1 million in the imperial period, during which time it was capital of a region of a similar size to Westeros.

 

Weren't you using population density figures from other eras?

 

You have your math wrong. Low life expectancy in the middle ages was mostly due to absurdly high child mortality, with only around 50% of children surviving past their early teens. Actually the child mortality was so bad, that the life expectancy at birth was only around 30-40 all the way to the 19th century, when you got better medical care.

So you'd have more like 25% of male population being of fighting age, not half.

 

The real middle ages didn't have to deal with year long winters on the regular. Old men in the North literally commit mass suicide during it by "going hunting" to make sure their supplied last for their families.

 

This has already been taken into account. With early child mortality included, life expectancy would be closer to 20.

 

How did you take this into account? You literally assume a straight population pyramid, and calculate based on that. Sure, your demography has way more people over the fighting age than realistically there would be, but at the same time you have way way too few children.