I couldn't help but notice that both the Ancient Spartans and the medieval Normans held territory of roughly 3,000 square miles in area (Normandy is roughly 50 miles by 80 miles, and the southern half of the Peloponnesian peninsula- Lacodaemon at its greatest extent- is roughly 60 miles by 50 miles), and yet the muster of Normandy at Hastings and the Assembly of the Spartiates were both armies roughly 5-10,000 strong.
In both cases, the average is approximately 2.5 soldiers per square mile. Based on research I've done, the average size of a Knight's Fee (the land a Knight owned to financially support his military adventures) was roughly 10 Hides (or 1200 acres, or basically 2 square miles) of land per Knight (believable considering that, since less than a third of the Norman army at Hastings was cavalry, 2,000-3,000 Knights could be supported by 4,000 square miles), but prior discussions on r/worldbuilding suggested that Men-At-Arms/Yeomen/foot-soldiers would have a similar amount of land needed to support them. I know that the Spartiates were also given shares of land (worked by Helots) to financially support them, but 256 acres per Spartiate (based on the aforementioned average of 2.5 soldiers per square mile) seems a bit small.
Are my calculations for soldiers per square mile off? Is it realistic to raise an army of 5,000-10,000 men on 3,000 to 4,000 square miles of land?
The 10th Century document known as the Burghal Hidage attributed roughly a hide of land to support one member of a burghal garrison. E.g. 120 acres should be enough to support, at least in theory, a soldier on foot. Of course, in practice, a virgate or less was usually sufficient land to sustain an entire household.