If each of the Imperial Legions under the Immortal Emperor Drakus Coaltongue numbered 10,000 troops, that would imply that the population of Eastrealm would be at least 7 million. Given that the population of Europe at the time of Charlemagne (9th century AD) was around 25 to 30 million, that actually seems a little low. Bachrach estimates that, out of a population of 7-8 million in the Carolingian regnum north of the Alps (575,000 sq. miles), there were 2 million men between 15 and 55 years of age (ie. fit for military service). Assuming that 4% of this age cohort was mobilized for expeditio (military service), Charlemagne commanded about 100,000 troops."The power of the sword is more sensibly felt in an extensive monarchy, than in a small community. It has been calculated by the ablest politicians that no State, without being soon exhausted, can maintain above the hundredth part of its members in arms and idleness. But although this relative proportion may be uniform, its influence over the rest of society will vary according to the degree of its positive strength. The advantages of military science and discipline cannot be exerted, unless a proper number of soldiers are united into one body..."
Edward Gibbon The History of the Decline and Fall of the Roman Empire, volume the first, chapter V, page 106. Printed for W. Strahan and T. Cadell, London 1776.
The Imperial Roman army (14 AD) numbered some 250,000 men, equally split between 25 legions and 250 units of auxiliaries. The population of the Roman Empire (2 million sq. miles) during that time is estimated to have been between 50 and 60 million.
John D. Durand (1977) Historical Estimates of World Population: An Evaluation, Population Studies Center, University of Pennsylvania, pp. 253-296.
J.C. Russell (1958) "Late Ancient and Medieval Population," Transactions of the American Philosophical Society 48(3), pp. 1-152.