There are two factors limiting the amount of man power a society can deploy, overall population and internal political cohesion. Of the two, the latter is the most important.
Medieval societies were societies built upon the military oppression and exploitation of the farmers (peasants.) They could never allow the peasants to become to well trained, armed or coordinated or they could defeat the aristocracy. They called up a few farmers as possible and forced them to provide their own weapons from converted agricultural tools and whatever armor they could improvise.
Farmers that got to skillful on the battlefield tended to end up mysteriously dead.
The European military warrior class the so-called "nobility" comprised roughly 5% of the population. Around 5% were clergy, artisans, traders etc and largely considered non-factors in warfare.
During the harvesting and planting seasons, essentially non of the farmer population could be called up out wrecking the nobles own fortunes worse than loosing a war would. In Winter time, armies could not travel so war occurred in the narrow summer months.
In theory, the nobles could require all peasant males in a certain age range, usually 17-50, to provide 40 days of military service a year during the summer. That would be roughly 15%-20% of the total population.But even in summer, no more than half the available man power could be done without on the farm so more like 7.5%-10%
However, save for the rare chance at plunder in a foreign land, peasants didn't get paid so they had little incentive to comply with their feudal obligations (which forced upon them by conquest) so getting enough men to show up was a constant struggle.
Neither did it help that well into early 1800s, military service of any duration beyond a couple of weeks was looked on as a death sentence. 2/3 of soldiers died of disease in unsanitary camps with little food and constant exposure. WWII was the first American war in which more soldiers died of enemy action than disease. Prior to that, wars were races to see who could get the most men to battle field before everyone dropped dead from dysentery, plague or whatever.
If fending off an invasion on his own land in what was likely to be a couple of brief battles, nobles could sometimes scrape up 15% or more of the farmers but largely because the farmers wanted to fend off the plunder of the invading army.
The end of the knights and aristocrats began when the growing urban population began to deploy large armies of well trained infantry units in the later 1300s (see the battle of the spurs.) These urban areas could sometime raise 50%-75% of the military age males, already equipped and trained and alliance of a couple of cities or more could easily out raise even the kings of the time. Their weakness lay in their inability to fight protracted wars at a distance without wrecking the economy.
The Swiss solved this problem by hiring out some men when they were young as mercenaries. It made money, got the boys of troublesome age out of town till they settled down, left a battle harden cadre of elders behind and in the worst case, they could call the mercenaries back. Ruled European battlefields for nearly 150 years with pikes and crossbows.
Arguably, every major empire in history arose when a very small society gained a significant advantage in internal cohesion and instead of worrying about internal revolution, could arm their entire adult male population if that is what it took. That is how the small backwoods town of Rome became an Empire. Conversely, when the Republic feel and the Legions chose the Emperors, trust broke down and an Empire with something like 30-40 times the population of the Republic couldn't deploy armies a tenth as large as the Republic did repeatedly in the Punic wars.
So, if you want to calculate the size of army a medieval society could raise, the primary factor is how the farmer majority and the urbanites view the enemy. If the commoners see the war as just more dynastic struggles, then the armies will be small, usually in the thousands, mostly aristocrats and mercenaries.
If they faced something like an invasion of Mongols, Ottomans or Vikings, who the commoners feared for their own sakes, then the armies could be quite large, tens of thousands, assuming the fighting occurred locally in summer.
Peasant rebellions would also raise up surprising amounts of man power if conditions were bad enough. See the Hussite rebellions.
(It's worth noting that the Mongols and Vikings attack with very small forces, relying on speed and maneuver to overwhelm local opposition before the levies could be called up. The so-called Mongol "Hordes" were usually outnumbered 10 to 1, but they rode so fast they seemed to be everywhere. Same thing for vikings. They could hit several places on the coast before the central land power heard of the first creating the impression of multiple forces hitting simutanously.)