In the Frankish-influenced regions of Europe in the High Middle Ages (c. 950-1300), kings, as well as powerful aristocrats, maintained an institution called the familia; in the case of the kings, the familia regis. This translates directly to "family" or "royal family," but a better translation would be household. The familia encompassed the lord or king's servants and retainers, the most important of whom were the unlanded household knights.
John and Edward I of England left the best records of their familias. From them, we can see that the total number of household knights in a 13th century Anglo-Norman king's familia could be as many as two hundred, with the number rising during wartime and decreasing in peacetime. Not all of them would remain with the great man constantly; many would be detached to manage estates (thus subsidizing their upkeep) or sent to garrison or command royal castles. But at any time, it is highly probable that a king would have no less than several dozen young, well-equipped knights available to meet immediate crises, in addition to any watchmen, armed servants, etc in the household.