Charlemagne’s empire had ten to twenty million subjects
From 800 to 887 a Frankish dominion we call the Carolingian Empire spanned Western and Central Europe. Popes crowned Charlemagne emperor in 800; after Louis the Pious died, civil war and the 843 partition left only a shadow of unity until Charles the Fat briefly glued the pieces back in 884.
Carolingians had been Frankish kings since 751 and Lombard kings in Italy since 774 when Leo III repaid Charlemagne’s protection with an imperial diadem. Contemporaries never said “Carolingian Empire”; they spoke of universum regnum, the whole kingdom, or Romanum imperium, while conducting business in Latin. The demographic heartland was Francia between Loire and Rhine, with Aachen as Charlemagne’s favourite seat; frontiers touched Córdoba’s emirate and, after 824, Pamplona beyond the Pyrenees, and ran north toward Saxon and Danish worlds.
Population estimates hover between ten and twenty million. Charles Martel, grandfather of the imperial line, never took the royal or imperial title yet dominated continental Western Europe north of the Pyrenees, leaving Saxons, Lombardy, and the Spanish March as the big remaining prizes. His 732 victory near Tours against a Muslim army that mixed Berber light horse with heavy Arab cavalry became a foundational Christian memory of the dynasty’s rise.
Charlemagne, who began ruling in 768, campaigned almost every year. He absorbed the Lombard kingdom in 774, suffered his worst defeat at Roncevaux Pass after a failed Spanish expedition in 778, and forced Duke Tassilo III of Bavaria to give up his title in 794. Where Roman ventures between Rhine and Elbe had collapsed within twenty years after Teutoburg Forest, he carried Frankish rule to the Elbe for good. His son Louis the Pious, made co-emperor in 813, inherited everything when Charlemagne died in the winter of 814.
Louis's reign dissolved into family feuds. His 817 settlement gave kingdoms to Lothar, Pepin and Louis the German; trying to fit in Charles the Bald provoked revolts in which his sons briefly dethroned him, before he was restored at Metz by 835. After Louis died in 840, Lothar claimed everything, lost at Fontenay in 841, and accepted the Treaty of Verdun in 843, which split the realm into western, middle and eastern kingdoms, the last a forerunner of Germany. Charles the Fat's reunion of 884 ended with his deposition in 887.
Source: Carolingian Empire