AD 650 to 1550.
The Middle Ages of Western Europe are commonly dated from the 5th century division of the Roman Empire (into the Western Roman Empire and the Eastern Roman Empire) and the barbarian invasions until the 16th century division of Christianity during the Protestant Reformation and the dispersal of Europeans worldwide in the start of the European overseas exploration.
The adjective "medieval" refers to anything of or relating to the Middle Ages.
Charlemagne was crowned emperor in Rome by the Pope on Christmas Day, 800. His rule briefly united much of modern day France, western Germany and northern Italy. For 200 years after Charlemagne's death, Europe was in conflict, with east and west competing for power and influence in the partly un-christianized expanses of far northern Europe, and power devolving to more localized authorities.