At its peak, there were somewhere between 50 and 90 million Roman citizens (about 20% of the world's population at that time!). Under the emperor Trajan, it stretched for 5 million square kilometers.
As the historian Christopher Kelly has described it:Then the empire stretched from Hadrian's Wall in drizzle-soaked northern England to the sun-baked banks of the Euphrates in Syria; from the great Rhine–Danube river system, which snaked across the fertile, flat lands of Europe from the Low Countries to the Black Sea, to the rich plains of the North African coast and the luxuriant gash of the Nile Valley in Egypt. The empire completely circled the Mediterranean ... referred to by its conquerors as mare nostrum—'our sea'.
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The Roman Empire reached the greatest extent under the emperor Trajan who conquered Dacia (most of today's Romania) in 106 and took Mesopotamia (Today's Iraq) from the Persians in 116. His successor, Hadrian, gave Mesopotamia back to the Persians.
The Roman Empire covered the following modern day countries or parts of modern countries:
Western Europe:Italy, Malta, Spain, Portugal, France, Belgium, Luxembourg, Holland south of the river Rhine, southern Germany and part of central Germany, Switzerland, Liechtenstein, Austria and England and Wales.
Eastern Europe: western Hungary, part of western Slovakia, Slovenia, Serbia, Croatia, Bosnia and Herzegovina, Montenegro, Macedonia, Albania, Greece, Bulgaria, part of Romania, part of Moldova and a slither of western Ukraine.
Asia: Turkey, Cyprus, Armenia, northern Iraq, Syria, Lebanon, Israel and Palestine, Jordan, and the northern part of the coast of the Red Sea in Saudi Arabia.
Africa: Egypt, the coastal part of Libya, Tunisia, the coastal part of Algeria, and northern Morocco.
Rome reached its Greatest Size in117 C.E. at which point it was 6.5 million sq. km (2.5 million square miles)
Trajan, who crossed the Danube added Dacia (Romania) to the Roman Empire, and he expanded into the East, although the Eastern provinces were abandoned by his successor Hadrian. Earlier, the Emperor Claudius added Britain to the Roman Empire.
a major challenge confronting the Roman Empire was determining how to govern people from many different regions.
A strong military
The Roman empire was important in ancient times because it was the dominant power in the West. The Romans gave their protection and culture to the world from the Atlantic ocean to the Black Sea, from North Africa to Britain and their culture even reached Scandinavia.
At the height of the Roman Empire in 117 AD, it's total size was 5,000,000 km2 (1,930,511 sq mi).