The Empire finally fell in the 15th century to the Ottoman Empire, with Constantinople surrendering in 1453.
The Empire itself existed for roughly a thousand years there was no precise 'founding' date, but rather a series of decisions made by the Roman Empire that saw the Byzantine Empire eventually split off and grow into its own entity. The term 'Byzantine Empire' postdates the Empire itself, and was popularized by historians during the 16th-19th centuries. The Empire preserved Roman legal traditions, but embraced substantial Hellenization, i.e. The Byzantine Empire or Eastern Roman Empire (known to its inhabitants as the Roman Empire) was the continuation of the Roman Empire during the Middle Ages, centered on its capital of Constantinople, and ruled by Emperors in direct succession to the Roman Emperors.