when did the roman empire end and start
It officially started in 27 BC, got split into the Western and Eastern Roman Empires in between and ended with the fall of Constantinople in 1453.
Roman Empire
 In 27 BC the Senate and People of Rome made Octavian "princeps" ("first citizen") with proconsular "imperium", thus beginning the Principate (the first epoch of Roman imperial history, usually dated from 27 BC to 284 AD), and gave him the name "Augustus" ("the venerated"). 
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Roman Empire [SEP] Transition from Republic to Empire
Though the old constitutional machinery remained in place, Augustus came to predominate it. Although the republic stood in name, contemporaries of Augustus knew it was just a veil and that Augustus had all meaningful authority in Rome. Since his rule ended a century of civil wars and began an unprecedented period of peace and prosperity, he was so loved that he came to hold the power of a monarch "de facto" if not "de jure". During the years of his rule, a new constitutional order emerged (in part organically and in part by design), so that, upon his death, this new constitutional order operated as before when Tiberius was accepted as the new emperor.