How many years passed from Augustus becoming emperor in 27 BC to the fall of the Western Roman Empire in AD 476?

How to get close to this number

Subtract the dates the question gives you, remembering that they sit on opposite sides of the start of the calendar era: count the years before it, count the years after it, and add them. There is no year zero, so the total lands just over five centuries, and 500 is the round figure for that span. Both endpoints are conventions, which is exactly why the question pins them rather than leaving the start and end open to argument.

The eastern continuation is the fact that reframes everything, and the explanation states it: Byzantium carried on for almost another thousand years, falling only in 1453. So the empire in total lasted roughly three times longer than the part most people mean, and the second half is routinely omitted from the story.

The comparison at the end is the one that recalibrates chronology: that fall is closer in time to the printing press than to Julius Caesar. Ancient history compresses in the mind into an undifferentiated distant past, and a date that sits between two familiar landmarks is the most effective way to break that compression.