How many capital cities were there in the entire history of Roman Empire?
There were only ever two main capitals of the Roman Empire; Rome itself and Constantinople, although the city of Milan, then known as Mediolanium, and Ravenna were also declared capitals for a number of decades towards the end of the Empire. In the 4th century AD, the Emperor Constantine declared Constantinople the new capital of Rome as it was closer to the more valuable trade routes of the Empire and was at far less risk of invasion that the Italian Peninsula of the time.
The capital of Rome then shifted numerous times between Rome and Constantinople, with the Empire eventually splitting into two separate entities towards the end of the century. Towards the end of the 5th century, the capital was then moved to Milan in order to deal with threats in Northern Europe more efficiently and finally to Ravenna due to the fact that it was one of the most highly fortified cities in Europe at the time.
In short, there were technically four Roman capitals during the history of the Empire, but only Rome and Constantinople ever held the position for a considerable amount of time.