Unlike Star Wars where the distances and speeds are just made up out of other words that maybe mean something, much of the way technology works in Star Trek is actually based on theory — yep, even the holodeck (someone build one already!).
As Gene Roddenberry himself wrote in 1966: “Science fiction? Absolutely not. Rather, real adventure in tomorrow’s space. Based upon the best scientific knowledge and estimates of what our astronauts of the future may face when they move out of our own solar system and into the vastness of our galaxy.”
Which means warp speed isn’t arbitrary, but actually has a known speed that corresponds to the real world.
To make it easier we’ll start at the beginning — any idea how fast warp 1 is?