How Smooth is the Earth?

One of the most interesting facts that I learned from the BBC TV series QI was that the Earth is smoother than a billiard ball. Unfortunately, like nearly every other fact I've remembered from that show, it is a load of bull (or should that be balls).

Shri Khalpada has created a three.js powered 3D globe of the Earth which allows you to view the Earth's elevation profile to scale (and when exaggerated). If you compare the 'to scale' globe in How Smooth is the Earth? to the exaggerated profile you immediately get a sense of how smooth the world actually is.

However, despite its relative smoothness, the Earth is not a smooth as a billiard ball. Alongside his visualization of the Earth's elevation profile Shri Khalpada links to Dr David Alcitore's paper Is a Pool Ball Smoother Than the Earth? (PDF) which concludes that "the Earth would make a terrible pool ball ... (the) Earth ball would ... be terribly non round compared to high-quality pool balls."

If you don't want to read a scientific paper comparing the Earth's smoothness to a billiard ball then XKCD's Bowling Ball does a very good job at explaining why the Earth is also not as smooth as a bowling ball.