How Smooth Is The Earth, Really?

When I was a kid, I remember reading a fact in a science book about the Earth being smoother than a billiard ball. This blew my mind - how could the Earth, with all its mountains and valleys, be smoother than a billiard ball?

Let's crunch some numbers. The Earth, while not a perfect sphere, is close to it and has a radius of about . The peak of Mount Everest, the highest point on Earth, is about above sea level. Proportionally, that same elevation on a billiard ball with a radius of would be: , which is about the thickness of a fine human hair or one-third the thickness of a sheet of paper.

Whether or not the Earth is actually smoother than a billiard ball is an interesting question. Here is a great paper on the subject, which summarizes that on the whole the earth isn't smoother than a billiard ball because of extreme peaks and valleys, but that the Earth is incredibly smooth over most of its surface. The point about Earth's smoothness is interesting either way, so let's dive in!

Here's a globe visualization of Earth's elevation profile, with options to exaggerate the elevation (as often seen in standard 2D elevation maps) or to view it at its true scale:

The visualization shows that the Earth is incredibly smooth when compared to its size.

Another interesting angle to think about this from is the Earth's layers. The Earth is made up of four main layers: the crust, mantle, the liquid outer core, and the solid inner core. All of our mountains and valleys are on the crust, which itself just a tiny fraction of the Earth's total volume.

Here is a view of the Earth's layers to scale, with the peak of Mount Everest sitting above the crust for reference, using data from NASA:

There doesn't necessarily need to be a deep takeaway from this, but here's one anyway: all of the life we know of in the universe is contained within a layer of the Earth that's about as thick as the skin of an apple. That is pretty humbling to think about.