Is Earth as smooth as a billiard ball? No, here’s why

You may have heard it has been said that if our planet were shrunk down to the size of a billiard ball, it would be smoother than it. In other words, the Earth is smoother than a billiard ball. Is that true?

Back in 2008, on the “Bad Astronomy” blog on discovermagazine.com, in the article titled “Ten things you don’t know about the Earth“, Phil Plait wrote about that, and he said “…according to the World Pool-Billiard Association, a pool ball is 2.25 inches in diameter and has a tolerance of +/- 0.005 inches.” and after making some calculations, he concluded that “… the urban legend is correct. If you shrank the Earth down to the size of a billiard ball, it would be smoother.”

Even the famous American astrophysicist, author and science communicator Neil deGrasse Tyson once tweeted about that, saying “If shrunk to a few inches across, Earth would feel as smooth as a billiard-hall cue ball.”.

Is Earth as smooth as a cue ball?
Is Earth as smooth as a billiard ball?
Is Earth as smooth as a billiard ball? Probably not.

In fact, the Earth is much smoother than one might think. It definitely would NOT look like this without water, for example. Yes, there are big mountains like the Himalayas and big trench under the oceans like the Mariana Trench. The highest point on Earth is the top of Mount Everest, at 8.85 km. The deepest point on Earth is the Mariana Trench, at about 11 km deep. But even those are very small compared to the Earth’s a diameter which is about 12,735 kilometers (on average).

According to the World Pool-Billiard Association, “All balls must be composed of cast phenolic resin plastic and measure 2 1/4 (±.005) inches [5.715 cm (± .127 mm)] in diameter”.

So, if we could shrink the Earth to the size of a billiard ball, the height of Mount Everest would be only 0.04 millimeters. The depth of the Mariana Trench would be only 0.045 millimeters. These measurements are inside the tolerance of 0.127 mm or 0.005 inches, no pits or bumps more than that, so the Earth is smoother than a billiard ball, right?

Wrong.

First of all, the specifications of the World Pool-Billiard Association does not say “there mustn’t be pits or bumps more than .005 inches”. This is only about diameter, the rule says that the diameter must be within 2 1/4 (± .005) inches. Smoothness is a very different thing.

Let’s we assume that we produced a billiard ball and covered its surface with medium sandpaper (grit particle size of 0.005 in, for more about grit sizes of a sandpaper see the Grit size table on the Wikipedia entry of sandpaper). By the definition of smoothness used by Phil Plait of Discover Magazine and Neil deGrasse Tyson, that billiard ball would also be “smooth” – which is obviously ridiculous.

The billiard-ball sized Earth’s smoothness would be equivalent to that of 320 grit sandpaper. Still not quite smooth, right?

So, it’s obvious that 0.005 inches (0.127 mm) official tolerance is for shape, for roundness, not for smoothness.

Is Earth as smooth as a cue ball? 320 grit silicon carbide sandpaper
The billiard-ball sized Earth’s smoothness would be equivalent to that of 320 grit sandpaper. Image: “320 grit silicon carbide sandpaper, with close-up view” on wikipedia.

Human fingers are very sensitive

According to a 2013 study titled “Feeling Small: Exploring the Tactile Perception Limits” published on Nature, a human finger can feel wrinkles as small as 10nm (nanometers), or 0.00001 millimeters, demonstrating that human tactile discrimination extends to the nanoscale. So, if the Earth were shrunk down to the size of a billiard ball, you would definitely feel the Mount Everest, which would be 0.04 millimeters high.

As round as a billiard ball

Speaking of roundness, is Earth as round as a billiard ball?

Earth’s equatorial diameter is 7,926 miles (12,756 km), but from pole to pole, the diameter is 7,898 miles (12,714 km) – a difference of only 28 miles (42 km).

If we take the bigger diameter and shrink it down, the difference would be 0.0049 inches (0.0125 mm). If we take the smaller diameter, the difference would be very slightly bigger, but almost the same. So yes, the Earth is as round as a billiard ball. But it’s almost at the limit.

Summary

  1. Is the Earth as smooth as a billiard ball? Answer: No.
  2. Is the Earth as round as a billiard ball? Answer: Yes.

You can also watch Vsauce’s great video titled How Much of the Earth Can You See at Once?, which also covers this very subject.

How Much of the Earth Can You See at Once? by Vsauce. In the video, at 14:40, Michael says “you may have heard it said that if the entire planet were shrunk down to the size of a billiard ball, it would be smoother than a billiard ball. … That seems believable, but as it turns out, it’s not true. The misconception stems from the interpretation of the World Pool-Billiard Association’s rules. According to them, a billiard ball must have a diameter of 2.25 in ±0.005 in. Some writers have taken this to mean that pits and bumps of ±0.005 in are allowed. Proportionally, on Earth, that would mean a mountain that was 28 km high. So, since Earth has none of those, it must be smoother than a billiard ball. Except, if bumps that high are actually allowed on a pool ball. A ball covered with 120 grit sandpaper would be within regulation. Clearly, the ±0.005 inches rule is more about roundness, deviation from a sphere, and not the texture.”

As you can see in the video above, as microscopic photography shown, imperfections on a billiard ball are only 1/100,000 inches, or about 0.5 μm deep and high. Scaled down to the size of a billiard ball, Earth’s Mariana trench would be 49 μm deep.

Let’s think it in another way: If a billiard ball was scaled up to Earth size, the difference between the highest peak and lowest point would be about just 223 meters (732 feet) at maximum. A billiard ball is way smoother than the Earth.

Sources

M. Özgür Nevres

I am a software developer, an ex-road racing cyclist, and a science enthusiast. Also an animal lover! I write about the planet Earth and science on this website, ourplnt.com. You can check out my social media profiles by clicking on their icons.

Latest posts by M. Özgür Nevres (see all)

12 thoughts on “Is Earth as smooth as a billiard ball? No, here’s why”

  1. Since you’re talking about Earth and billiards, I’d like to point out that Earth is about 3400 times flatter than a regulation pool table. (Calculating the bulge of a 4′ x 8′ section of a sphere with radius of 6371 meters gives 146 nanometers compared to requirement of +/-0.5mm per WPA & BCA)

    I love saying it – The Earth is flatter than a pool table!

  2. I am curious, I’m not 100% sure how all of this works so i could be wrong but the measure of smoothness is also related to the proximity of these height differences right? So your sandpaper example implies that the highest and lowest points of the planet repeat over and over again outwards from a single point(up, down, up, down, up, down) . There is only one point that is the highest and another point that is the lowest with some distance in between, it’s not like there is a mountain and trench tangent every x amount of distance consecutively. The rest of the height differences in the geography are much smaller over a larger area. Am I not thinking of this correctly? This is a really cool idea whether its true or not =)

    1. Hi,

      Thanks for the comment. For some places in the world, you’re right. But a lot of other places, there are big differences in elevation. The Himalayas is just an example, also the Alps. For instance, Nanga Parbat’s Rupal Face rises approximately a whopping 4,600 meters, or 15,000 feet, above its base. You would definitely feel it if the Earth were shrunk down to the size of a billiard ball.

  3. I heard Neil deGrasse Tyson state this claim on Joe Rogan last week – that the earth, if shrunk to the size of a billiard ball, would be as smooth as one. I had not heard this before. My immediate reaction was, NO WAY. It appears I was correct!

  4. If we are talking about a nice new shiny pool ball, I would agree. But compare that with the average one you pick up in a bar and it would be significantly more rough.

    The largest deformation on earth from its base is Mauna Loa which rises 5000m from its base. This is around 0.0008 of its radius.

    Compare that with a hair on a billiard ball.

    A hair is on average 75 microns or or .003″, which then divided by 1.25″ it becomes 0.0024 of its radius. A hair on a billiard ball is 3 times higher than the greatest deformation on the surface of the earth.

    A particle of dust is about 10 microns (.00039″) so what we are looking at is effectively a dusty pool ball with a few places two pieces of dust high, and a few scratches 3 parts of dust deep.

    For all reasonable arguments I would call that as smooth.

  5. This is nonsense. 14 meters? Funny because that also happens to be the same fact associated with the worlds roundest object -https://www.youtube.com/watch?v=ZMByI4s-D-Y&ab_channel=Veritasium

    So are you telling me, an ordinary cue ball is as smooth as the worlds roundest object? AKA billiard balls are also the worlds roundest object LOL Surely not.

  6. I guess I’m not allowed to post youtube links here but if you search “worlds roundest object”, you’ll see why this article is nonsense because it claims in the last paragraph, that an ordinary billiard ball is as smooth as the worlds roundest object. The 14 meters between the tallest mountain, and deepest valley is how smooth that object would be if it were earth sized. No way in hell a billiard ball is just as smooth as an object that cost millions to make, and made to be perfectly round, smooth, and exactly 1 kg

    1. Hi, Hugo. Thanks for the comment. You’re right, sort of. I made an arithmetical error. But a billiard ball is still way smoother than the Earth.

      Earth is rounder than a billiard ball, I already mentioned that in the article, and that “world’s roundest object” is rounder than Earth. I think there’s no problem here.

      Diameter of Earth 12,742,000 meters
      Diameter of a billiard ball 0.05715 meters
      Mariana trench 11,000 meters
      Everest 8,848 meters
      Mariana + Everest = 19,848 meters

      If the Earth scaled down to a billiard ball size, the difference between the Mariana Trench and Mount Everest would be about 89μm. This is way bigger the imperfections on a billiard ball (0.5 μm). A billiard ball is still way smoother than Earth.

      As you pointed out, I made a mistake while calculating the differences if a billiard ball was scaled up to the size of Earth.

      Imperfections on a billiard ball: 0.5 μm. Let’s multiply that with 2, we now have 1 μm of difference between the lowest and highest point.

      if we have 1 μm difference on a ball with a diameter of 0.05715 meters,
      How many meters difference we would have on a ball with a diameter of 12,742,000 meters?

      0.000001 meters -> ‬0.05715 meters
      x -> 12,742,000 meters

      x = 12,742,000 * 0.000001 / ‬0.05715
      x = 223 meters

      If a billiard ball was scaled up to Earth size, the difference between the highest peak and lowest point would be about just 223 meters at maximum. A billiard ball is still way smoother than the Earth. But the difference is more than 14 meters, you’re right (I fixed the article, thanks for pointing that out).

  7. I see a problem in your logic.

    A billiard ball is only the solid part of it.

    However, the Earth is NOT only the solid part of the crust. If you discount liquids and gasses that make a planet… then Earth would only be a thin shell (you would remove the magma from the mantle too).

    Jupiter and Saturn would cease to exist, as they are mostly gas which slowly becomes liquid towards their cores, due to pressure.

    Earth IS covered in water (which makes it even more smooth all around… with bumps only on the patches with continents.

    The comparison with grit paper is not apt there too, because the grit size is constant across the grit paper, while on Earth, only tiny patches would have mountains comparable in size with the grit size.

    But then, you must also cover the Earth in atmosphere, which IS a part of the planet.

    And that is very smooth. Smoother than a billiards ball.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.