A bump of one part in seven hundred
Shrink Earth to a Marble and You Could Not Feel Everest
Mountains feel enormous because you are very small. Against the whole planet they barely register.
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Step 1 of 5
Everest is 8.8 kilometres tall. Earth is 6,371 kilometres to the middle.
The last two bars are drawn at the smallest size the chart allows. They are still too big. Divide one by the other and the mountain is about one seven-hundredth of the radius. It is the largest bump on the surface and it is still a fraction of a per cent.
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Step 2 of 5
Shrink it to something you can hold.
Take Earth down to a marble two centimetres across. Everest becomes a bump about fourteen micrometres high — thinner than a sheet of paper, around a fifth the width of a hair. The deepest trench becomes a scratch of similar depth.
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Step 3 of 5
Your fingertips are good, but not that good.
People can detect surface features down to a few micrometres under the right conditions, so a fourteen-micrometre ridge is not literally beyond feeling. But you would have to be looking for that one ridge, on a polished sphere, knowing where it was.
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Step 4 of 5
The flattening is the bigger deviation, and nobody mentions it.
Earth spins, so it bulges at the equator. The equatorial radius beats the polar radius by 21 kilometres — more than twice Everest's height. If you want to know the biggest way Earth departs from a sphere, it is not the mountains.
You are further from the centre of the Earth standing on Chimborazo in Ecuador than on Everest, because Chimborazo sits on the bulge.
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Step 5 of 5
The point is not that mountains are small. It is that Earth is huge.
Both true. Scale decides which one matters. Nothing about Everest shrinks. What the comparison shows is that human scale and planetary scale are almost unrelated. Anything we can walk up sits in a very thin skin on top of something enormous.
You will often see this put as 'Earth is smoother than a billiard ball'. Whether that is true depends entirely on which tolerance you pick for the ball, so it is best left out — the marble comparison stands on its own.
The short version
Everest is about a seven-hundredth of Earth's radius, so on a two-centimetre model it would be a bump around fourteen micrometres high — and the equatorial bulge is more than twice as large a deviation.
Try it yourself
Find a globe and run a finger over it. Mountains are painted on, not moulded, because at that scale there is nothing to mould. That is not a shortcut — it is accurate.