At the moment there are deep seas and high mountains. But imagine that the land elevation of the Earth is equal everywhere. How deep would the ocean be in that case?


2 Answers 2


An approximation can be obtained quite simply by dividing the volume of water in the oceans by the surface area of an ellipsoid with a smooth surface representing the idealized Earth in your question.

The volume of Earth's oceans, seas and bays is $1.332 \times 10^9 \text{ km}^3$.

The equatorial radius of Earth (semi-major axis of the spheroid) is $a = 6378.1 \text{ km}$. The polar radius of Earth (semi-minor axis) is $c = 6356.8 \text{ km}$.

The surface area of the oblate ($c < a$) spheroid is:

$$S = 2 \pi a^2 \left( 1 + \frac{1 - e^2}{e}\tanh^{-1} e \right)$$

where $e^2 = 1 - \frac{c^2}{a^2}$.

Which gives us $\approx 0.51 \times 10^9 \text{ km}^2$.

Dividing the volume of the oceans by this results gives us $\approx 2.6 \text{ km}$.

Note: Earth is not a sphere. An ellipsoid is a better representation of our Earth. Nevertheless, the answer to your question would have been approximately the same had I used a sphere instead, as suggested in the title of your question.

  • 1
    $\begingroup$ Do you think that because of all the mountains and seadephts the sizes you used (6378 and 6356) are wright? $\endgroup$
    – Marijn
    Commented Feb 3, 2016 at 20:27
  • 1
    $\begingroup$ You can try and add the water of all lakes and lagoons, as well as the water in rivers and ice in glaciers and mountaintops, and see how much a variation you get. I am not much familiarized with the Snowball Earth hyphotesis. $\endgroup$
    – carnendil
    Commented Feb 3, 2016 at 20:54
  • 6
    $\begingroup$ @userLTK -- It's the other way around. If this hypothesis is correct, ice sheets up to 3 km thick ice covered the continents, but not the oceans. The oceans would have been covered by a much thinner layer of ice, possibly with partially open water near the equator. $\endgroup$ Commented Feb 7, 2016 at 14:15
  • 1
    $\begingroup$ @DavidHammen Thanks, and that makes sense. Ice would build up on land but perhaps stay liquid in the salty oceans, with, as you said, a thinner ice layer on top. Sea level must have dropped perhaps as much as a mile in that case. $\endgroup$
    – userLTK
    Commented Feb 8, 2016 at 4:40
  • 2
    $\begingroup$ Even with a smooth Earth, the oceans wouldn't be a uniform depth. For the same reason Earth is an oblate spheroid, the Earth + water would be a slightly larger oblate spheroid. The ocean would be shallower at the poles and deeper at the equator by the same ratio as the Earth's axes, so 1/290. $\endgroup$
    – kwknowles
    Commented Apr 11, 2016 at 3:43

510,100,000 square kilometers of surface area, and a total of 1,386,000,000 cubic kilometers of water gives you a 2.717 kilometer column of water across the whole planet if it was billiard ball smooth, but the same basic shape.

  • 1
    $\begingroup$ I should note that there will be some variance, in the range of metres due to tidal and rotational effects, and very very minor variances due to local thermal conditions. $\endgroup$
    – Ash
    Commented Aug 16, 2017 at 11:16
  • 3
    $\begingroup$ Hopefully, you mean ideally snooth rather than the much rougher surface of a billiard ball. Earth is already smoother than a billiard ball. $\endgroup$
    – Spencer
    Commented Feb 11, 2018 at 1:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.