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Ellipsoid Volume Calculator

Find an ellipsoid’s volume.

How it is calculated

The volume of an ellipsoid is V = (4/3) × π × a × b × c, where a, b and c are the three semi-axes: the distances from the centre to the surface along three perpendicular directions. Each is half of the full length across the shape in that direction. All three must be positive and in the same unit, and the volume comes out in cubic units of that length. When all three are equal the formula reduces to the volume of a sphere, (4/3)πr³. The tool gives volume only; surface area of a general ellipsoid has no simple closed formula and is not calculated.

Worked example

Take semi-axes a = 5, b = 3 and c = 2. Product: 5 × 3 × 2 = 30. Multiply by 4/3 × π ≈ 4.18879: 4.18879 × 30 = 125.66 cubic units.

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Common mistakes

  • Entering full diameters instead of semi-axes; the volume then comes out 8 times too large.
  • Mixing units, for example one axis in centimetres and another in millimetres.
  • Using the formula for a shape that is not really an ellipsoid, such as a box with rounded corners or a lemon-shaped solid.
  • Reading the result in square units; volume is always in cubic units.
  • Expecting the same tool to give surface area; it returns volume only.

About this calculator

This calculator applies the formula V = (4/3)πabc, where a, b and c are the three semi-axes of the ellipsoid — a sphere is just the special case where all three are equal. It's the three-dimensional generalization of the circle-to-ellipse relationship.

It's used by students and engineers computing the volume of egg-shaped tanks or vessels, geologists estimating the volume of irregular ore or mineral deposits modeled as ellipsoids, and — notably — in medical imaging, where radiologists estimate tumor or organ volume from three measured diameters using this exact formula.

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Comments (1)

  • Editorial team

    A quick sanity check needs no calculator: an ellipsoid fills about 52% of the box that just encloses it, because the ratio is π ÷ 6, roughly 0.5236. Multiply the full length, width and height of the box and see whether your result lands near half of it. If it is far off, a diameter was probably typed where a semi-axis belongs. What object are you approximating with an ellipsoid, and how did you measure its three dimensions?

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