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Ellipsoid Volume from Three Semi-Axes

Calculate ellipsoid volume from three semi-axes with converted units, positive geometric inverses and explicit model limits.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

An ellipsoid with perpendicular semi-axes 2, 3 and 4 cm has volume 32π cm³. Its full axis lengths are 4, 6 and 8 cm.

V = (4/3)πabc

Worked example

Enter these known values and leave the other values blank.

Semi-axis A
2 cm
Semi-axis B
3 cm
Semi-axis C
4 cm
Volume
100.53 cm³

Assumptions and limitations

  • All three measurements are positive semi-axes from the center to the surface. An ellipsoid has three perpendicular axes; full diameters must be halved before entry.
  • Measurements must describe the same shape. Clear a quantity you want to infer instead of supplying conflicting measurements. Unit selectors are converted before the geometric relationships are applied.
  • Calculations use 64 significant digits with full-precision π; result formatting rounds the displayed value separately. These are ideal geometric models, without material allowances or measurement uncertainty.

Common questions

Does the ellipsoid formula also cover a sphere?

Yes. Setting all three semi-axes to the same radius gives V = 4πr³/3. Two equal semi-axes describe a spheroid.

References

Require real, positive geometric inverses and the stated shape domain before displaying derived results. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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