Ellipsoid volume calculator
Enter the three semi-axes: half the length, half the width and half the height of the oval solid.
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How to use it
- Enter semi-axis a, semi-axis b, semi-axis c and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Volume = 4/3 × π × a × b × c. Surface area ≈ 4π × (((ab)^p + (ac)^p + (bc)^p) / 3)^(1/p) with p = 1.6075.
Example
Inputs: Semi-axis a = 3, Semi-axis b = 2, Semi-axis c = 1, Length unit = Centimeter (cm). Result: Volume: 25.1327 cm³; Surface area (approximate): 48.9719 cm²; Volume in liters: 0.025133 L.
Limits and caveats
- Volume is exact; surface area is an approximation with at most about 1.061% relative error, since a general ellipsoid has no simple closed form.
- When all three axes are equal the formula gives the exact sphere area.
- Results are in the cube or square of the unit you chose, so enter every dimension in that same unit.
Questions about this tool
What is the ellipsoid volume formula?
Volume = 4/3 × π × a × b × c, the sphere formula with r³ replaced by the product of the semi-axes.
Do I enter full axes or semi-axes?
Enter semi-axes. A solid 6 long, 4 wide and 2 high has semi-axes 3, 2 and 1.
Why is the surface area approximate?
A general ellipsoid has no simple exact area formula; Thomsen's formula used here stays within about 1.061%.