Ellipsoid Volume Calculator
Calculate the volume of an ellipsoid from its three semi-axes
Volume
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Ellipsoid Volume Calculator Formula
Volume of an ellipsoid:
V = (4/3) × π × a × b × c
a = semi-axis along x, b = semi-axis along y, c = semi-axis along z
How to Use This Calculator
- Enter semi-axis a (horizontal extent from center).
- Enter semi-axis b (vertical extent from center).
- Enter semi-axis c (depth extent from center).
- Click Calculate Volume to see the result.
Frequently Asked Questions
What is a semi-axis?
A semi-axis is the distance from the center of the ellipsoid to its surface along a given direction. It is half the full axis length. For a sphere, all three semi-axes are equal to the radius.
What is the difference between an ellipsoid and a sphere?
A sphere has three equal semi-axes (a = b = c = r). An ellipsoid has three semi-axes that may all differ. When a = b = c, you can use our sphere volume calculator instead. When a = b ≠ c, the shape is a spheroid (like an oblate or prolate planet).
What units does this calculator use?
This calculator is unit-agnostic. If all semi-axes are in meters, the result is in cubic meters (m³). Use the same unit for all three inputs.
Where are ellipsoid calculations used in real life?
Ellipsoid volumes are used in geodesy (Earth is an oblate spheroid), medicine (estimating organ or tumor volumes from imaging scans), and physics (modeling atomic nuclei and planetary bodies).
What is a prolate vs. oblate spheroid?
A prolate spheroid is elongated like a rugby ball (a = b < c), while an oblate spheroid is flattened like Earth (a = b > c). Both are special cases of an ellipsoid where two of the three semi-axes are equal.
Can I share my calculation?
Yes. After clicking Calculate, the URL updates with your input values. Copy and share the URL to let anyone else see the same pre-filled form and result.