Ellipsoid Volume Calculator
Calculate the volume of an ellipsoid from its three semi-axes
By Drew Budwin · Last updated July 2026 · Methodology
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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 the sphere 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?
Geodesy relies on them because Earth itself is an oblate spheroid, not a true sphere. Medical imaging uses the formula to estimate organ and tumor volumes from scan measurements. Physicists also model atomic nuclei and planetary bodies as ellipsoids.
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.
How is the ellipsoid formula used in medical imaging?
Radiologists estimate organ and tumor volumes from CT or MRI scans by measuring three perpendicular diameters, then applying V ≈ (4/3)π × (d₁/2) × (d₂/2) × (d₃/2). Enter the three semi-axis measurements here to get the volume estimate.
How does Earth's ellipsoidal shape affect calculations?
Earth is an oblate spheroid with equatorial radius ≈ 6,378 km and polar radius ≈ 6,357 km. Its volume is about 1.08 × 10¹² km³. Enter a = b = 6,378 and c = 6,357 to verify. The poles are about 21 km closer to the center than the equator.
What happens when all three semi-axes are equal?
When a = b = c = r, the ellipsoid becomes a sphere and the formula reduces to (4/3)πr³. Verify this with the sphere calculator using the same radius.