What is the formula for the volume of an ellipsoid?

V = (4/3)π·a·b·c, where a, b, and c are the three semi-axes (half the lengths of the axes). When a = b = c = r this reduces to the familiar sphere formula V = (4/3)πr³.

A semi-axis is half the full axis length. If an ellipsoid measures 10 cm along the x-axis, then a = 5 cm. Think of it like the radius of a sphere but in each of three directions.

What is the difference between a prolate and oblate spheroid?

Both are special cases where two semi-axes are equal. A prolate spheroid (like a rugby ball) has a > b = c. An oblate spheroid (like a flattened Earth) has a = b > c.

Does the unit matter?

Only consistency matters. All three axes must use the same unit. The result is then in that unit cubed — e.g. if you enter centimeters, the volume is in cm³.

Can I use this for a sphere?

Yes. Set a = b = c = r. The calculator will return (4/3)πr³, which is the standard sphere volume formula.

How precise is the result?

The tool uses JavaScript's built-in Math.PI (15+ significant digits) and displays the result rounded to 6 significant figures. For most engineering and academic purposes this is more than sufficient.

Volume of an Ellipsoid Calculator

Enter the three semi-axes a, b, and c to instantly compute the volume of any ellipsoid using V = (4/3)π·a·b·c.

Semi-Axes Input

Semi-axis a (x-direction)

Semi-axis b (y-direction)

Semi-axis c (z-direction)

Unit

Result

Enter all three semi-axes and click Calculate.

Quick Reference Examples

Summary

An ellipsoid is a three-dimensional surface where every cross-section is an ellipse. Its volume depends on the three semi-axes a, b, and c — the half-lengths along the x, y, and z axes respectively. This calculator applies the standard formula V = (4/3)π·a·b·c to give an exact result in any unit you choose.

How it works

Enter semi-axis a (half-length along the x-axis).
Enter semi-axis b (half-length along the y-axis).
Enter semi-axis c (half-length along the z-axis).
Select your unit of measurement (mm, cm, m, in, ft, etc.).
The volume is computed instantly using V = (4/3)π·a·b·c.
Copy the result or view the step-by-step formula breakdown.

Use cases

Calculate the volume of a water tank or pressure vessel with an ellipsoidal shape.
Determine the volume of a prolate or oblate spheroid in physics problems.
Estimate the size of biological cells or organs modeled as ellipsoids.
Verify geometry homework or exam calculations.
Engineering design: check capacity of dome-capped silos or capsule containers.
Astronomy: approximate the volume of non-spherical celestial bodies.
Check that a sphere (a=b=c=r) gives the expected (4/3)πr³.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu