Ellipsoid Axes
Volume & Area Results
An Ellipsoid Volume Calculator is a specialized 3D geometry tool designed to find the total internal space of an ellipsoid. You can think of an ellipsoid as a sphere that has been stretched or squashed in different directions. This calculation is widely used in astronomy to measure planets, in physics, and in advanced 3D rendering.
How the Volume is Calculated
A standard sphere has a single radius because it is perfectly round. An ellipsoid, however, has three different radii extending from its center, known as semi-axes (labeled a, b, and c). These map to the length, width, and depth of the shape.
Volume Formula: V = 4/3 × π × a × b × c
To find the volume, you simply multiply the lengths of the three semi-axes together, multiply that result by Pi (π), and then multiply by the fraction 4/3. This formula is a direct expansion of the standard sphere volume formula.
How to Use This Tool
- Enter the length of the first semi-axis (A) extending along the x-axis.
- Enter the length of the second semi-axis (B) extending along the y-axis.
- Enter the length of the third semi-axis (C) extending along the z-axis.
- The calculator instantly processes the formula to provide the total volume and identifies what specific type of ellipsoid you have created.
Frequently Asked Questions
What is the difference between an oblate and a prolate ellipsoid?
An oblate ellipsoid looks like a slightly squashed sphere or a disc, similar to the shape of the Earth or an M&M candy. This happens when two axes are equal but the third is shorter. A prolate ellipsoid is stretched out like a football or a cigar. This occurs when two axes are equal and the third is significantly longer.
What is a scalene ellipsoid?
A scalene ellipsoid (also called a triaxial ellipsoid) is a shape where all three semi-axes (a, b, and c) have completely different lengths. It is neither perfectly round, nor purely disc-shaped, nor perfectly cigar-shaped.
What are the cross areas shown in the calculator?
If you were to slice the ellipsoid perfectly in half along the XY or XZ planes, the exposed flat surface would be an ellipse. The cross area values show you exactly how much 2D area those specific slices cover, using the standard ellipse area formula (π × axis1 × axis2).