Calculators
Ellipsoid Calculator
Calculate ellipsoid volume and three central elliptical cross-section areas from perpendicular semi-axis lengths.
Measure an ellipsoid using its three semi-axes.
An ellipsoid has three perpendicular semi-axis lengths a, b, and c, each measured from the center to the surface. Divide full axis lengths by two before entering them. Volume V = 4πabc/3. The central sections in the ab, ac, and bc planes are ellipses with areas πab, πac, and πbc. These are flat areas through the center, not the curved surface area of the ellipsoid. For a = 5, b = 3, and c = 2, volume is 40π ≈ 125.663706144 cubic units, and section areas are 15π, 10π, and 6π square units. Equal semi-axes give a sphere; two equal semi-axes give a spheroid. Use consistent length units and positive dimensions from 1e-50 to 1e50. Results use browser floating-point arithmetic rounded to 12 significant digits. This calculates a solid ellipsoid, not a hollow shell. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Should I enter radii or full axis lengths?
Enter semi-axes: half of each full axis length. All three lengths must use the same unit and be greater than zero.
What is the ellipsoid volume formula?
Volume is 4πabc/3, where a, b, and c are the three perpendicular semi-axis lengths.
Are the section areas the surface area?
No. The three areas are flat central elliptical cross-sections: πab, πac, and πbc. This tool does not calculate curved surface area.
Can I calculate a sphere or spheroid?
Yes. Use three equal lengths for a sphere or two equal lengths for a spheroid. The same volume formula applies.
Are my dimensions uploaded?
No. Calculation and copying run in your browser. Decimal and scientific notation are accepted; use values from 1e-50 to 1e50.