Ellipsoid Volume Calculator
Calculate ellipsoid volume from three semi-axes (a, b, c) or full diameters. Includes surface area approximation and step-by-step math.
The product of the three semi-principal orthogonal radii.
Generalizes the sphere formula V = (4/3)πr³ when all three perpendicular radii differ.
The volume of an ellipsoid is V = (4/3) × π × a × b × c, where a, b, and c are the lengths of the three semi-principal axes (half of the full diameters). For an ellipsoid with semi-axes 3 in, 4 in, and 5 in, the volume is 251.33 cubic inches (1.09 US gallons).
Ellipsoid Volume Calculator Formula
| Variable | Definition | Standard Units |
|---|---|---|
| V | Internal volume of the ellipsoid | in³, ft³, cm³, or m³ |
| a | First semi-principal axis length (half of width) | in, ft, cm, or m |
| b | Second semi-principal axis length (half of depth) | in, ft, cm, or m |
| c | Third semi-principal axis length (half of height) | in, ft, cm, or m |
Ellipsoid Geometry: Generalizing the Sphere
An ellipsoid is a sphere that has been stretched or compressed independently along three perpendicular spatial axes. When a = b = c, the formula simplifies to the standard sphere formula: (4/3)πr³. When two axes are equal (a = b ≠ c), the solid is a spheroid—either oblate (like planet Earth) or prolate (like an American football).
Common Calculation Mistakes to Avoid
- Using full axis lengths instead of semi-axes (inflates calculated volume by 8×)
- Confusing the exact volume formula with the approximate surface area formula
Frequently Asked Questions
What is the formula for the volume of an ellipsoid?▼
What is the difference between a spheroid and an ellipsoid?▼
What is the surface area of an ellipsoid?▼
How do you find the volume of an ellipsoid from full diameter measurements?▼
Authoritative Sources & Reference Standards
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — National Institute of Standards and Technology (NIST). Verified 2026-10-01.
Official SI unit definitions, conversion factors (Appendix B), and precision standards for cubic meters, liters, and US customary units.
- Common Core State Standards for Mathematics: High School Geometry (Geometric Measurement and Dimension HSG.GMD.A.1–3) — National Governors Association Center for Best Practices & Council of Chief State School Officers. Verified 2026-10-01.
Curricular standards for volume formulas of cylinders, pyramids, cones, and spheres, including Cavalieri’s principle.