Ellipsoid Volume Calculator
Volume:
Surface Area:
Understanding Ellipsoids
Volume Formula
V = (4/3)πabc
where a, b, c are semi-axes lengths
Triaxial Ellipsoid
All three semi-axes are different
Oblate Spheroid
Two equal semi-axes, third is shorter
Prolate Spheroid
Two equal semi-axes, third is longer
Surface Area
Approximate formula by Knud Thomsen:
S ≈ 4π((a^p×b^p + a^p×c^p + b^p×c^p)/3)^(1/p)
where p ≈ 1.6075
Exact Formula
Involves elliptic integrals
Approximation
Error < 1.061%
Special Cases
Simplifies for spheroids
Applications
Physics
Planetary and molecular modeling
Engineering
Pressure vessel design
Biology
Cell and organ modeling
Advanced Properties
Geometric Properties
- Principal Curvatures
- Gaussian Curvature
- Mean Curvature
- Focal Points
Physical Properties
- Moment of Inertia
- Center of Mass
- Gravitational Field
- Fluid Dynamics
Mathematical Analysis
- Parametric Equations
- Cross Sections
- Coordinate Systems
- Symmetry Groups