Ellipsoid Calculator
Calculate the volume, surface area, and other properties of an ellipsoid using its three semi-axes lengths.
Ellipsoid Volume and Surface Area Calculator
Calculate the volume and surface area of an ellipsoid with our easy-to-use calculator. Learn about ellipsoid formulas, real-world applications, and explore interactive examples.
An ellipsoid is a three-dimensional shape where all plane cross-sections are either ellipses or circles. Our ellipsoid calculator helps you determine both the volume and surface area using its three semi-axes lengths. Essential for physics, engineering, and mathematical modeling.
Formula
Volume = (4/3)πabc
Surface Area ≈ 4π((ab)^1.6 + (ac)^1.6 + (bc)^1.6 / 3)^(1/1.6)
Where:
- a:length of the first semi-axis (in your chosen unit of length)
- b:length of the second semi-axis (in your chosen unit of length)
- c:length of the third semi-axis (in your chosen unit of length)
- π:pi, approximately equal to 3.14159
How to Calculate Ellipsoid Volume
To calculate the volume of an ellipsoid, multiply the product of the three semi-axes by 4π/3...
Real-World Applications
Ellipsoids are used to model planetary bodies, atomic electron clouds, and many natural phenomena...
Frequently Asked Questions
What is the difference between a sphere and an ellipsoid?
A sphere is a special case of an ellipsoid where all three semi-axes are equal. When a ≠ b ≠ c, you have a scalene ellipsoid; when two are equal, you have a spheroid.
Why is the surface area formula approximate?
Unlike volume, there is no simple exact formula for the surface area of a general ellipsoid. The formula provided is Knud Thomsen's approximation, accurate to within 1.061%.