Ellipsoid Volume Calculator
Calculate the volume of an ellipsoid using three semi-axes a, b, and c. Formula: V = (4/3) x pi x a x b x c. Covers spheroids, rugby balls, and planets.
How to use this tool
- Enter semi-axis a, semi-axis b and semi-axis c in the fields above.
- Results update instantly as you type โ or click Calculate.
- Read your volume and the full breakdown beneath it.
Formula
V = (4/3) x pi x a x b x c
How it works
Multiply all three semi-axes together, multiply by pi, then by 4/3: V = &frac43;ฯabc.
Worked example
Ellipsoid a=5, b=4, c=3
- a=5, b=4, c=3
- a x b x c = 60
- V = (4/3) x pi x 60 = 80 x pi
- V = 251.3274...
Volume = 251.3274 cubic units
Common mistakes to avoid
- Swapping semi-axes for full axes โ each input must be a semi-axis (half the width along each dimension), not the full diameter.
- Treating all three semi-axes as equal when the shape is actually a spheroid (two axes equal, one different), and using the sphere formula instead of the general ellipsoid formula.
- Omitting the 4/3 factor and computing pi*a*b*c, which gives three-quarters of the correct volume.
Key terms
- What are semi-axes?
- The three half-lengths along the x, y, and z axes of the ellipsoid; when all equal r you get a sphere.
- What is a prolate spheroid?
- An ellipsoid with two equal short axes and one longer axis, like a rugby ball.
Frequently asked questions
- What is a semi-axis?
- A semi-axis is half the total extent of the ellipsoid along one coordinate direction. If an ellipsoid measures 10 cm wide along the x-axis, then a = 5 cm. All three inputs a, b, c should be semi-axes.
- How do I use this for a prolate spheroid, like a rugby ball?
- A prolate spheroid has two equal semi-axes. Set two of the inputs (e.g., b and c) to the same value (the equatorial radius) and the third (a) to the polar semi-axis. The formula still applies.
- Does this formula work for a sphere?
- Yes. When a = b = c = r, the formula gives V = (4/3)*pi*r^3, which is the standard sphere volume.