Volume of a ellipsoid calculator
Enter the dimensions of a ellipsoid and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.
Volume
100.530 96m³
- Surface area
- 111.604 03
Show the working
- Semi-axis a = 4
- Semi-axis b = 3
- Semi-axis c = 2
- Volume = 4/3 * pi * 4 * 3 * 2 = 100.531
- Surface area = 4 * pi * ((4^1.6075 * 3^1.6075 + 4^1.6075 * 2^1.6075 + 3^1.6075 * 2^1.6075)/3)^(1/1.6075) = 111.604
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- volume = (4/3) pi a b c
- surface area uses Knud Thomsen's approximation, accurate to about 1%
The exact surface area of a general ellipsoid needs elliptic integrals; the approximation used here is the standard engineering one.
Switch the volume unit to litres or US gallons to read the capacity directly.
Related calculators
- Volume of a sphere
- Volume of a cylinder
- Volume of a cone
- Volume of a rectangular box
- Volume of a hemisphere
- Volume of a hexagonal prism
- Volume of a hollow cylinder
- Volume of a rectangular pyramid
- Volume of a regular dodecahedron
- Volume of a regular icosahedron
- Volume of a regular octahedron
- Volume of a regular tetrahedron
- All geometry calculators →