Ellipsoid Volume Calculator
Calculate the volume and approximate surface area of an ellipsoid from its three semi-axes a, b, and c.
Everyday Uses
Kitchen estimates
Eggs, melons, and avocados are ellipsoids — estimate their volume for recipes or fun food math.
Party planning
Estimate the volume of rugby-ball balloons or egg-shaped decorations for helium or filler.
Tanks and containers
Many tanks and floats are ellipsoidal — calculate capacity from the three measured dimensions.
School projects
A hands-on way to learn how the sphere formula generalizes when the three axes differ.
Frequently Asked Questions
How do you calculate the volume of an ellipsoid?
The volume of an ellipsoid is V = (4/3) × π × a × b × c, where a, b, and c are the three semi-axes — half the total width along each perpendicular direction. Example: an ellipsoid with semi-axes 6, 4, and 3 has volume (4/3)π(6)(4)(3) ≈ 301.6 cubic units. When a = b = c the formula reduces to the familiar sphere volume (4/3)πr³.
What is a semi-axis?
A semi-axis is the distance from the center of the ellipsoid to its surface along one of the three principal directions — half the full axis length. If an egg-shaped object is 12 cm long, 8 cm wide, and 6 cm tall, its semi-axes are a = 6, b = 4, and c = 3. Always halve full diameters before entering them.
How is the surface area of an ellipsoid calculated?
A general (triaxial) ellipsoid has no exact closed-form surface area — it requires elliptic integrals. This calculator uses the Knud Thomsen approximation: SA ≈ 4π[((ab)ᵖ + (ac)ᵖ + (bc)ᵖ)/3]^(1/p) with p ≈ 1.6075, which is accurate to within about 1.06% for all ellipsoids. For a sphere it gives the exact value 4πr².
What is the difference between a sphere, a spheroid, and an ellipsoid?
A sphere has all three semi-axes equal (a = b = c). A spheroid has exactly two equal semi-axes — oblate if flattened like Earth (a = b > c), prolate if stretched like a rugby ball (a = b < c). A triaxial ellipsoid has all three semi-axes different. All three shapes use the same volume formula V = (4/3)πabc.