How to calculate the volume of an ellipsoid
An ellipsoid looks like a sphere stretched along three mutually perpendicular directions. Measure the full length, width and height across its center, or measure from its center to its surface. Select Full diameters if you have the edge-to-edge dimensions; the calculator divides each one by two before using the formula. Choose a length unit shared by all three dimensions. You will see cubic units, liters, US gallons, the radius of a sphere with equal volume and three central cross-sectional areas.
The exact ellipsoid volume formula
The volume is V = 4πabc/3, where a, b and c are the three semi-axes. A semi-axis is a radius, not the complete diameter. The order does not matter: swapping a, b and c leaves the product unchanged. If you measured three full diameters A, B and C, an equivalent formula is V = πABC/6. This distinction is important: putting full diameters directly into the semi-axis formula makes the answer eight times too large.
Worked example: a stretched sphere
Suppose the three semi-axes are 3 cm, 2 cm and 1.5 cm. Their product is 9 cm³. Multiply by 4π/3 to get 12π ≈ 37.699 cm³, or approximately 0.0377 liters. The same object measured across its center has full diameters of 6 cm, 4 cm and 3 cm; the Full diameters setting gives the same answer. If all three radii were 3 cm instead, the ellipsoid would be a sphere: V = 36π ≈ 113.097 cm³.
Surface area is approximate
Unlike volume, the surface area of a general ellipsoid does not have a simple elementary formula. This tool uses the Knud Thomsen approximation with exponent p = 1.6075: S ≈ 4π[((ab)^p + (ac)^p + (bc)^p)/3]^(1/p). It is exact for a sphere and usually close for ordinary stretched ellipsoids, but it is not an exact result for three unequal axes. For precise coating, manufacturing or scientific work, use a numerical method and state the approximation used.
What the other results mean
The equal-volume sphere radius is the cube root of abc. Each central cross-section is an ellipse: its area is πab, πac or πbc. Capacity in liters uses 1 cubic meter = 1,000 liters; US gallons use exactly 3.785411784 liters per gallon. These are mathematical volumes, not guarantees that a real egg, melon or irregular tank contains that much. For liquid capacity measure the inside, not the outside, and account for wall thickness and unfilled space.
When to use a different solid
An ellipsoid is a useful approximation for some oval objects, but a rugby ball, egg or pressure vessel may have a different outline. If the object has straight cylindrical walls and rounded caps, use the general volume calculator and choose Capsule. A cylinder or box also has a different formula. For rough irregular solids, displacement in a graduated container can give a more practical measurement than assuming a perfect shape.
Frequently asked questions
What is the ellipsoid volume formula?
Multiply the three semi-axes a, b and c, then multiply by 4π/3. For full diameters A, B and C, use πABC/6 instead.
How do I enter full diameters?
Select Full diameters, then enter the three perpendicular edge-to-edge measurements. The calculator halves them before applying the semi-axis formula.
Is the surface area exact?
No. The tool uses the Knud Thomsen approximation with p = 1.6075; it is exact when all three axes are equal but approximate for a general ellipsoid.
When is an ellipsoid a sphere?
When a, b and c are equal. Then the formula reduces to the sphere volume 4πr³/3 and its surface area is 4πr².
Can I use centimeters and inches together?
Choose one unit for all three inputs. Convert mixed measurements to that unit first, using the unit converter, to avoid a wrong result.
Last updated: October 17, 2026