Ellipsoid Calculator

How to use the Ellipsoid Calculator

1. 1Enter the three semi-axes a, b and c.
2. 2Pick the units or options from the menus if the ellipsoid volume tool offers them.
3. 3Read the ellipsoid volume in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the ellipsoid volume

Biologists and cooks estimate the volume of eggs, fruit and cells by measuring three lengths. Engineers use ellipsoids for tanks and radomes, and geographers for the shape of the Earth, which is flattened at the poles.

The semi-axes are half the full lengths in each direction. A spheroid, a special case with two equal axes, covers both the flattened (oblate) and stretched (prolate) forms.

How the ellipsoid volume is worked out

Volume = 4⁄3 × π × a × b × c. There is no simple exact formula for the surface area; this tool uses Knud Thomsen's formula with an exponent of 1.6075, accurate to about one percent. An ellipsoid with semi-axes 5, 3 and 2 has a volume of 125.66 and a surface area of about 134.8. If all three semi-axes are equal, the shape is a sphere and the formulas give the usual 4⁄3 π r³ and 4 π r².

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Exact volume
• Accurate surface area estimate
• Three independent semi-axes

Mistakes to avoid with ellipsoid volume

Make sure to enter the semi-axes, which are half of the full width, height and depth, and not the full lengths. Using full lengths makes the volume eight times too large. The surface area is an approximation, and it is least accurate for very flat or very long shapes.

On phone and computer

On a phone, type into the boxes one after another and read the ellipsoid volume underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the ellipsoid volume move. The ellipsoid calculator works the same on both. A sphere is the special case of an ellipsoid, so check it with Sphere Calculator. Volume Calculator and Surface Area Calculator handle other solids, and Capsule Calculator covers a rounded cylinder.

Features

• Enter half-lengths
• Equal axes give a sphere
• The area is approximate
• Clear messages when the ellipsoid volume inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions