About Ellipsoid Volume Calculator
This ellipsoid volume calculator uses V = 4/3 πabc. The surface area has no simple exact formula, so it uses Knud Thomsen’s approximation, which is within about 1.1% and is labelled as approximate. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Semi-axes 6, 4 and 3 give a volume of 301.5929. When all three are equal the ellipsoid is a sphere.
How to use Ellipsoid Volume Calculator
- Choose the solid from the list.
- Enter its dimensions in the boxes, labelled with the measurement each one means.
- Pick the unit you measured in, and the volume unit you want, such as litres or gallons.
- Read the volume, the surface area and the table of every unit.
- Compare the labelled diagram with your object to be sure each number is in the right box.
- Open the step-by-step working to see both formulas filled in with your numbers.
Features
- Twelve solids, each with volume, total surface area, formulas and working.
- A labelled schematic diagram for every solid.
- Eight length units for the inputs.
- Volume in cubic units, litres, millilitres, US and imperial gallons, quarts, cups and fluid ounces.
- Cone frustum, capsule, ellipsoid and hollow tube, which many calculators leave out.
- Regular-polygon prisms with any number of sides from 3 to 1000.
- Helpful messages, such as when an inner radius is not smaller than the outer one.
Ellipsoid volume
The sphere formula with three different radii.
V = 4/3 π a b cWorked examples
a = 5, b = 3, c = 2 gives V = 125.6637
Surface area about 134.815.
Privacy: how it works
- All the calculations run in your browser tab. The dimensions you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Use the inside dimensions when you want the capacity of a container, and the outside ones for the space it takes up.
- For a pyramid with a square base, enter the same number for length and width.
- A capsule is a cylinder with a hemisphere on each end. Enter the cylinder length only, not the overall length.
- To fill a tank to part of its height, enter that height instead of the full height.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your measurements are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your measurements are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What are semi-axes?
Half the widths of the ellipsoid along its three perpendicular axes.
Is the surface area exact?
No. It is an approximation with an error of about one percent at most.
More Volume Calculator pages
- Volume CalculatorPick a solid, enter its dimensions and get the volume and surface area with formulas, steps, a diagram and litres or gallons.
- Cylinder Volume CalculatorEnter the radius and height of a cylinder.
- Sphere Volume CalculatorEnter the radius of a sphere.
- Cone Volume CalculatorEnter the radius and height of a cone.
- Cube Volume CalculatorEnter the edge of a cube.
- Cuboid Volume CalculatorEnter the length, width and height of a box.
- Box Volume CalculatorEnter the inside length, width and height of a box.
- Pyramid Volume CalculatorEnter the base length, base width and height of a pyramid.
- Hemisphere Volume CalculatorEnter the radius of a hemisphere.
- Prism Volume CalculatorEnter the number of base sides, the side length and the prism height.
- Frustum Volume CalculatorEnter the bottom radius, top radius and height of a truncated cone.
- Capsule Volume CalculatorEnter the radius and the length of the cylindrical part.
- Pipe Volume CalculatorEnter the outer radius, inner radius and length of a pipe.