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Volume of an ellipsoid calculator

The volume of an ellipsoid from its three semi-axes: V = 4⁄3·π·a·b·c. It also reports the surface area (Thomsen's approximation) — set all three axes equal and it becomes a sphere. Useful for eggs, tanks, planets and any squashed sphere.

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Enter Semi-axis a, Semi-axis b, Semi-axis c and the Volume of an ellipsoid calculator works out Volume, Surface area (approx.) straight away. For instance, with Semi-axis a = 5, Semi-axis b = 3 and Semi-axis c = 4 it returns Volume = 251.327 and Surface area (approx.) = 199.502.

How to use it

  1. Enter your values: Semi-axis a, Semi-axis b, Semi-axis c.
  2. Read the result instantly: Volume, Surface area (approx.).

Frequently asked questions

What does the Volume of an ellipsoid calculator actually compute?

It takes Semi-axis a, Semi-axis b and Semi-axis c and derives Volume and Surface area (approx.) from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

3 values: Semi-axis a, Semi-axis b and Semi-axis c. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Semi-axis a = 5, Semi-axis b = 3 and Semi-axis c = 4, the calculator returns Volume = 251.327 and Surface area (approx.) = 199.502. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Semi-axis a = 10, Semi-axis b = 6 and Semi-axis c = 8 instead, Volume goes from 251.327 to 2,011 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Semi-axis a = 3, Semi-axis b = 2 and Semi-axis c = 2, Volume comes out at 50.266. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.

What is the most common mistake?

Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.

What is the difference between the Volume of an ellipsoid calculator and the Cylinder volume calculator?

This one returns Surface area (approx.); the Cylinder volume calculator returns Surface area. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Sphere volume calculator is the closest one after this: Compute the volume and surface area of a sphere from its radius.

What else is worth having open alongside it?

Cone volume calculator and Aquarium volume calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Calculate VolumeVolume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.How-toCircle: Circumference and AreaCircumference is 2πr, area is πr². Here's how radius, diameter and π fit together, both formulas worked through, and how not to mix them up.How-toWhat Wattage of Heater Does an Aquarium Need? Volume Is Only Half the AnswerThe same tank needs a 100 W heater in a warm flat and 300 W in an unheated room. The variable is the gap between the water and the room, which most rules of thumb drop entirely. Plus why two smaller heaters beat one big one, and where this calculator's recommendation stops being trustworthy.How-toHow Much Substrate Does an Aquarium Need? Depth, Weight and Grain SizeThe depth follows the job: a bare display, a planted tank whose roots need room, an under-gravel plate. Then comes the number people are unprepared for — substrate is what puts a filled tank past what a piece of furniture can hold. Plus why fine sand compacts and coarse gravel traps waste.ExplainerHow Many Fish Can a Tank Hold? The Inch-per-Gallon Rule Is WrongEvery stocking calculator implements a length-per-volume rule, and waste output scales with body mass, not length. A fish twice as long makes nearly five times the ammonia. Run through the tool's five methods, the same tank comes back holding anywhere from 6 to 12 fish.How-toCooking Measurement ConversionsA few anchors — cups, tablespoons, grams — cover most recipes. Here's the handful worth memorising, why weight beats volume, and when to reach for a scale.