FreeToolStation

Sphere Calculator

Any sphere measurement gives you the rest.

Geometry Calculators Free, no sign-up Runs in your browser
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Radius
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Diameter
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Volume
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Surface area
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Volume in litres
MeasureValue

About the Sphere Calculator

Sphere Calculator works in all four directions. Radius, diameter, volume and surface area each determine the others, so you enter whichever you have. Going backwards from volume involves a cube root and from surface area a square root, and both are easy to get wrong by hand.

The volume formula, four thirds pi r cubed, has the cube in it, which is why small changes in radius make large changes in volume. A ball ten per cent larger in radius holds about a third more. The same relationship is why the ratio of surface area to volume falls as a sphere grows.

One figure in the table is worth knowing: a sphere fills about 52.4 per cent of the smallest cube that contains it, exactly pi over six. That is the upper bound on how efficiently you can pack a single ball into a box, and it is why spherical packaging wastes so much space.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

Looking for something this does not cover? FreeToolStation.com is a second collection of the same kind of everyday tools, and it is worth a look if sphere calculator is only part of what you are working on.

How to use the Sphere Calculator

  1. Choose i know the and measurement inThe fields below change to match what you pick, so only the figures that matter to your case are asked for.
  2. Enter valueDecimals are fine, and thousands separators are accepted and ignored.
  3. Read the radius, diameter and volumeThe figures update as you type. The Calculate button is there if you would rather press something, but nothing waits for it.
  4. Copy or check the resultCopy the summary with the copy button, or open the table to check it row by row and read the formula with your own numbers in it.

Features

  • Shows radius, diameter, volume, surface area and volume in litres together, so you are not running it twice
  • A results table you can read across
  • Prints the formula with your own figures substituted in
  • Updates as you type, with no button to press and no page reload
  • Copy the result in one click
  • Free, no sign-up, and it runs entirely in your browser

Who uses this tool

The sphere calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

  • Finding the volume of a spherical tank in litres
  • Working out the radius from a known volume
  • Getting the surface area of a ball or dome
  • Comparing a sphere's volume with its enclosing box

Frequently asked questions

How do I find the radius from the volume?

Multiply by three, divide by four pi, and take the cube root. The calculator does it when you choose volume as the known value.

Why does doubling the radius make eight times the volume?

Because the radius is cubed. Two cubed is eight, so every linear doubling multiplies volume by eight.

What is a hemisphere's volume?

Half of the figure here. The surface area of a hemisphere is half the sphere plus the flat circular face.

If the sphere calculator is not quite what you need, these other free tools solve closely related problems, and there are 16 more in geometry calculators.

Volume Calculator

Volume of boxes, cylinders, spheres, cones and tanks.

Geometry Calculators Use tool

Circle Calculator

Radius, diameter, circumference and area of a circle.

Geometry Calculators Use tool

Checked and rebuilt on 2026-10-14. The method this calculator uses is described in the section above, and corrections go through the contact page.