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Sphere from Volume Calculator

Find a sphere's radius from its volume.

How it is calculated

The sphere volume formula V = (4/3)·π·r³ is solved for the radius: r = (3V / 4π)^(1/3). From that radius the tool also gives the diameter d = 2r and the surface area A = 4πr². The radius and diameter are shown to four decimals, the surface area to two.

The volume must be greater than zero, otherwise there is no result. The tool has no unit selector and labels results as generic units: if the volume is in cubic centimetres, the lengths are in centimetres and the surface area in square centimetres, and the same holds for any other consistent unit.

Worked example

A spherical tank holds 1000 cubic units. First 3V / 4π = 3000 / 12.566 = 238.73. The cube root of 238.73 is the radius: 6.2035 units. The diameter is 2 × 6.2035 = 12.4070 units. The surface area is 4π × 6.2035² = 483.60 units².

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Common mistakes

  • Mixing up litres and cubic metres: 1 m³ is 1000 litres, so convert to one consistent volume unit before entering it.
  • Reading the first result as the diameter; the main figure is the radius, the diameter is the separate line and is twice as large.
  • Expecting the radius to grow in proportion to the volume; it grows with the cube root, so doubling the volume increases the radius by only about 26%.
  • Using the formula for an internal capacity and forgetting wall thickness: the result is the inner radius if you entered the inner volume.
  • Entering a volume of 0 or a negative value, which gives no result.

About this calculator

This calculator inverts the sphere volume formula, V = (4/3)πr³, to solve for radius: r = (3V/4π)^(1/3). From that radius it also reports the diameter (2r) and surface area (4πr²), so a single known volume gives you every other size measurement of the sphere.

It comes up whenever volume is the number you actually have but size is what you need — sizing a spherical storage tank or pressure vessel to fit a given capacity, working out the radius of a water droplet or gas bubble from its measured volume in a lab, or checking a ball's diameter from a manufacturing spec. Engineers, chemistry and physics students, and packaging designers all use it the same way.

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