Sphere Volume Calculator: V = 4/3 pi r^3

The volume of a sphere, or the radius for a volume.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • V = \frac{4\pi r^3}{3}
  • r = \sqrt[3]{\frac{3V}{4\pi}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the volume: volume = 4 pi / 3 x radius^3
  2. Put the values in (every value in its SI unit): volume = 4 pi / 3 x 0.15^3
  3. The answer: volume: 0.0141372 m3
  4. The same answer in other units: 14.1372 litres; 14137.2 cm3; 0.499249 ft3; 3.73464 US gallons

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Radius; Volume (leave it as it is if this is what you are finding) 0.014137167 m3.

  1. The formula, arranged to find the radius: radius = cube root of ((volume) / (4 pi / 3))
  2. Put the values in (every value in its SI unit): radius = cube root of ((0.0141372) / (4 pi / 3))
  3. The answer: radius: 0.15 m
  4. The same answer in other units: 15 cm; 150 mm; 5.90551 inches

Common questions

What is the formula for the volume of a sphere?

Four thirds times pi times the radius cubed. A sphere of radius 0.15 m has a volume of 14.1 litres.

How do I find the radius from the volume?

Multiply the volume by 3, divide by 4 pi and take the cube root.

What is the surface area of a sphere?

4 pi times the radius squared.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school mathematics text (volume of a sphere).

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