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Sphere Volume Calculator

How do I find the volume of a sphere?

How it is calculated

For a sphere of radius r, the tool computes volume V = 4/3 × π × r³ and surface area A = 4 × π × r². Use the radius, which is half the diameter; if you only know the diameter, halve it first. Volume comes out in cubic units and area in square units of whatever length unit you entered (cm gives cm³ and cm²). The radius must be greater than zero. Results use the full value of π and are rounded to two decimals. Note that doubling the radius multiplies the surface area by 4 and the volume by 8.

Worked example

Take a ball with radius 5 cm. Cube the radius: 5³ = 125. Volume = 4/3 × π × 125 ≈ 523.60 cm³. For the surface, square the radius: 5² = 25, so area = 4 × π × 25 ≈ 314.16 cm². As a check, 1 cm³ of water weighs about 1 g, so this ball holds roughly 0.52 litres.

Try this example →

Common mistakes

  • Entering the diameter in the radius field, which makes the volume 8 times too large.
  • Mixing up cubic and square units: volume is in cm³ (or litres after converting), surface area in cm².
  • Forgetting that 1,000 cm³ equals 1 litre when converting a tank's volume.
  • Measuring the outer radius of a hollow ball and treating it as the capacity; wall thickness reduces the inner radius.
  • Rounding π to 3 by hand, which already shifts the volume by almost 5%.

About this calculator

This calculator computes a sphere's volume (4/3 × π × r³) and surface area (4 × π × r²) from its radius, the two measurements that describe how much space a sphere takes up and how much material it would take to cover it.

It's used in physics and engineering problems involving balls, tanks, and spherical containers — estimating how much liquid or gas a spherical tank holds, or how much paint or coating covers a spherical surface — as well as in geometry classes teaching 3D solids. It also comes up in real-world estimation, like comparing the volume of two differently sized balls or planets.

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