Volume of a sphere: formula, calculator and worked example

What the symbols mean

$V$: the volume
$r$: the radius: centre to surface

When to use it

Use it for balls, bubbles, planets, ball bearings, scoops and spherical tanks. Solve for r to get the size of a sphere holding a given volume. Doubling the radius multiplies the volume by 8.

Worked example

A ball has a radius of 6 cm. What is its volume? (r = 6)

Start from the formula.
$V = \frac{4}{3} π r^{3}$
Substitute $r$ = $6$ and work it out.
$V = \frac{4}{3} π \cdot 6^{3}$
$= \frac{4}{3} π \cdot 216$
$\approx 904.779$

Answer V ≈ 904.78 cm³

Why it works

Archimedes showed that a sphere fills exactly two thirds of the cylinder that just contains it. That cylinder has volume $πr²×2r = 2πr³$ , and two thirds of it is $43/πr³$ .

Common mistakes

Squaring the radius instead of cubing it.
Using the diameter as r, which gives eight times the volume.
Mixing it up with the surface area $4πr²$ .

Volume of a sphere

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