Sphere Volume Calculator

Enter the radius of a sphere to get its volume, surface area and great-circle circumference, drawn to scale. Click the diameter on the drawing to change it.

Dimensions

Sphere
Blueprint · Isometric Click an amber dimension to edit it · isometric, not to printed scale

Result

Volume of a sphere

A sphere encloses the most volume for its surface of any shape, following the four-thirds rule V = 4⁄3·πr³. Its surface area, 4πr², is exactly four times the area of the circle through its centre.

Editing on the drawing

Click the diameter leader on the figure and type a new value — the radius is set to half and the sphere redraws to scale.

How to find the volume of a sphere

A sphere is the most efficient solid there is: for a given surface area it encloses more volume than any other shape. A single measurement — the radius — describes it completely.

The formulas

The volume follows the four-thirds rule, and the surface area is exactly four times the area of the great circle through the centre.

V = 4⁄3·πr³
A = 4πr²

Worked example

Take a sphere of radius 48.

Step 1 — volume

Four-thirds of π times the radius cubed.

V = 4⁄3 × π × 48³ = 4⁄3 × π × 110,592 ≈ 463,247
Step 2 — surface area

Four times the great-circle area.

A = 4π × 48² = 4π × 2,304 ≈ 28,953
Step 3 — great-circle circumference

The widest way round.

C = 2π × 48 ≈ 301.6

What else the calculator returns

You also get the diameter and the great-circle circumference — the distance around the sphere at its widest. Because a sphere has no flat faces to measure across, the figure uses a diameter leader you can click to edit.

Where it comes up

Sphere volumes describe balls and bearings, domes and spherical tanks, droplets and bubbles, and planets. The four-thirds rule is also why a sphere is the shape liquids take in free fall — it minimises surface for the volume held.

Frequently asked questions

How do you find the volume of a sphere?

Use the four-thirds rule with the radius: V = 4⁄3·πr³.

I have the diameter — what then?

Halve it to get the radius (r = d/2), or type the diameter on the figure and the radius is set for you.

How do I find the radius from the volume?

Rearrange the formula: r = ∛(3V / 4π).

Why is the surface area 4πr²?

It works out to exactly four times the area of the sphere's great circle, πr². The result comes from calculus and holds for every sphere.

What is a great circle?

Any circle drawn on the sphere whose centre is the sphere's own centre — the largest circle that fits on it, such as the equator, with circumference 2πr.