Sphere Volume Calculator

Work out sphere volume instantly with clear inputs, formula shown and shareable results.

About Sphere Volume Calculator

Archimedes showed that a sphere occupies two thirds of its circumscribing cylinder, which gives V = ⁴⁄₃πr³. The surface area 4πr² is exactly the derivative of the volume with respect to r.

Formulas

Volume

V = ⁴⁄₃πr³

Surface area

S = 4πr²

Worked example

With the default values below, Sphere Volume Calculator returns Volume of 904.7787. Change any input above and every figure here is recalculated in your browser.

Inputs used

Input givenone of Radius, Diameter: Radius
Valueminimum 0: 6

Results

Volume: 904.7787
Surface area: 452.3893
Radius used: 6.0000
Volume in litres if inputs are cm: 0.9048

Step by step

1Values used
2Volume
3Surface area
4Volume= 904.7787
5Surface area= 452.3893
6Radius used= 6.0000
7Volume in litres if inputs are cm= 0.9048

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Radius 6 gives what volume?

⁴⁄₃π × 216 = 288π ≈ 904.778684 cubic units.

Why is dV/dr = S?

Growing the radius by dr adds a thin shell of thickness dr over the whole surface, so the added volume is S·dr.