Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Volume grows with the cube of the radius, so a small measurement error compounds fast. Doubling a sphere's radius doesn't double its volume, it multiplies it by eight, which means a measuring mistake that looks minor on the radius can throw the volume off by a wide margin.
Before you rely on it
What to check
Double-check the radius measurement specifically, since any error there gets tripled in effect once it runs through the cube.
The common error
Where people go wrong with sphere volume & surface area calculator
Assuming volume scales the same way surface area does. Surface area scales with the square of the radius and volume with the cube, so the two grow at very different rates as a sphere gets larger.
Sensitivity evidence
How radius changes the volume
| Radius | Volume | Surface area |
|---|---|---|
| 3.2 | 137.3 | 128.7 |
| 3.6 | 195.4 | 162.9 |
| 4worked example | 268.1 | 201.1 |
| 4.4 | 356.8 | 243.3 |
| 4.8 | 463.2 | 289.5 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Radius | 4 |
| Volume | 268.1 |
| Surface area | 201.1 |
Where the inputs come from
Enter the radius of the sphere, half of its diameter, in one unit. Measure at the widest point, and use the inside radius for containers. The calculator gives volume, four thirds pi r cubed, and surface area, four pi r squared. Remember that volume is in cubic units, so a radius in inches gives cubic inches, which you can convert to gallons or liters with the unit conversion pages.
When the result stops applying
A hollow shell's volume is the difference between two spheres. Rounding pi and the radius introduces small errors. Units must be cubed consistently.
What to compare it with
Half a sphere is on the hemisphere calculator, other solids on the cylinder, cone and capsule pages, and rings on the annulus calculator. The circle area page gives the cross-section, and the aquarium and unit conversion calculators convert volumes to gallons and liters.
People also ask
Frequently asked questions
What is the formula for the volume of a sphere?
Four thirds times pi times the radius cubed. A radius of 4 gives about 268 cubic units.
How does volume change when the radius doubles?
It multiplies by eight, since volume depends on the cube of the radius, so a ball with twice the radius holds eight times as much.
What is the surface area of a sphere?
Four times pi times the radius squared, which is exactly four times the area of its largest circle.