Case 1
- Radius
- 5
523.598776
Open with these valuesSphere Volume Calculator
523.598776units³
Result: 523.598776 units³Four thirds of π times the radius cubed. The radius enters as a cube, so doubling it multiplies the volume by eight: a ball of radius 5 holds 523.6 units³, one of radius 10 holds 4188.8. If you measured across the ball, halve that first.
Worked examples
How it's calculated
V = ⁴⁄₃ × π × r³
- StepMeasure the radius — half the width across the middle.
- StepEnter it in any single length unit.
- ResultRead the volume in the cube of that unit.
What this number means
Doubling the radius multiplies the volume by eight
The radius enters as a cube, so the volume grows with 2³ = 8. Radius 5 holds 523.6 units³ and radius 10 holds 4188.8 — eight times as much from twice the measurement.
Any length unit works, cubed
Enter the radius in one single length unit; the volume comes back in the cube of that unit. The formula fixes no unit of its own.
Every row of the table is an exact multiple of π
Radius 5 is 500π ÷ 3, radius 2 is 32π ÷ 3. The decimal beside it is only that same number written out, so any row can be checked by hand.
Commonly misread
The ball measures 10 across, so I enter 10.
Halve it first: the radius is 5. Entering the diameter instead overstates the volume eightfold, 4188.8 in place of 523.6.
The volume of a sphere is πr³.
It is four thirds of that. Radius 1 gives 4.188790, and dropping the four thirds understates every result by a quarter.
A half sphere needs a formula of its own.
It is exactly half of this figure, ⅔πr³. The separate hemisphere calculator additionally accounts for the flat circular face.
Reference table
| Radius | Exact | Volume |
|---|---|---|
| 0.5 | π ÷ 6 | 0.523599 |
| 1 | 4π ÷ 3 | 4.188790 |
| 2 | 32π ÷ 3 | 33.510322 |
| 5 | 500π ÷ 3 | 523.598776 |
| 10 | 4000π ÷ 3 | 4188.790205 |
Questions
How do you calculate the volume of a sphere?
Cube the radius, multiply by π and then by four thirds. A radius of 5 gives 500π ÷ 3, about 523.6 cubic units.
I have the diameter, not the radius.
Halve it. A ball 10 units across has a radius of 5, and entering 10 by mistake overstates the volume eightfold.
Why does the volume grow so fast?
Because the radius is cubed. Doubling the radius multiplies the volume by 2³ = 8, which is why a slightly larger ball holds far more than it looks.
What is the volume of a half sphere?
Exactly half of this, or ⅔πr³. There is a separate hemisphere calculator that also gives the flat circular face.
Sources and last check
Information, not professional advice.