What this calculator does
The volume of a sphere is the space enclosed inside a ball shape, found from the radius alone using V = 4/3 × π × r³. It is the figure behind everything from how much a spherical tank holds to how much material a cast ball or scoop of ice-cream contains.
This calculator keeps that one figure as the headline result, taking just a radius and returning the volume of sphere directly, with the surface area and litre capacity given underneath. For the surface area as the primary focus instead, the full sphere calculator covers both together.
The formula
The sphere volume formula is V = 4/3 × π × r³: the radius cubed, multiplied by π and by four-thirds. Cubing the radius is what makes volume grow so quickly as a sphere gets larger, much faster than its surface area or diameter.
| Term | Meaning |
|---|---|
| V | Volume: the space enclosed inside the sphere, 4/3 × π × r³. |
| r | Radius: the distance from the centre of the sphere to its surface. |
| π | Pi, approximately 3.14159, the constant linking a sphere’s radius to its volume and surface area. |
The inputs explained
| Field | What to enter |
|---|---|
| Radius | The radius of the sphere, from its centre to the surface. |
When to use it
Sizing a spherical tank or dome
A spherical storage tank, dome or pressure vessel has its capacity fixed entirely by the radius, and volume of a sphere gives that figure directly.
Estimating material for a cast or moulded ball
A ball bearing, cast sphere or moulded scoop uses a volume of material equal to the sphere volume formula applied to its radius, useful for costing or weight estimates once density is known.
Working a sphere volume formula problem
A geometry or physics question giving a radius and asking for volume is solved directly here, without separately cubing the radius and multiplying by 4/3π by hand.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does sphere volume change with the radius?
The volume and surface area of a sphere across a range of radius values.
| Radius | Volume | Surface area |
|---|---|---|
| 1 | 4.189 | 12.566 |
| 2 | 33.510 | 50.265 |
| 5 | 523.599 | 314.159 |
| 10 | 4,188.79 | 1,256.64 |
| 15 | 14,137.17 | 2,827.43 |
| 20 | 33,510.32 | 5,026.55 |
Questions
What is the volume of sphere formula?
V = 4/3 × π × r³, where r is the radius. Cubing the radius means volume grows very quickly as a sphere gets bigger.
How do you find sphere volume from the diameter instead of the radius?
Halve the diameter to get the radius first, then apply V = 4/3 × π × r³ as usual. Using the full diameter in place of the radius would overstate the volume by a factor of eight.
How do you find sphere volume in litres?
Measure the radius in centimetres, calculate V = 4/3 × π × r³ to get cubic centimetres, then divide by 1,000, since 1 litre equals 1,000 cubic centimetres.
Why does sphere volume grow faster than its surface area?
Volume is proportional to the radius cubed while surface area is only proportional to the radius squared, so as a sphere scales up, its volume accelerates away from its surface area.
For surface area as the headline figure, or both together, see the full sphere calculator. For the volume of a cone instead, see the cone volume calculator.