Sphere Volume Calculator
Calculate the volume of a sphere from its radius or diameter. Free sphere volume calculator that also returns surface area with the formula and steps shown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Sphere Volume Calculator Works
Enter the radius or diameter of a sphere and this calculator returns its volume and surface area. Use the dropdown to switch between radius and diameter input; the calculator handles the halving for you and shows every step.
The Formulas
Volume = 4⁄3 × π × r³ Surface area = 4 × π × r²
Cube the radius for the volume; square it for the surface area. If you start from the diameter, divide by 2 to get the radius first.
Worked Example
For a sphere with a radius of 6:
- Volume = 4⁄3 × π × 6³ = 4⁄3 × π × 216 = π × 288 ≈ 904.78 cubic units
- Surface area = 4 × π × 6² = 4 × π × 36 ≈ 452.39 square units
Volume by Radius
| Radius | Volume (4⁄3 πr³) | Surface area (4πr²) |
|---|---|---|
| 1 | 4.19 | 12.57 |
| 3 | 113.10 | 113.10 |
| 6 | 904.78 | 452.39 |
| 10 | 4,188.79 | 1,256.64 |
Where Sphere Volume Is Used
Sphere volume appears in physics, engineering and everyday estimation: the capacity of ball-shaped tanks and domes, the volume of planets, droplets and bubbles, and the displacement of spherical objects in fluid. Because volume grows with the cube of the radius, doubling the radius multiplies the volume by eight.
Frequently asked questions
What is the formula for the volume of a sphere?+
The volume of a sphere is V = 4⁄3 × π × r³, where r is the radius. You cube the radius, multiply by pi, then by four-thirds. For a sphere of radius 6, the volume is 4⁄3 × π × 216 ≈ 904.78 cubic units.
How do I find the volume of a sphere from the diameter?+
Halve the diameter to get the radius, then apply V = 4⁄3 × π × r³. For a diameter of 12, the radius is 6 and the volume is about 904.78 cubic units. This calculator accepts either the radius or the diameter directly.
What is the surface area of a sphere?+
The surface area of a sphere is A = 4 × π × r². For a radius of 6 that is 4 × π × 36 ≈ 452.39 square units. Notice this equals exactly four times the area of a flat circle with the same radius.
Why is there a four-thirds in the sphere volume formula?+
The 4⁄3 factor comes from integrating the cross-sectional area of the sphere over its diameter (a result first derived by Archimedes). It reflects that a sphere fills exactly two-thirds of the cylinder that just encloses it.
What units does the sphere volume use?+
Enter the radius or diameter in any unit and the volume comes out in that unit cubed — centimetres give cubic centimetres, inches give cubic inches, and so on. Just keep the input in a single consistent unit.