A sphere is fully described by a single measurement — its radius. From that one value this calculator returns the volume, surface area, diameter, and great-circle circumference, useful for tanks, balls, domes, planets, and geometry homework.
How it works
Every result comes from the radius r using standard formulas:
- Volume = 4/3 · π · r³
- Surface area = 4 · π · r²
- Diameter = 2 · r
- Great-circle circumference = 2 · π · r
Because volume scales with the cube of the radius and area with the square, doubling the radius makes a sphere eight times the volume and four times the surface area. This cube relationship is why spherical containers grow capacity dramatically with small increases in radius.
Reference table: radius 1 to 10
| Radius (r) | Volume | Surface area | Diameter |
|---|---|---|---|
| 1 | 4.19 | 12.57 | 2 |
| 2 | 33.51 | 50.27 | 4 |
| 3 | 113.10 | 113.10 | 6 |
| 5 | 523.60 | 314.16 | 10 |
| 10 | 4,188.79 | 1,256.64 | 20 |
Notice that at radius 3, volume and surface area are numerically equal — a coincidence of the specific units, not a general rule.
Worked examples
Football (soccer ball). A standard football has a circumference of about 68–70 cm, so its radius is approximately 68 / (2π) ≈ 10.8 cm. Volume ≈ 4/3 · π · 10.8³ ≈ 5,272 cm³ (about 5.3 litres of air inside), and surface area ≈ 4 · π · 10.8² ≈ 1,463 cm². The actual panel area of the leather casing must cover this surface.
Storage tank. A spherical propane tank with a radius of 0.6 m holds a volume of 4/3 · π · 0.6³ ≈ 0.905 m³ ≈ 905 litres. A tank with radius 1.2 m (double the radius) holds 4/3 · π · 1.2³ ≈ 7.24 m³ ≈ 7,240 litres — eight times more, confirming the cube-scaling relationship.
Astronomy. Earth has a mean radius of about 6,371 km. Surface area = 4 · π · 6371² ≈ 510 million km² — matching the quoted figure for Earth’s total surface. Volume ≈ 1.08 trillion km³.
The great-circle circumference
The great-circle circumference is the largest possible circle you can draw around a sphere — the equator of a ball, for instance. It equals 2 · π · r, identical to a flat circle of the same radius. This is the measurement used in geography (the equatorial circumference of a planet) and navigation (great-circle routes are the shortest paths between two points on a sphere).
Units and precision
The calculator uses whatever unit you enter for the radius — centimetres, metres, feet, inches, or any other. Volume comes out in cubic units of that measure, surface area in square units, and diameter and circumference in the same linear unit. Keep one unit throughout and the relationships are exact. All calculations run in your browser and nothing is uploaded.