Sphere calculator
This sphere calculator needs just one measure: radius, diameter, volume, surface area or great-circle circumference. With r = 5 the volume is 523.6 and the surface area 314.16 – plus every other measure and the full calculation steps.
Example: Known value: Radius r · Radius r 5 → Result: Volume V = 523.5988 · Surface area S = 314.1593. Source: Wikipedia – Kugel (Volumen, Oberfläche). Updated: .
How it is calculated
A sphere is fully defined by its radius. Everything else follows from it: volume, surface area, diameter and the circumference of the largest circle on the sphere (the great circle). If you know the volume instead of the radius, the calculator solves for the radius first.
The formulas
- Volume: V = 4/3 · π · r³
- Surface area: S = 4 · π · r²
- Diameter: d = 2 · r
- Great-circle circumference: C = 2 · π · r
- Radius from volume: r = ∛(3V ÷ 4π); from surface area: r = √(S ÷ 4π)
How to use it
Pick the measure you know and enter its value. Example: a ball with r = 5 cm has a volume of 4/3 · π · 125 = 523.6 cm³ and a surface area of 4 · π · 25 = 314.16 cm². Double the radius and the surface area grows fourfold while the volume grows eightfold. The length unit is up to you; all results use the same unit, with areas squared and volumes cubed.
Frequently asked questions
How do you calculate the volume of a sphere?
V = 4/3 · π · r³. For a radius of 5 that gives 4/3 · π · 125 = 523.6 cubic units.
How do you calculate the surface area of a sphere?
S = 4 · π · r². This is exactly four times the area of the largest circle through the centre.
How do you find the radius from the volume?
r = ∛(3V ÷ 4π). The calculator does this step for you when you choose volume as the known value.
What is the difference between radius and diameter?
The diameter is twice the radius: d = 2 · r. The radius runs from the centre to the surface, the diameter straight across the whole sphere.
Sources and legal basis
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