How this calculator works
A sphere is the set of all points a fixed distance from a centre, so a single number, the radius, describes it completely. The diameter is twice the radius, the surface area is 4πr² and the volume is 4/3 πr³. This calculator runs each relation backwards too: a known volume gives r = ∛(3V/(4π)), and a known surface area gives r = √(A/(4π)). That makes it useful both for measuring a ball and for sizing one from a required volume or paint area.
Formula
d = 2r; A = 4πr²; V = (4/3)πr³; r = ∛(3V/(4π)); r = √(A/(4π)).
Worked example
A sphere of radius 3 m has a diameter of 6 m, a surface area of 36π ≈ 113.097 m² and a volume of 36π ≈ 113.097 m³. A diameter of 10 m gives a radius of 5 m, a surface area of 100π ≈ 314.159 m² and a volume of 500π/3 ≈ 523.599 m³.
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Frequently asked questions
Why do the volume and surface area match at radius 3?
It is a coincidence at that one radius. Setting 4/3 πr³ equal to 4πr² gives r = 3, so both numbers are 36π. At any other radius the two values differ.
Can I enter a volume in litres?
Yes. The volume field accepts cubic metres, litres, cubic feet and cubic inches. The engine converts to cubic metres before calculating, so the radius comes back in the length unit you choose.
What is the difference between a sphere and a ball?
In everyday language they are the same. In mathematics a sphere is only the curved surface, while a ball includes the solid interior. The volume here refers to the solid ball.