Find a sphere’s radius from either its volume or its surface area — the reverse of the usual radius-to-volume calculation.
How it works
From volume: r = ∛(3V ÷ 4π). From surface area: r = √(SA ÷ 4π). A sphere with volume 4,188.79 has a radius of 10; one with surface area 314.159 has a radius of 5.
What this does not include
This is the reverse of this site’s sphere volume calculator, which goes from radius to volume and surface area rather than back the other way.
How to use this calculator
- Choose whether you know the volume or the surface area.
- Enter that value.
A worked example
From a known volume of 4188.79: radius = 10.
From a known surface area of 314.159: radius = 5.
What the variables mean
| Variable | Meaning |
|---|---|
| Volume or surface area | Any one known sphere measurement |
Edge cases worth knowing
Either volume or surface area alone is enough to find the radius — both fully determine the same sphere, so this calculator accepts whichever measurement is available rather than requiring both.
A volume of zero collapses the sphere to a point, so the calculator declines to show a result for that input.
Why do volume and surface area give different radius formulas?
Volume scales with the cube of radius while surface area scales with its square, so solving each formula for r requires a different root — a cube root for volume, a square root for surface area.
When would you know a sphere’s volume or surface area but not its radius?
A common real-world case is knowing how much material fills a spherical container (its volume) or how much material covers it (its surface area) without having measured the radius directly.
Does this work for a hemisphere?
No — the formulas here are specific to a full sphere; a hemisphere’s volume and surface area formulas differ and would need separate calculations.
