How this calculator works
First recover radius from the selected measurement, then calculate the whole curved surface. Surface area grows with radius squared while volume grows with radius cubed. Their quotient is therefore inversely proportional to radius. The comparison table holds shape fixed and changes size; its factors are dimensionless, while the radius column is in metres.
Formula
A = 4πr²; V = 4πr³/3; A/V = 3/r; r = 3/(A/V). Scaling radius by k scales area by k² and volume by k³.
Worked example
Radius 3 m gives area 36π m², volume 36π m³ and ratio 1 m⁻¹. Doubling radius gives four times the surface and eight times the volume. A ratio of 1.5 m⁻¹ instead gives radius 2 m and area 16π m².
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Frequently asked questions
Why is the ratio measured in inverse metres?
Square metres divided by cubic metres leave one divided by metres. It is not itself a length.
Does this include the inside of a hollow ball?
No. It calculates one spherical surface. Calculate the inner and outer radii separately and add their areas if both need coating.
Can the surface-to-volume ratio determine size?
Yes, for a sphere with positive radius. The radius is three divided by that ratio in consistent units.