How this calculator works
A great circle cuts the sphere through its centre, so its circumference is 2πr. A smaller latitude circle cannot be used directly. The sphere area divided by its enclosed volume simplifies to 3/r, allowing a radius to be recovered from that ratio alone. All modes refer to a solid ball with a smooth spherical surface. The scaling table explains why large balls have less surface per unit volume.
Formula
r = d/2 = C/(2π) = √[S/(4π)] = ∛[3V/(4π)] = 3/q, where q = S/V.
Worked example
A great-circle circumference of 6π m gives r = 3 m. Its surface area is 36π m² and enclosed volume is 36π m³, so q = 1 per metre. A ratio of 1.5 per metre instead gives r = 2 m.
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Frequently asked questions
Can I use an equatorial measurement?
Yes, if it follows a great circle. A circumference measured on a smaller parallel circle needs its position as additional information.
What units belong to surface area divided by volume?
Area divided by volume has units of inverse length. For example, m²/m³ is 1/m. The input provides inverse-length unit choices.
Does this work for a hollow shell?
The area refers to the outside spherical surface and the volume to the full enclosed ball. A shell material volume alone cannot determine its outer radius without thickness or inner radius.