Sphere Surface Area Calculator
The surface area of a sphere from its radius — exactly four times the circle you see when you look at it.
A sphere of radius r has surface area 4πr².
How the sphere surface area calculator works
A sphere of radius r has surface area 4πr². The result Archimedes was proudest of is that this equals the curved surface of the cylinder that just contains the sphere — he had it carved on his tomb. If you have the diameter rather than the radius, halve it first.
Formula: cube 6a²; box 2(lw+lh+wh); sphere 4πr²; cylinder 2πr(r+h); cone πr(r+l); pyramid a² + 2a·s
Worked examples
| Inputs | Total surface area | Note |
|---|---|---|
| Radius 2 | 50.2655 | 4π × 4 ≈ 50.265 |
| Radius 5 | 314.1593 | ≈ 314.16 |
| A football, radius 11 cm | 1,520.5308 | about 1,520 cm² |
FAQFrequently asked questions
What is the surface area of a sphere?
4πr², where r is the radius. For radius 2 that is about 50.27 square units.
I only know the diameter — what now?
Halve it to get the radius, then the formula applies.
Why is it four times the circle?
It is a genuine geometric fact, first proved by Archimedes: the sphere's surface equals the curved surface of its enclosing cylinder, which works out at 4πr².
What about a hemisphere?
Half the sphere plus the flat circular face: 2πr² + πr² = 3πr².
How does it compare with volume?
Volume is 4πr³/3. The surface-area-to-volume row shows the ratio, which matters for heating, cooling and dissolving.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.