Sphere Calculator
Volume, surface area and circumference of a sphere from its radius or diameter — balls, tanks, planets.
Volume = 4⁄3πr³ and surface area = 4πr².
How the sphere calculator works
Volume = 4⁄3πr³ and surface area = 4πr². Doubling the radius makes the surface four times larger and the volume eight times larger, which is why small objects cool faster than large ones.
Formula: V = 4/3 πr³; A = 4πr²
Worked examples
| Inputs | Volume | Note |
|---|---|---|
| radius 6 | 904.778684 | 904.78 |
| diameter 22 cm (football) | 5,575.279763 | ≈ 5,575 cm³ |
FAQFrequently asked questions
Why is the volume 4⁄3πr³?
Archimedes showed a sphere fills exactly two thirds of the cylinder that just contains it: ⅔ × πr² × 2r.
How do I get the radius from the volume?
r = ∛(3V ÷ 4π).
What is a hemisphere's volume?
Half: ⅔πr³. Its total surface area is 3πr² (curved part plus the flat disc).
What units?
Whatever you entered, cubed for volume and squared for area.
How much does the Earth's volume change with a small radius change?
Volume grows with r³, so a 1% larger radius means about 3% more volume.
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)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.