Sphere Surface Area Calculator
The surface area of a sphere is the total area of the curved surface enclosing the sphere. It is calculated as A = 4 * π * r², where r is the radius. This calculator also computes the volume V = (4/3) * π * r³. The ratio of surface area to volume decreases as the sphere grows larger, a principle important in physics and biology.
Sphere formulas
Surface Area = 4 * π * r²
Volume = (4/3) * π * r³
Diameter = 2 * r
Reference values
| Radius | Surface Area | Volume |
|---|---|---|
| 1 cm | 12.57 cm² | 4.19 cm³ |
| 5 cm | 314.16 cm² | 523.60 cm³ |
| 10 cm | 1,256.64 cm² | 4,188.79 cm³ |
| 1 m | 12.57 m² | 4.19 m³ |
Sphere surface area calculator: frequently asked questions
What is the surface area formula for a sphere?
A = 4 * π * r², where r is the radius. This is the total area of the curved surface.
What is the volume formula?
V = (4/3) * π * r³. The surface area to volume ratio increases as radius decreases.
How do I find radius from diameter?
Radius = Diameter / 2. If you know the diameter, simply divide by two.
What is the relationship between surface area and volume?
For a sphere, surface area is proportional to r², while volume is proportional to r³. As objects scale up, volume increases faster than surface area.
What are practical applications?
Understanding surface area helps with heat transfer calculations, paint coverage, and material properties for spherical objects.
Official sources
- Khan Academy: Volume and surface area.
- NIST: National Institute of Standards.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.