Sphere Calculator
Calculate the surface area and volume of a sphere from its radius. Also supports reverse calculation: find the radius from volume or surface area.
About this Calculator
Calculate the surface area and volume of a sphere from its radius. Also supports reverse calculation: find the radius from volume or surface area.
Formula & Calculations
Formula
Surface Area = 4πr²; Volume = ⁴⁄₃πr³; Reverse: r = √(SA/(4π)), r = ∛(3V/(4π))Where:
- r=Radius of the sphere
- SA=Surface area of the sphere
- V=Volume enclosed by the sphere
Assumptions
- π is approximated as 3.1415926536 (Math.PI).
- All values use consistent units; input radius in a unit, output uses the same unit system.
- Cube roots are computed using Math.cbrt for precision.
Calculation Examples
Example 1
SA = 4π × 9 ≈ 113.0973. V = ⁴⁄₃π × 27 ≈ 113.0973.
Example 2
r = ∛(3 × 523.6 / (4π)) ≈ 5. SA = 4π × 25 ≈ 314.1593.
Frequently Asked Questions
How is the sphere volume formula derived?
The volume formula V = ⁴⁄₃πr³ comes from integral calculus and was first discovered by Archimedes. It represents the limit of the sum of infinitesimally thin disks stacked to form the sphere.
What is the relationship between surface area and volume of a sphere?
The surface area is the derivative of the volume with respect to the radius: d/dr(⁴⁄₃πr³) = 4πr². This means a small change in radius produces a surface-area-proportional change in volume.