Surface Area of a Sphere Calculator
Calculate the surface area of a sphere from its radius using A = 4πr². A sphere is the set of all points at distance r from a centre, and its outer skin has area exactly four times that of a flat circle of the same radius. Enter the radius and read the surface area in square units.
Formula
Surface area = 4πr²
- The surface area of a sphere is 4πr², which is exactly four times the area of a great circle (πr²) through its centre.
- The result uses the square of the radius's unit: a radius in cm gives an area in cm².
- If you know the diameter d instead, use r = d ÷ 2, so the area becomes πd².
- A hemisphere's curved surface is half of this (2πr²); its total surface including the flat base is 3πr².
Example: sphere of radius 5
Inputs
- Radius (r): 5
With r = 5, the surface area is 4π × 5² = 4π × 25 = 100π ≈ 314.16 square units.
Frequently asked questions
What is the formula for a sphere's surface area?
A = 4πr², where r is the radius. It is four times the area of the circle you would get by slicing the sphere through its centre.
How is surface area different from volume?
Surface area (4πr²) measures the outer skin in square units, while volume (4⁄3 πr³) measures the space inside in cubic units.
Can I use the diameter instead of the radius?
Yes — divide the diameter by 2 to get the radius first. Equivalently, the surface area equals πd² when d is the diameter.
What units does the answer use?
The surface area is in the square of the unit you use for the radius. A radius in metres gives an area in square metres.
How do I find the radius from the surface area?
Rearrange A = 4πr² to r = √(A ÷ (4π)).