How to find the surface area of a sphere
The surface area of a sphere is four pi times the radius squared: SA = 4 × π × r². For a radius of 2, SA = 4 × π × 4 ≈ 50.27 square units. To find how much the sphere holds inside, use the sphere volume calculator.
A memorable way to see the factor of 4 is Archimedes' result that a sphere's surface equals exactly four times the area of a circle cut through its centre. That circle has area πr², so the sphere has 4πr². The same relationship means a sphere's surface matches the curved side of the cylinder that fits snugly around it.
How to use this calculator
Enter the radius — the distance from the centre to the surface. If you only have the diameter, halve it first. The result is in square units. For a pointed solid instead, try the cone volume calculator.
- Diameter instead of radius is the usual error and makes the answer four times too large.
- Square the radius before multiplying, since 4πr² is not the same as (4πr)².
- Circumference to radius: divide a measured circumference by 2π if you cannot reach the centre.
Worked example
A ball has a 2-inch radius. Surface area = 4 × π × 2² = 4 × π × 4 ≈ 50.27 square inches — useful for estimating paint or material to cover it. The surface area of a sphere is exactly four times what the area of a circle calculator gives for the same radius.
Frequently asked questions
- What is the formula for the surface area of a sphere?
- SA = 4 × π × r², where r is the radius. Square the radius, multiply by pi, then by 4.
- What is the surface area of a sphere with radius 2?
- About 50.27 square units (4 × π × 4).
- How is this different from sphere volume?
- Surface area (4πr²) measures the outer skin in square units; volume ((4/3)πr³) measures the space inside in cubic units.
- What units is the surface area in?
- Square units of whatever you measured the radius in — square inches, cm², m², etc.
- What happens to the surface area if I double the radius?
- It quadruples, because the radius is squared. A sphere of radius 4 has a surface area of about 201.06 square units, four times the 50.27 of a radius-2 sphere, while its volume grows eightfold.