Sphere Surface Area Calculator
Calculate the total surface area of a sphere from its radius. Uses the formula A = 4 x pi x r^2, useful for physics, chemistry, and material science.
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How to use this tool
- Enter radius in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your surface area and the full breakdown beneath it.
Formula
A = 4 x pi x r^2
How it works
Use the formula A = 4πr². Square the radius, multiply by pi, then by 4.
Worked example
Sphere with radius 4
- r = 4
- r^2 = 16
- A = 4 x pi x 16 = 64 x pi
- A = 201.0619...
Surface Area = 201.0619 square units
Common mistakes to avoid
- Confusing sphere surface area (4 x pi x r^2) with sphere volume (4/3 x pi x r^3); the formulas look similar but differ in the leading fraction and the exponent.
- Entering the diameter instead of the radius; divide the measured diameter by 2 before entering.
- Forgetting the factor of 4 and computing pi x r^2 instead of 4 x pi x r^2.
Key terms
- What is surface area?
- Surface area is the total area of all outer surfaces of a 3D object.
- Why is a sphere's formula 4 pi r^2?
- The formula comes from calculus integration over the sphere's surface; it equals exactly 4 times the area of a great circle.
Frequently asked questions
- Why does the sphere surface area formula include the factor 4?
- A sphere's surface area equals exactly four times the area of its great circle, giving the factor of 4.
- How is this different from the volume of a sphere?
- Surface area measures the outer shell in square units (A = 4*pi*r^2). Volume measures the interior space in cubic units (V = 4/3*pi*r^3).
- I need to paint a spherical tank of diameter 3 m. How much surface area do I have?
- r = 1.5 m, so A = 4 x pi x 1.5^2 = approximately 28.27 m^2.