What Is the Surface Area of a Sphere?
A sphere is a perfectly round three-dimensional object where every point on the surface is the same distance (the radius) from the center. Its surface area is the total area covering the outside of the ball. This calculator finds that area instantly from a single input — the radius — and also reports the diameter and volume for convenience.
How to Use This Calculator
Enter the radius of your sphere in any unit (meters, centimeters, inches, etc.). The calculator returns the surface area in square units of that same unit. For example, a radius in centimeters gives a surface area in square centimeters. The diameter and volume are shown as bonus results.
The Formula Explained
The surface area of a sphere is given by $$SA = 4\pi r^{2}$$, where \(r\) is the radius and \(\pi \approx 3.14159\). The radius is squared, multiplied by \(\pi\), and then by 4. Interestingly, this surface area is exactly four times the area of a flat circle with the same radius (\(\pi r^{2}\)).
Worked Example
Suppose a sphere has a radius of 5 units. Then $$SA = 4 \times \pi \times 5^{2} = 4 \times 3.14159 \times 25 \approx 314.16 \text{ square units.}$$ Its diameter is \(2 \times 5 = 10\) units, and its volume is \(\frac{4}{3} \times \pi \times 5^{3} \approx 523.6\) cubic units.
FAQ
What if I only know the diameter? Divide the diameter by 2 to get the radius, then enter that value.
Does the unit matter? Use any unit you like — the surface area comes out in the square of that unit, and volume in its cube.
Why is the surface area \(4\pi r^{2}\)? It is a classic result of integral calculus; remarkably, it equals the lateral surface area of the smallest cylinder that contains the sphere.
