What Is the Surface Area of a Sphere?
A sphere is a perfectly round three-dimensional object where every point on its surface is the same distance — the radius (r) — from the center. The surface area is the total area covering the outside of the sphere. This calculator uses the classic formula \(A = 4\pi r^{2}\) to compute it instantly, and also returns the diameter and volume as helpful extras.
How to Use This Calculator
Simply enter the radius of your sphere in any unit you like (centimeters, inches, meters, etc.). The calculator returns the surface area in square units of that same measurement. For example, if you enter the radius in centimeters, the surface area will be in square centimeters (cm²).
The Formula Explained
The surface area formula is \(A = 4\pi r^{2}\), where π (pi) ≈ 3.14159 and r is the radius. The factor of 4π comes from integral calculus, but you can think of it as the sphere having exactly four times the area of a flat circle with the same radius (\(\pi r^{2}\)). The bonus volume formula is \(V = \frac{4}{3}\pi r^{3}\).
Worked Example
Suppose a ball has a radius of 5 cm. Then $$A = 4 \times \pi \times 5^{2} = 4 \times 3.14159 \times 25 \approx 314.16 \text{ cm}^{2}.$$ The diameter is \(2 \times 5 = 10\) cm and the volume is \(\frac{4}{3} \times \pi \times 125 \approx 523.6 \text{ cm}^{3}\).
FAQ
What if I only know the diameter? Divide the diameter by 2 to get the radius, then enter that value.
What units does the result use? The surface area uses the square of whatever unit you used for the radius — square centimeters, square inches, and so on.
Why is the answer four times the area of a circle? A neat geometric fact: a sphere's surface area equals exactly four great circles of the same radius, hence the 4 in \(4\pi r^{2}\).
