Sphere Surface Area Calculator
Surface area of a sphere or ball from its radius, diameter or circumference, with the volume as a bonus.
A sphere’s surface area and volume are both driven by the same single measurement — its radius. This calculator solves for both together, and you can start from whichever value you already know: radius, diameter, volume, or even the surface area itself. Enter any one of the four, and the calculator works out the radius first, then reports all the others.
This reverse-solving ability matters because not every real-world sphere gives you its radius directly — a tank’s rated volume or a dome’s specified surface area are often what you start with instead.
Sphere Surface Area Formula
Given Radius
Surface Area = 4πr²
Given Diameter
Surface Area = πd², since d = 2r
Given Volume
Radius = ∛(3V ÷ 4π), then Surface Area = 4πr²
Given Surface Area Itself
Radius = √(Surface Area ÷ 4π) — useful for working backward to find the radius, diameter, or volume when the surface area is what you already know.
Surface Area and Volume, Solved Together
Because both quantities come from the same radius, this calculator reports Surface Area = 4πr² and Volume = (4/3)πr³ together every time, no matter which of the four fields you started from.
Worked Example: Starting from Radius
A sphere with a 6-ft radius: Surface Area = 4 × π × 6² ≈ 452.39 square feet, Volume = (4/3) × π × 6³ ≈ 904.78 cubic feet, Diameter = 2 × 6 = 12 feet.
Solving from Volume or Surface Area (Reverse Lookup)
If you only know the volume or the surface area — say, from a tank’s rated capacity or a dome’s spec sheet — the calculator finds the radius first and then reports every other measurement from it.
Worked Example: Starting from Volume
A sphere with a volume of 4,188.79 cubic feet: Radius = ∛(3 × 4188.79 ÷ 4π) = 10 ft, Surface Area = 4 × π × 10² ≈ 1256.64 square feet, Diameter = 2 × 10 = 20 feet.
Worked Example: Starting from Surface Area
A sphere with a surface area of 314.16 square feet: Radius = √(314.16 ÷ 4π) = 5 ft, Volume = (4/3) × π × 5³ ≈ 523.60 cubic feet, Diameter = 2 × 5 = 10 feet.
Surface Area vs. Volume — Why Both Matter
These answer different practical questions even though they come from the same sphere. Surface area is what you need for a material estimate that covers the whole outer shell — painting a dome, coating a ball, or wrapping a spherical tank. Volume is what you need for capacity — how much water a spherical tank holds, or how much material fills a ball. Since one measurement determines both, this calculator always reports them side by side.
Frequently Asked Questions
How do I find a sphere’s surface area if I only know its volume?
Enter the volume directly. The calculator solves for the radius using Radius = ∛(3V ÷ 4π), then reports the surface area, diameter, and radius together.
What’s the surface area formula in terms of diameter instead of radius?
Surface Area = πd², which comes from substituting r = d/2 into the radius formula (4πr²). You can enter the diameter directly and the calculator handles this conversion for you.
Does this work for a hemisphere?
No — this calculator solves for a full sphere. A hemisphere’s surface area and volume use different formulas (a curved half-shell plus a flat circular base), so it isn’t the same calculation.