Volume and surface of a sphere, from one number.
Enter a radius, or switch to diameter, and read the volume at once, with the surface area, diameter and great-circle circumference broken out and the formula shown for each.
Your sphere
The distance from the center of the sphere to its surface.
A label only. It does not change the math: the volume carries cubic units and the surface area square units.
What these numbers mean
How a sphere grows with its radius
Diameter and circumference grow in step with the radius, surface area grows with the square of the radius, and volume grows with the cube.
| Radius | Diameter | Circumference | Surface area | Volume |
|---|
Spheres, explained
How to find the volume of a sphere
A sphere is a perfectly round solid, the shape of a ball, a planet or a water tank: every point on its surface sits the same distance, the radius, from the center. Its volume is four thirds of pi times the radius cubed, written V = (4/3) * pi * r^3. Because the radius is cubed, volume climbs fast: double the radius and the sphere holds eight times as much.
Volume is always in cubic units. If the radius is in centimeters the volume is in cubic centimeters, and 1000 cubic centimeters make one liter, a quick way to turn a radius into a capacity you can picture.
Surface area, diameter and circumference
The surface area of a sphere is 4 * pi * r^2, exactly four times the area of its great circle. It is in square units, never cubic, and it is what you need for the material that wraps a ball, the paint on a dome or the heat a planet radiates. The diameter is twice the radius, and the great-circle circumference, the distance around the widest slice, is 2 * pi * r.
A useful fact hides in these formulas: for a given volume, the sphere has the smallest surface area of any shape. That is why soap bubbles and falling water drops pull themselves round, since a rounder shape needs less surface and so less energy to hold together.
Using radius or diameter in the calculator
Type a radius and every result updates at once: volume as the headline figure plus surface area, diameter and circumference in the breakdown, each with its formula. If you measured across a ball you have the diameter, not the radius, so switch the input to diameter mode and the calculator halves it for you.
The unit selector is a label, so the numbers stay the same whether you call them centimeters, inches, feet or meters. Just remember the volume comes out in cubic units of whatever you chose, and the surface area in square units.
Common questions
What is the formula for the volume of a sphere?
Volume equals four thirds of pi times the radius cubed, or V = (4/3) * pi * r^3. Cube the radius, multiply by pi (about 3.14159), then multiply by 4 divided by 3. The answer is in cubic units.
What is the surface area of a sphere?
The surface area is 4 * pi * r^2, four times pi times the radius squared. It comes out in square units, such as square centimeters, because area multiplies two lengths.
Why does a sphere have the smallest surface area for its volume?
Of every possible shape holding the same volume, the sphere wraps it in the least surface. Nature uses this to save energy, which is why bubbles, water drops and large bodies like planets settle into a round shape.
I only know the diameter, not the radius. What do I do?
The radius is half the diameter, so divide the diameter by 2 and enter that. This calculator also lets you switch the input to diameter mode, where you type the diameter directly and it converts to the radius for you.
Results use pi as about 3.14159265. Values are rounded for display; the underlying math keeps full precision. Volume is in cubic units, surface area in square units, and diameter and circumference in the linear unit you enter.