Math
Sphere Calculator
Calculate the volume, surface area, diameter, and great-circle circumference of a sphere from its radius. Exact formulas, instant results.
Sphere dimensions
Volume
113.0973
- Diameter
- 6
- Circumference
- 18.8496
- Surface area
- 113.0973
- Radius
- 3
Frequently Asked Questions about the Sphere Calculator
What is the formula for the volume of a sphere?
Volume equals four-thirds times pi times the radius cubed: V = (4/3) x pi x r^3. For a radius of 5 inches, that works out to (4/3) x pi x 125, which is roughly 523.60 cubic inches. The cube in the exponent means volume grows rapidly - doubling the radius increases volume by a factor of 8.
What is the formula for the surface area of a sphere?
Surface area equals four times pi times the radius squared: SA = 4 x pi x r^2. For a radius of 5 inches, that gives 4 x pi x 25, which is roughly 314.16 square inches. Because area scales with r^2 and volume with r^3, larger spheres enclose proportionally more volume per unit of surface area.
How do I find the diameter or circumference of a sphere?
Diameter is twice the radius: d = 2r. The great-circle circumference - the longest circle you can draw around the sphere, like the equator on a globe - is C = 2 x pi x r. For a radius of 5 inches, the diameter is 10 inches and the circumference is roughly 31.42 inches.
Can I calculate a sphere from its diameter instead?
Yes. Divide the diameter by 2 to get the radius, then enter that value. A diameter of 10 inches corresponds to a radius of 5 inches, which gives a volume of roughly 523.60 cubic inches and a surface area of roughly 314.16 square inches.
Why must the radius be greater than zero?
A sphere with a zero or negative radius has no geometric meaning - there is nothing to measure. The calculator returns no result for a radius of 0 or less, and also skips blank or non-numeric entries.