Sphere Volume Calculator
Find the volume and surface area of a sphere from its radius, diameter or circumference, or work back from a volume to the size of ball that holds it.
The volume of a sphere is four thirds times pi times the radius cubed, and its surface area is four times pi times the radius squared. A sphere with a 5 cm radius holds 523.6 cubic cm and has a surface of 314.16 square cm. Enter a radius, diameter, circumference or volume and the calculator finds the rest.
Results are computed for a perfect sphere and rounded to two decimals. Real objects are rarely perfectly round, and the calculator does not account for wall thickness, so for a hollow ball or tank measure the inside if you want the volume it holds.
Volume
523.6 cubic cm
- Surface area
- 314.16 square cm
- Radius
- 5 cm
- Diameter
- 10 cm
- Circumference
- 31.42 cm
- In liters
- 0.52 L
- In US gallons
- 0.14 gal
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About the Sphere Volume Calculator
Archimedes proved the ratios behind both formulas in On the Sphere and Cylinder: the surface is four times the area of the sphere's largest circle, and the volume is four times a cone with that circle as its base and the radius as its height. In modern notation that is 4 pi r squared and four thirds pi r cubed. Because the radius is cubed, the volume climbs quickly with size: a 12 in diameter ball holds 904.78 cubic inches, about 3.92 US gallons. Often the radius is the hard part to measure, so the calculator also starts from a diameter, a circumference taken with a tape around the widest point, or a volume. A basketball with a 29.5 in circumference has a radius of 4.7 in and holds 433.53 cubic inches, or 7.1 liters. Working backward, 1,000 cubic cm, one liter, fills a sphere of radius 6.2 cm. Liters and US gallons come from exact unit definitions.
Frequently asked questions
What is the formula for the volume of a sphere?+
V = 4/3 times pi times r cubed. For a 5 cm radius that is 4/3 times pi times 125, which is 523.6 cubic cm. If you know the diameter, halve it first; the calculator does that for you.
How do I find the radius from the volume?+
Multiply the volume by 3, divide by 4 times pi, and take the cube root. A volume of 1,000 cubic cm gives a radius of 6.2 cm. Choose volume as the measure you know and the calculator works it out.
How much does a 1 meter radius sphere hold?+
4.19 cubic meters, which is 4,188.79 liters. Doubling the radius multiplies the volume by eight, because it grows with the cube of the radius.
What is the surface area used for?+
It tells you how much material covers the sphere, such as paint for a spherical tank, leather for a ball or insulation for a spherical tank. For a 5 cm radius it is 314.16 square cm, four times the area of its largest circle.
Formulas: Archimedes, On the Sphere and Cylinder, Book I; Weisstein EW, "Sphere," MathWorld. Units: NIST Handbook 44, Appendix C.
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