How to use the sphere volume calculator
- Under What do you know? pick Radius, Diameter or Circumference. The circumference is the distance around the widest part, which you can measure on a real ball with a tape.
- Choose the Unit of length. Inches are selected to start, and kilometers and miles are there for planets.
- Type the number. Switching between radius, diameter and circumference keeps the same sphere and converts your number.
- Read the Volume, the same volume in liters, US gallons, cubic feet and cubic meters, then the surface area, the other measurements and the hemisphere (half sphere) figures.
The formulas
V = 4⁄3 × π × r³ A = 4 × π × r²
From a diameter, V = πd³ ÷ 6. From a circumference, r = C ÷ 2π. A hemisphere has half the volume, 2⁄3πr³, and a total surface area of 3πr² (the curved half plus the flat circle). Archimedes proved these results in On the Sphere and Cylinder, and MathWorld lists them. Gallons use the exact US definition, 1 US gallon = 231 cubic inches = 3.785411784 liters (NIST SP 811, Appendix B.8).
Worked example
The calculator opens with r = 5 inches. V = 4⁄3 × π × 5³ = 523.5988 in³, which is 8.5802 liters or 2.2667 US gallons. The surface area is 314.1593 in², the diameter is 10 in, the circumference is 31.4159 in and the hemisphere volume is 261.7994 in³.
Limits and edge cases
- The result is for a solid, perfectly round sphere. For a hollow ball, subtract the inner sphere's volume from the outer one's.
- Real balls and planets are not perfect spheres. Earth is slightly flattened, so a sphere with its mean radius is a close estimate.
- Every number must be greater than 0 and at most 1,000,000,000,000. Thousands commas are fine; use a period for decimals. Very large results show as powers of ten.
- Gallons are US gallons, not imperial gallons.
- The flat circle through a sphere's middle is on the circle area and circumference calculator. Other solids are on the cylinder volume calculator and the cube and box volume calculator, and the volume converter covers units that are not listed.
Sphere volume FAQ
How do I find the volume of a sphere from its diameter?
Use V = π × d³ ÷ 6, the same as 4/3 × π × r³ with r = d ÷ 2. A sphere 10 inches across has V = π × 1,000 ÷ 6 = 523.5988 cubic inches. In the calculator, press Diameter and type 10.
How do I find the volume of a sphere from its circumference?
Find the radius with r = C ÷ (2π), then use V = 4/3 × π × r³. A men's NBA basketball is 29.5 inches around, so r = 4.6951 inches and V = 433.5259 cubic inches, about 7.1042 liters.
What is the volume of a hemisphere?
Half the sphere's volume: V = 2/3 × π × r³. For r = 5 that is 261.7994. A solid hemisphere's total surface area, with its flat base, is 3πr², which is 235.6194 for r = 5.
How are the surface area and volume of a sphere related?
The surface area is A = 4πr² and the volume is V = 4/3 × πr³, so A = 3V ÷ r. For r = 5 that is 3 × 523.5988 ÷ 5 = 314.1593. Archimedes also showed that a sphere's volume is two thirds of the cylinder that just contains it.
What is the volume of the Earth?
A sphere with Earth's mean radius of 6,371 km has a volume of about 1.08321 × 10¹² cubic kilometers, which matches NASA's Earth fact sheet. Earth is slightly flattened at the poles, so this is a very close estimate rather than an exact figure.
Sources: Wolfram MathWorld, Sphere; NASA, Earth Fact Sheet; Wikipedia, Basketball (ball); NIST Special Publication 811, Appendix B.8.