How to find the volume of a sphere
The volume of a sphere is four-thirds pi times the radius cubed: V = (4/3) × π × r³. For a radius of 3, V = (4/3) × π × 27 ≈ 113.10 cubic units. The sphere's outer skin is found with the surface area of a sphere calculator.
Because the radius is cubed, volume grows extremely fast with size. Doubling the radius multiplies the volume by eight, so a ball twice as wide holds eight times as much — a fact that matters when scaling tanks, bearings or dosages.
How to use this calculator
Enter the radius — the distance from the centre to the surface. If you only know the diameter, halve it first. The volume is returned in cubic units. For a pointed solid, try the cone volume calculator.
Entering the diameter by mistake is the most common error and makes the answer eight times too large. Keep the unit consistent as well: a radius in centimetres returns cubic centimetres, which you divide by 1,000 to get litres. Any positive radius works, and very small radii return correspondingly small volumes rather than zero.
Worked example
A ball has a 3 cm radius. Volume = (4/3) × π × 3³ = (4/3) × π × 27 ≈ 113.10 cubic centimetres.
Converted to capacity that is about 0.113 litres. The figure above is the full solid volume, which is also the amount of water the ball would displace if fully submerged. A sphere fills exactly two thirds of the smallest cylinder that contains it, which you can check with the cylinder volume calculator.
Frequently asked questions
- What is the formula for the volume of a sphere?
- V = (4/3) × π × r³, where r is the radius. Cube the radius, multiply by pi, then by 4/3.
- What is the volume of a sphere with radius 3?
- About 113.10 cubic units ((4/3) × π × 27).
- How do I find volume from the diameter?
- Divide the diameter by 2 to get the radius, then apply V = (4/3) × π × r³.
- What units is the volume in?
- Cubic units of whatever you measured the radius in — cubic inches, cm³, m³, etc.
- How does a sphere's volume compare with the cylinder that encloses it?
- A sphere fills exactly two thirds of the smallest cylinder that contains it — one with the same radius and a height equal to the diameter. Archimedes proved this result, and it gives a quick way to sanity-check any sphere volume you calculate.