Volume Calculator (box, cylinder, sphere, cone)

Volume and surface area formulas

Volume measures the space a solid occupies; surface area measures the skin around it. Both come from the solid's dimensions, and the answers are in cubic and square versions of whatever units you enter.

Box: V = l × w × h  ·  Cube: V = a³

Cylinder: V = πr²h  ·  Sphere: V = 4/3 πr³

Cone: V = ⅓ πr²h

The pattern behind them

Anything with straight parallel sides — a box, a cylinder — is just its base area multiplied by its height. Anything that tapers to a point, like a cone or pyramid, is exactly one third of the matching straight solid, which is why the cone formula is the cylinder's with a ⅓ in front. A sphere sits between: its volume is ⅔ of the cylinder that would just contain it, a result Archimedes was proud enough of to have carved on his tomb.

Volume grows fast

Because volume depends on three dimensions, doubling a sphere's radius makes it eight times the volume while the surface area only quadruples. That mismatch — volume rising faster than surface — is why large objects struggle to shed heat and why small creatures lose it so quickly.

Worked example

A cylinder of radius 5 cm and height 10 cm holds π × 25 × 10 ≈ 785.4 cm³ — just under 0.8 litres. A sphere of radius 3 cm holds 4/3 × π × 27 ≈ 113.1 cm³. Convert the result to litres or gallons with thevolume converter, or find a mass from it using the density calculator.

Exact for the ideal solid

The formulas are exact; what is approximate is the assumption that your object is that solid. Real containers have wall thickness, so internal and external volume differ — often by more than people expect on small vessels. Tanks have dished rather than flat ends. And as with area, the precision of the answer is set by your measurements rather than by the arithmetic, so a volume quoted to six figures from a tape-measure reading is overstating what is known.