Volume Calculator: Cylinder, Cone, Sphere, Cube

What is volume?

Volume is the space inside a three-dimensional shape, measured in cubic units such as cubic centimetres or cubic metres. Use it to find how much a container holds, how much concrete a slab needs, or how much water fills a pool.

Volume and surface area formulas

Solid	Volume	Surface area
Cube	s³	6s²
Rectangular prism	l × w × h	2(lw + lh + wh)
Cylinder	πr²h	2πr(r + h)
Cone	⅓πr²h	πr(r + √(r² + h²))
Sphere	4/3 πr³	4πr²
Pyramid	⅓ × l × w × h	lw + the four triangular faces

Worked examples

A cube

A cube with side 3 has volume 3³ = 27 and surface area 6 × 9 = 54.

A cylindrical can

With radius 2 and height 5, the volume is π × 4 × 5 = 20π, about 62.83. The surface area is 2π × 2 × (2 + 5) = 28π, about 87.96.

A cone

With radius 3 and height 4, the volume is ⅓ × π × 9 × 4 = 12π, about 37.70. The slant height is √(9 + 16) = 5, so the surface area is π × 3 × (3 + 5) = 24π, about 75.40.

A sphere

With radius 3, the volume is 4/3 × π × 27 = 36π, about 113.10.

Units and conversion

Use one unit throughout. One cubic metre equals 1,000 litres, and one litre equals 1,000 cubic centimetres. For the flat faces of a solid, the area calculator gives each face on its own.

Common volume mistakes

The classic mistake is entering the diameter where the formula needs the radius, which makes cylinder and cone volumes four times too large and sphere volumes eight times too large. Another is forgetting the ⅓ in cones and pyramids. Mixing units, such as a radius in centimetres and a height in metres, also gives a wrong answer. For a circular base, check the radius with the circle calculator.

Frequently asked questions

What is the difference between volume and surface area?

Volume is the space inside a solid, measured in cubic units. Surface area is the total area of its outer faces, measured in square units. Volume tells you how much a tank holds, and surface area tells you how much paint covers it.

How do you find the volume of a cylinder?

Multiply pi by the radius squared, then by the height: V = πr²h. A cylinder with radius 2 and height 5 has volume π × 4 × 5 = 20π, about 62.83 cubic units.

Why does a cone hold one third of a cylinder?

A cone and a cylinder with the same base and height are related by a factor of three: the cone’s volume is exactly one third. That is why the cone formula is ⅓πr²h, and why the pyramid formula has the same ⅓.

How do you convert cubic metres to litres?

Multiply by 1,000. One cubic metre holds 1,000 litres, and one litre equals 1,000 cubic centimetres. So a tank of 2.5 cubic metres holds 2,500 litres.

What is the volume of a sphere?

The volume of a sphere is four thirds times pi times the radius cubed: V = 4/3 × πr³. A sphere with radius 3 has volume 36π, about 113.10 cubic units. Cubing the radius means small errors in the radius grow quickly.

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Related topics on this page: volume of a cylinder, volume of a sphere, cone volume, surface area, cubic units, litres and cubic metres