Volume Calculator — cube, box, sphere, cylinder, cone

How it works

Volume is the amount of three-dimensional space a solid contains, measured in cubic units. Choose a solid and its volume follows from a standard formula:

• Cube: side³ = a³
• Box (rectangular prism): length × width × height = a·b·c
• Sphere: (4/3) × π × radius³ = (4/3)πr³
• Cylinder: base area × height = πr²h
• Cone: one third of the matching cylinder = (1/3)πr²h

Volume spans three dimensions, so it scales with the cube of a linear size: double every dimension and the volume grows eightfold. A neat relationship: a cone holds exactly one third of the cylinder with the same base and height.

Worked example

A box 4 × 3 × 2 has volume 4 × 3 × 2 = 24 cubic units. A sphere of radius 3 has volume (4/3) × π × 3³ = 36π ≈ 113.1. A cylinder of radius 2 and height 5 holds π × 2² × 5 = 20π ≈ 62.83 — and a cone with that same base and height holds a third of it, ≈ 20.94. A cube of side 3 is 3³ = 27.

Frequently asked questions

How do I find the volume of a box?

Multiply length, width and height: a × b × c. A 4-by-3-by-2 box holds 24 cubic units. A cube is the special case where all three edges are equal, so its volume is side³.

How do I find the volume of a cylinder?

Multiply the area of the circular base (πr²) by the height: πr²h. A cylinder of radius 2 and height 5 holds π × 4 × 5 = 20π ≈ 62.83 cubic units. It's a stack of identical circular discs, so base area times height gives the total.

Why is a cone's volume a third of a cylinder's?

For the same base radius and height, a cone holds exactly one third of the cylinder — so V = (1/3)πr²h. It's a classic result (known since antiquity): three cones fill the matching cylinder exactly. The same "one third of the prism" rule holds for any pyramid.

How do I find the volume of a sphere?

Cube the radius, multiply by π, and multiply by 4/3: V = (4/3)πr³. A sphere of radius 3 holds (4/3)π × 27 = 36π ≈ 113.1. If you know the diameter, halve it for the radius first.

What units does volume use?

Cubic units of whatever you measured — metres give cubic metres (m³), centimetres give cm³. This calculator treats the dimensions as plain numbers, so keep every dimension in the same unit and the volume comes out in that unit cubed. (One litre is 1000 cm³.)

Why does volume grow so fast with size?

Because it spans three dimensions. Scaling a solid by a factor stretches it in all three directions, so the volume scales by that factor cubed — doubling the size gives 8× the volume, tripling gives 27×. This is why large objects have far more capacity (and mass) than their size suggests.