The five formulas
Box: length x width x height. Cylinder: pi x radius squared x height. Sphere: four thirds of pi x radius cubed.
Cone: one third of pi x radius squared x height, which is a third of the cylinder that would hold it. Square-based pyramid: one third of the base area times the height.
Worked example
A box 30 cm by 20 cm by 15 cm has a volume of 30 x 20 x 15 = 9,000 cm³.
That is 9 litres, or 0.009 m³. Its surface area is 2 x (600 + 450 + 300) = 2,700 cm².
Choosing the right shape
A box is any shape with six rectangular faces, including a cube. A cylinder has straight sides and circular ends.
A cone has one circular base and a point. A pyramid here means a square base and a point directly above the centre.
Inputs for the volume calculator
Shape
Pick the solid. The measurement boxes change to the dimensions that shape needs.
Length, width and height
The three sides of a box, at right angles to each other.
Radius and height
Used by the cylinder and the cone. The radius is half the width across the circular face.
Side of the square base
Used by the pyramid, along with its height.
Measurement unit
The unit your measurements are in. The answer is given in cubic metres and litres.
CALCULATOR QUESTIONS
Volume calculator questions
How do I work out the volume of a box?
Multiply length by width by height. A 30 by 20 by 15 cm box is 9,000 cm³.
Why is a cone a third of a cylinder?
A cone with the same base and height fills exactly one third of the cylinder around it. The same is true of a pyramid and its box.
What is the difference between volume and surface area?
Volume is the space inside, in cubic units. Surface area is the total area of the outside faces, in square units.
Can I measure in feet?
Yes. Choose feet and the answer is converted to cubic metres and litres, with cubic feet shown too.