Volume Calculator

Work out the volume and surface area of a cube, box, cylinder, sphere, cone or square pyramid in the unit you measure in — and the volume in litres and US gallons.

Your details

For a cone or pyramid, the straight height from the base to the tip.

Volume

60 m³

Surface area
94 m²
In litres
60,000 L
In US gallons
15,850.3 US gal
  • Every length is in the unit you chose, so the volume is in that unit cubed. The surface area counts every face, the base included. The pyramid has a square base and its apex above the centre.

Visual breakdown

  • Volume in m³Calculated60 m³
  • LitresCalculated60,000 L
  • US gallonsCalculated15,850.3 gal

  1. 1

    Volume of a box

    V = length × width × height

    = 4 × 3 × 5 m

    = 60 m³

  2. 2

    Surface area

    S = 2 × (lw + lh + wh)

    = 94 m²

  3. 3

    In litres and US gallons

    volume × (metres per unit)³ × 1,000, then ÷ 3.785411784

    = 60 m³

    = 60,000 L · 15,850.3 US gal

A box 4 m long, 3 m wide and 5 m high has a volume of 60 m³, which is 60,000 litres. Its surface area is 94 m².

What this calculates

Choose a shape, a unit and its dimensions. This works out the volume in that unit cubed, the surface area, and the volume in litres and US gallons. It covers the cube, box, cylinder, sphere, cone and square pyramid. To convert between units of volume alone, use the volume converter.

The formula

Box

V = length × width × height

Cylinder

V = π × r² × height

Sphere

V = 4⁄3 × π × r³

Cone

V = ⅓ × π × r² × height

Square pyramid

V = ⅓ × base² × height

A cube is a box with equal sides, so V = side³. The surface area of a box is 2 × (lw + lh + wh).

Worked example

A cone of radius 3 m and height 4 m holds ⅓ × π × 9 × 4 = 37.6991 m³.

When to use it, and the mistakes to avoid

Use it for a tank, a pool, a box or crate, a pipe, a pile of soil or gravel, or the capacity of a container.

The mistakes that cost the most:

  • Using the diameter as the radius. The radius is half the diameter.
  • Mixing units. Measure every dimension in the same unit.
  • Forgetting the third. A cone or pyramid is a third of its cylinder or prism.
  • Using the slanted height. Use the straight height from the base to the tip.
  • Mixing up gallons. This shows US gallons; an imperial gallon is about 20% bigger.

FAQ

How do I calculate the volume of a box?

Multiply the length by the width by the height. A box 4 m long, 3 m wide and 5 m high holds 4 × 3 × 5 = 60 cubic metres, which is 60,000 litres. A cube is a box with equal sides, so its volume is the side cubed.

What is the volume of a cylinder?

π times the radius squared times the height. With a radius of 2 cm and a height of 5 cm it is π × 4 × 5 = 62.83 cm³. That is the area of the circular base multiplied by the height.

Why are the cone and pyramid one third?

A cone holds exactly a third of the cylinder with the same base and height, and a pyramid a third of the matching prism. This calculator gives the cone as ⅓ × π × r² × h and the square pyramid as ⅓ × base² × h.

How do I convert the volume to litres or gallons?

One cubic metre is 1,000 litres, and one US gallon is 3.785411784 litres. The calculator converts from the unit you chose, so 27 cubic feet is 764.555 litres, or 201.974 US gallons. For other units, use the volume converter.

What does the surface area include?

Every face of the shape, the base or bases included. For a box it is 2 × (lw + lh + wh); for a sphere 4πr². Use it to estimate paint, wrapping or material to cover the outside.

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