Skip to content
Math & Statisticsgeometry

Volume Calculator

Volume of the common solids, in cubic metres, litres, cubic feet and gallons. All volumes scale with the cube of a linear dimension, so doubling any one measurement of a box doubles the volume but doubling all three multiplies it by eight.

Also called: volume of a shape, cubic metres calculator.

Volume
3

3 cubic metres, which is 3,000 litres or 105.94 cubic feet. All three dimensions multiply, so doubling each one multiplies the volume by eight.

In litres
3,000
In cubic feet
105.94
In US gallons
792.52
Surface area
13
Volume per unit of surface
0.23
On the shape
All three dimensions multiply, so doubling each one multiplies the volume by eight.
How this is calculated
Method and background

How this is calculated

Each shape uses its own formula and everything converts through cubic metres. For the round shapes the first input is taken as the diameter rather than the radius, because that is what people measure. The sphere formula, four thirds pi r cubed, and the cone being exactly one third of its enclosing cylinder are the two results worth remembering: a cone, a hemisphere and a cylinder of the same radius and height are in the ratio 1:2:3.

each solid has its own formula, but all scale with the cube of a linear dimension
l, w, h
Length, width, height
r
Radius

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a rectangular box

Shape
Rectangular box
Length or diameter
2
Width
1.5
Height
1
Dimensions in
Metres

Volume3

2 x 1.5 x 1; surface 2(3 + 2 + 1.5)

Open this example

a cone is a third of its cylinder

Shape
Cone
Length or diameter
2
Width
1.5
Height
3
Dimensions in
Metres

Volume3.14

boundary: pi x 1 x 1 x 3 / 3 is exactly pi

Open this example

Method and limits

What it assumes

  • Regular solids with the dimensions entered.

What it deliberately does not model

  • Real containers have wall thickness, so internal and external volume differ.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Is the first input a radius or a diameter?
A diameter, for the round shapes. It is what you can actually measure on a real object, and halving it is the step people forget.
How many litres in a cubic metre?
Exactly a thousand. The litre is defined as a cubic decimetre, so the conversion is by definition rather than measurement.