# Measurement of volume

Volume is the
quantity of three-dimensional space enclosed by a closed surface, for example,
the space that a substance (solid, liquid, gas, or plasma) or shape occupies or

contains.[1] Volume is often quantified numerically using the SI derived unit,
the cubic metre. The volume of a container is generally understood to be the
capacity of the container, i. e. the amount of fluid (gas or liquid) that the
container could hold, rather than the amount of space the container itself
displaces.
Three
dimensional mathematical shapes are also assigned volumes. Volumes of some
simple shapes, such as regular, straight-edged, and circular shapes can be
easily calculated using arithmetic formulas. Volumes of a complicated shape can
be calculated by integral calculus if a formula exists for the shape's
boundary. Where a variance in shape and volume occurs, such as those that exist
between different human beings, these can be calculated using three-dimensional
techniques such as the Body Volume Index. One-dimensional figures (such as
lines) and two-dimensional shapes (such as squares) are assigned zero volume in
the three-dimensional space.

The volume of
a solid (whether regularly or irregularly shaped) can be determined by fluid
displacement. Displacement of liquid can also be used to determine the volume
of a gas. The combined volume of two substances is usually greater than the
volume of one of the substances. However, sometimes one substance dissolves in
the other and the combined volume is not additive.

In
differential geometry, volume is expressed by means of the volume form, and is
an important global Riemannian invariant. In thermodynamics, volume is a
fundamental parameter, and is a conjugate variable to pressure.

## Units

Any unit of length gives a corresponding unit of volume: the volume of a cube whose sides have the given length. For example, a cubic centimetre (cm

^{3}) is the volume of a cube whose sides are one centimetre (1 cm) in length.
In the International System of Units (SI), the standard unit of volume is the cubic metre (m

^{3}). The metric system also includes the litre (L) as a unit of volume, where one litre is the volume of a 10-centimetre cube. Thus- 1 litre = (10 cm)
^{3}= 1000 cubic centimetres = 0.001 cubic metres,

so

- 1 cubic metre = 1000 litres.

Small amounts of liquid are often measured in millilitres, where

- 1 millilitre = 0.001 litres = 1 cubic centimetre.

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