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

Volume measurements from the 1914 The New Student's Reference Work.
Approximate conversion to millilitres:^[3]

	Imperial	U.S. liquid	U.S. dry
Gill	142 mL	118 mL	138 mL
Pint	568 mL	473 mL	551 mL
Quart	1137 mL	946 mL	1101 mL
Gallon	4546 mL	3785 mL	4405 mL

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 (cm³) 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 (m³). 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.

Various other traditional units of volume are also in use, including the cubic inch, the cubic foot, the cubic mile, the teaspoon, the tablespoon, the fluid ounce, the fluid dram, the gill, the pint, the quart, the gallon, the minim, the barrel, the cord, the peck, the bushel, and the hogshead.