# Volume

**Volume**(also called

**capacity**) is a quantification of how much space an object occupies. The SI unit for volume is the cubic metre (American spelling meter).

The **volume** of a solid object is a numerical value given to describe the three-dimensional concept of how much space it occupies. One-dimensional objects (such as lines) and two-dimensional objects (such as squaress) are assigned zero volume in three-dimensional space.

** Volume** in acoustics is used as a synonym for

*loudness*. It is a common term for the amplitude or the level of sound. See also: DB(A), Sone, phon

Less commonly, in mathematics, ** volume** can refer to the amount of space an

*n*-dimensional object fills up, for some

*n*> 3. Volumes are

*defined*by means of integral calculus, by the decomposition of complex sets into small

**volume elements**. Volume (

*Cx*

^{3}) is the antiderivative of area (

*Cx*

^{2}). More simply, for a perfect closed curve, which is the sphere in three dimensions, the volume is the simple integral of the surface area. Thus, the surface area of a sphere is 4πr

^{2}, and the volume is 4/3πr

^{3}.

## Volume formulae

- A cube:
**s**(where s is the length of a side)^{3} - A rectangular prism:
**l w h**(**l**ength,**w**idth,**h**eight) - A cylinder:
**π r**(r = radius of circular face, h = distance between faces)^{2}h - A sphere:
**4 π r**(r = radius of sphere)^{3}/ 3 - A cone:
**π r**(r = radius of circle at base, h = distance from base to tip)^{2}h / 3 - any prism that has a constant cross sectional area along the height**:
**A h**(A = area of the base, h = height) - any figure (calculus required):
**∫ A dh**(where h is any dimension of the figure, and A is the area of the cross sections perpendicular to h described as a function of the position along h) (this will work for any figure (no matter if the prism is slanted or the cross sections change shape).

## Volume measures: SI

A commonly used SI unit for volume is the litre (American spelling liter), and one thousand litres is the volume of a cubic metre, which was formerly termed a *stere*. A cubic centimeter is the same volume as a millilitre.

## Volume measures: USA

Traditional US measures of volume:

- US fluid ounce, about 29.6 ml (this volume of water weighs one ounce)
- US pint = 16 ounces, or about 473 ml (this volume of water weighs one pound)
- US quart = 32 ounces or two pints, or about 946 ml
- US gallon = 128 ounces or four quarts, about 3.785 l

## Volume measures: UK

Traditional UK measures of volume:

- UK fluid ounce, about 28.4 ml (weight of this volume of water is 28.3 g, or nearly one ounce, 28.4 g)
- UK pint = 20 fluid ounces, or about 568 ml
- UK quart = 40 ounces or two pints, or about 1.136 l
- UK gallon = 160 ounces or four quarts, or about 4.546 l

## Volume measures: cooking

Traditional cooking measures for volume also include:

- teaspoon = 1/6 ounce
- tablespoon = 1/2 ounce or 3 teaspoons
- cup = 8 ounces or 1/2 pint

## Relationship to density

The volume, of an object, is equal to its mass divided by its average density. This is a rearrangement of the calculation of density as mass per unit volume.

## Volume comparisons

To help compare different volumes, see Orders of magnitude (volume)

## See also

## External links

- Volume or capacity conversion of English and American units to metric units
- Conversions of volume, capacity, cubic metres, kilograms, weight of water and milliliters to liters - prefixes