Volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length (cubed) is interrelated with volume. 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. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume).
| Volume | |
|---|---|
A measuring cup can be used to measure volumes of liquids. This cup measures volume in units of cups, fluid ounces, and millilitres. | |
Common symbols | V |
| SI unit | cubic metre |
Other units | Litre, fluid ounce, gallon, quart, pint, tsp, fluid dram, in3, yd3, barrel |
| In SI base units | m3 |
| Extensive? | yes |
| Intensive? | no |
| Conserved? | yes for solids and liquids, no for gases, and plasma |
Behaviour under coord transformation | conserved |
| Dimension | L3 |
In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Zero-, one- and two-dimensional objects have no volume; in fourth and higher dimensions, an analogous concept to the normal volume is the hypervolume.