El volumen es una magnitud métrica de tipo escalar definida como la extensión en tres dimensiones de una región del espacio. Es una magnitud derivada de la longitud, ya que se halla multiplicando la longitud, el ancho y la altura. Matemáticamente el volumen es definible no sólo en cualquier espacio euclídeo, sino también en otro tipo de espacios métricos que incluyen por ejemplo a las variedades de Riemann. Desde un punto de vista físico, los cuerpos materiales ocupan un volumen por el hecho de ser extensos, fenómeno que se debe al principio de exclusión de Pauli. La noción de volumen es más complicada que la de superficie y en su uso formal puede dar lugar a la llamada paradoja de Banach-Tarski. La unidad de medida de volumen en el Sistema Internacional de Unidades es el metro cúbico. Para medir la capacidad se utiliza el litro. Por razones históricas, existen unidades separadas para ambas, sin embargo están relacionadas por la equivalencia entre el litro y el decímetro cúbico: 1 dm3 = 1 litro = 0,001 m3 = 1000 cm3.

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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.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.

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