The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional objects (such as lines) and two-dimensional objects (such as squares) are assigned zero volume in the three-dimensional space.
Volumes of straight-edged and circular shapes are calculated using arithmetic formulas. Volumes of other curved shapes are calculated using integral calculus, by approximating the given body with a large amount of small cubes or concentric cylindrical shells, and adding the individual volumes of those shapes. The volume of irregularly shaped objects can be determined by displacement.
The generalization of volume to arbitrarily many dimensions is called content.citation needed] In differential geometry, volume is expressed by means of the volume form.
Volume and Capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units).
Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure.