Volume

Volume is the amount of space that a three-dimensional object or region occupies or contains. It is a measure of capacity in space, and is distinct from mass, though related through density. In the metric system, volume is typically expressed in cubic meters (m^3) or liters, with 1 liter equal to 0.001 cubic meters, and 1 cubic centimeter (cm^3) equals 1 milliliter (mL).

In geometry, the volume of common shapes is given by: cube V = a^3; rectangular prism V = l × w × h; cylinder V = π r^2 h; sphere V = (4/3)π r^3; cone V = (1/3)π r^2 h; square pyramid V = (1/3) B h, where B is the base area.

For regular shapes the volume can be computed from these formulas, while irregular objects are typically measured by water displacement: the rise in a graduated cylinder equals the object's volume. Liquids are measured directly with graduated cylinders or measuring jugs. Containers specify a nominal volume or capacity, indicating how much they can hold.

Volume can also denote a quantity per unit time, known as volume flow rate Q, measured in cubic meters per second (m^3/s). Mass and volume are related by density ρ, with m = ρV. In mathematics, volume generalizes to the three-dimensional measure of a region in space and, in higher dimensions, to hypervolume.