The volume of any solid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.Volume is presented as ml or cm³.

Volumes of straight-edged and circular shapes are calculated using arithmetic formulae.

In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.

Volume and capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in liters or its derived units), and volume being how much space an object displaces (commonly measured in cubic metrics or its derived units).

Volume and capacity are also distinguished in a capacity management setting, where capacity is defined as volume over a specified time period.

Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure.

{3} \pi r^3 |r = radius of sphere
which is the integral of the Surface Area of a sphere |- |An ellipsoid: |$\backslash frac\{4\}\{3\}\; \backslash pi\; abc$ |a, b, c = semi-axes of ellipsoid |- |A pyramid: |$\backslash frac\{1\}\{3\}Ah$ |A = area of the base, h = height of pyramid |- |A cone (circular-based pyramid): |$\backslash frac\{1\}\{3\}\; \backslash pi\; r^2\; h$ |r = radius of circle at base, h = distance from base to tip |- |Any figure (calculus required) |$\backslash int\; A(h)\; \backslash ,dh$ |h = any dimension of the figure, A(h) = area of the cross-sections perpendicular to h described as a function of the position along h. This will work for any figure if its cross-sectional area can be determined from h (no matter if the prism is slanted or the cross-sections change shape). ^*

|}

(The units of volume depend on the units of length - if the lengths are in meters, the volume will be in cubic meters, etc)

The volume of a parallelepiped is the absolute value of the scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix.

The volume of any tetrahedron, given its vertices a, b, c and d, is (1/6)·|det(a−b, b−c, c−d)|, or any other combination of pairs of vertices that form a simply connected graph.

Volume measures: cooking

Traditional cooking measures for volume also include:

• teaspoon = 1/6 U.S. fluid ounce (about 4.929 mL)
• teaspoon = 1/6 Imperial fluid ounce (about 4.736 mL)
• teaspoon = 5 mL (metric)
• tablespoon = ½ U.S. fluid ounce or 3 teaspoons (about 14.79 mL)
• tablespoon = ½ Imperial fluid ounce or 3 teaspoons (about 14.21 mL)
• tablespoon = 15 mL or 3 teaspoons (metric)
• tablespoon = 5 fluidrams (about 17.76 mL) (British)
• cup = 8 U.S. fluid ounces or ½ U.S. liquid pint (about 237 mL)
• cup = 8 Imperial fluid ounces or ½ fluid pint (about 227 mL)
• cup = 250 mL (metric)