Volume

The volume of a solid object is, classically, a (positive) value given to describe the 3-dimensional concept of how much space said object "uses up". This means that neither a 1-dimensional object (a line), nor a 2-dimensional object, has a defined 3-dimensional volume (they each have a volume of zero). It can also be used to refer to the amount of space an n-dimensional object uses up, although this usage is uncommon.

The volume of an object is the mass divided by the average density. For physical objects of known uniform density, this is one of the ways to find the volume.

In terms of volume measurements, volume may also be termed capacity.

Common equations for volume:

• A cube: s3 (where s is the length of a side)
• A rectangular prism: l w h (length, width, height)
• A cylinder: π r2 h (r = radius of circular face, h = distance between faces)
• A sphere: 4 π r3 / 3 (r = radius of sphere)
• A cone: π r2 h / 3 (r = radius of circle at base, h = distance from base to tip)
• any prism that has a constant cross sectional area along the height**: A h (A = area of the base, h = height)
• any figure (calculus required): ∫ A dh (where h is any dimension of the figure, and A is the area of the cross sections perpendicular to h described as a function of the position along h) (this will work for any figure (no matter if the prism is slanted or the cross sections change shape).

A commonly used SI unit for volume is the liter, and one thousand liters is the volume of a cubic meter, which was formerly termed a stere. A cubic centimeter is essentially the same as a milliliter.

• US fluid ounce, about 29.6 ml (this volume of water weighs one ounce)
• US pint = 16 ounces, or about 473 ml (this volume of water weighs one pound)
• US quart = 32 ounces or two pints, or about 946 ml
• US gallon = 128 ounces or four quarts, about 3.785 l

• UK fluid ounce, about 28.4 ml (weight of this volume of water is 28.3 g, or nearly one ounce, 28.4 g)
• UK pint = 20 fluid ounces, or about 568 ml
• UK quart = 40 ounces or two pints, or about 1.136 l
• UK gallon = 160 ounces or four quarts, or about 4.546 l

Traditional cooking measures for volume also include:

To help compare different volumes, see these pages: