Volume

Volume (English: volume) is the measure of three-dimensional space that a thing or object occupies. It is one of the fundamental measures in physics and mathematics, and is defined by length, width and height when the object is a solid.

In the International System of Units (SI), the unit of volume is the cubic meter (m³). In everyday use, the liter and milliliter are commonly used; one liter is equal to one thousand cubic centimeters (cm³), which is one thousandth of a cubic meter.

Calculating volume

Simple geometric shapes have specific formulas. For a rectangular box, volume equals length × width × height. For a cylinder, volume equals the area of the circular base multiplied by the height. For a sphere, volume is calculated as four-thirds times pi times the radius cubed. For irregular shapes, integral calculus is used.

Actual measurement

The volume of a solid object with an irregular shape can be determined by water displacement: the object is placed in a container of water, and the rise in the water level equals the volume of the object. This method is related to Archimedes' principle. Liquids are measured in graduated containers such as calibrated cylinders.

Relationship to density

Volume is directly related to density (mass divided by volume). Therefore, if two of these three values are known, the third can be calculated. The volume of gases changes significantly when temperature and pressure change, unlike that of liquids and solids.