 Density

Density, or volumic mass, is a measure of mass per unit volume. The average density of an object equals its total mass divided by its total volume. An object made from a comparatively dense material (such as iron) will have more mass than an equal-sized object made from some less dense substance (such as aluminium).

A tables of densities of some materials:

## Notation, units, and properties

The standard symbol used for density is ρ, the Greek letter rho. So we have

where

m is the object's total mass ([M]; kg)
V is the object's total volume ([L³]; m³)

The SI unit of density is the kilogram per cubic metre (kg/m³), but grams per cubic centimeter (g/cm³) and kilograms per litre (kg/L) are also commonly used. Liquid water has a density of about 1000 kg/m³ (or 1 kg/L or 1 g/cm³), solid iron has a density of about 8000 kg/m³, and air at room temperature and atmospheric pressure has a density of about 1.2 kg/m³.

The density of an object or substance depends on its temperature, with higher temperature usually (but not always) resulting in lower density. This temperature-density relationship is captured by the substance's volumetric thermal expansion coefficient β. The density of a gas (and to a much lesser extent also that of a solid or liquid) further depends on the pressure, with higher pressure resulting in higher density. The density of a gas is very dependent on the gas laws.

The density of an object does not have to be uniform, for instance if the object is composed of different materials, or if its pressure or temperature is not the same everywhere. The density of a moving gas may vary if its velocities yield a Mach number higher than about 0.3. In this case, one defines the density at a specific point by taking a tiny sphere around that point and dividing the mass contained within that sphere by the sphere's volume.

## Other units

In Imperial units or U.S. customary units, the units of density include pounds per cubic foot (lb/ft³), pounds per cubic yard (lb/yd³), pounds per cubic inch (lb/in³), ounces per cubic inch (oz/in³), pounds per gallon (for U.S. or imperial gallons) (lb/gal), pounds per U.S. bushel (lb/bu), in some engineering calculations slugs per cubic foot, and other less common units.

The maximum density of pure water at a pressure of one standard atmosphere is 999.861 kg/m³; this occurs at a temperature of about 3.98°C (277.13 K).

From 1901 to 1964, a litre was defined as exactly the volume of 1 kg of water at maximum density, and the maximum density of pure water was 1.000 000 kg/L (now 0.999 972 kg/L). However, while that definition of the litre was in effect, just as it is now, the maximum density of pure water was 0.999 972 kg/dm³. During that period students had to learn the esoteric fact that a cubic centimeter and a milliliter were slightly different volumes, with 1 mL = 1.000 028 cm³. (often stated as 1.000 027 cm³ in earlier literature).

Specific gravity

Another form of measurement closely associated with density is specific gravity. The specific gravity of a material is the density of that material compared to the density of some standard. For solids and liquids, the most common standard is water, whose density is 1.00 gram per cubic centimeter. The specific gravity of iron, then, is its density (7.87 grams per cubic centimeter) divided by the density of water (1.00 gram per cubic centimeter). You can see that the numerical value for the specific gravity of a solid or liquid is always the same as that of its density.

The reason is that the divisor in every case is 1 gram per cubic centimeter, the density of water. For iron, the specific gravity is 7.87. The only difference between density and specific gravity for solids and liquids is that specific gravity has no label. In dividing 7.87 grams per cubic centimeter by 1.00 gram per cubic centimeter, the labels divide out (cancel), leaving only the number.

The specific gravity of gases is somewhat more difficult since the most common standards are air (density = 1.293 grams per cubic centimeter) or hydrogen (density = 0.0899 gram per cubic centimeter). The specific gravity of oxygen using air as a standard, then, is its density (1.429 grams per cubic centimeter) divided by the density of air (1.293 grams per cubic centimeter), or 1.105. Using hydrogen as a standard, the specific gravity of oxygen is 1.429 grams per cubic centimeter ÷ 0.0899 gram per cubic centimeter, or 15.9.