Unlike density, which has units of mass per volume, specific gravity is a pure number, i.e., it has no associated unit of measure. If the densities of the substance of interest and the reference substance are known in the same units (e.g., both in g/cm3 or lb/ft3), then the specific gravity of the substance is equal to its density divided by that of the reference substance. Similarly, if the specific gravity of a substance is known and the density of the reference substance is known in some particular units, then the density of the substance of interest, in those units, is equal to the product of its specific gravity and the density of the reference substance.
The most widely used reference substance for determining the specific gravities of solids and liquids is water. Because the density of water is very nearly 1 g/cm3, the density of any substance in g/cm3 is nearly the same numerically as its specific gravity relative to water. In the English system of units the density of water is about 62.4 lb/ft3, so the near equality between specific gravity and density is not preserved in this system. Specific gravities of gases are often given with dry air as the reference substance. Because the densities of all substances vary with temperature and pressure, the temperature and (particularly for gases) the pressure for both the reference substance and the substance of interest are often included when precise values of specific gravities are given.
A number of experimental methods for determining the specific gravities of solids, liquids, and gases have been devised. A solid is weighed first in air, then while immersed in water; the difference in the two weights, according to Archimedes' principle, is the weight of the water displaced by the volume of the solid. If the solid is less dense than water, some means must be adopted to fully submerge it, e.g., a system of pulleys or a sinker of known mass and volume. The specific gravity of the solid is the ratio of its weight in air to the difference between its weight in air and its weight immersed in water.
Two methods are commonly used for determining the specific gravities of liquids. One method uses the hydrometer, an instrument that gives a specific gravity reading directly. A second method, called the bottle method, uses a "specific-gravity bottle," i.e., a flask made to hold a known volume of liquid at a specified temperature (usually 20°C;). The bottle is weighed, filled with the liquid whose specific gravity is to be found, and weighed again. The difference in weights is divided by the weight of an equal volume of water to give the specific gravity of the liquid. For gases a method essentially the same as the bottle method for liquids is used. Specific gravities of gases are usually converted mathematically to their value at standard temperature and pressure (see STP).
Specific gravity, SG, is expressed mathematically as:
where is the density of the substance, and is the density of water. (By convention ρ, the Greek letter rho, denotes density.) The density of water varies with temperature and pressure, and it is usual to refer specific gravity to the density at 4°C (39.2°F) and a normal pressure of 1 atm. The given temperature and pressure are preferred because it is when water has its maximum density. In this case is equal to 1000 kg·m−3 in SI units (or 62.43 lbm·ft−3 in United States customary units).
Given the specific gravity of a substance, its actual density can be calculated by inverting the above formula:
Occasionally a reference substance other than water is specified (for example, air), in which case specific gravity means density relative to that reference.
Specific gravity is by definition dimensionless and therefore not dependent on the system of units used (e.g. slugs·ft−3 or kg·m−3). However, the two densities must of course be converted to the same units before carrying out the numerical ratio calculation.
For information about the measurement of and uses of specific gravity, see relative density.
(Samples may vary, and these figures are approximate.)