Specific gravity
Common symbols	SG
SI unit	Unitless
Derivations from other quantities	${\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}}$

Relative density, also called specific gravity,^[1][2] is a dimensionless quantity defined as the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest (at 4 °C or 39.2 °F); for gases, the reference is air at room temperature (20 °C or 68 °F). The term "relative density" (abbreviated r.d. or RD) is preferred in SI, whereas the term "specific gravity" is gradually being abandoned.^[3]

If a substance's relative density is less than 1 then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water, then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.

Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm (101.325 kPa). Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry. In British brewing practice, the specific gravity, as specified above, is multiplied by 1000.^[4] Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, must weight (syrups, juices, honeys, brewers wort, must, etc.) and acids.

Basic calculation

Relative density (${\displaystyle RD}$) or specific gravity (${\displaystyle SG}$) is a dimensionless quantity, as it is the ratio of either densities or weights

where ${\displaystyle RD}$ is relative density, ${\displaystyle \rho _{\mathrm {substance} }}$ is the density of the substance being measured, and ${\displaystyle \rho _{\mathrm {reference} }}$ is the density of the reference. (By convention ${\displaystyle \rho }$, the Greek letter rho, denotes density.)

The reference material can be indicated using subscripts: ${\displaystyle RD_{\mathrm {substance/reference} }}$ which means "the relative density of substance with respect to reference". If the reference is not explicitly stated then it is normally assumed to be water at 4 °C (or, more precisely, 3.98 °C, which is the temperature at which water reaches its maximum density). In SI units, the density of water is (approximately) 1000 kg/m³ or 1 g/cm³, which makes relative density calculations particularly convenient: the density of the object only needs to be divided by 1000 or 1, depending on the units.

The relative density of gases is often measured with respect to dry air at a temperature of 20 °C and a pressure of 101.325 kPa absolute, which has a density of 1.205 kg/m³. Relative density with respect to air can be obtained by

where ${\displaystyle M}$ is the molar mass and the approximately equal sign is used because equality pertains only if 1 mol of the gas and 1 mol of air occupy the same volume at a given temperature and pressure, i.e., they are both ideal gases. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0 °C and 1 atmosphere whereas carbon dioxide has a molar volume of 22.259 L under those same conditions.

Those with SG greater than 1 are denser than water and will, disregarding surface tension effects, sink in it. Those with an SG less than 1 are less dense than water and will float on it. In scientific work, the relationship of mass to volume is usually expressed directly in terms of the density (mass per unit volume) of the substance under study. It is in industry where specific gravity finds wide application, often for historical reasons.

True specific gravity of a liquid can be expressed mathematically as:

where ${\displaystyle \rho _{\mathrm {sample} }}$ is the density of the sample and ${\displaystyle \rho _{\mathrm {H_{2}O} }}$ is the density of water.

The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air:

where ${\displaystyle W_{A,{\text{sample}}}}$ represents the weight of the sample measured in air and ${\displaystyle {W_{\mathrm {A} ,\mathrm {H_{2}O} }}}$ the weight of an equal volume of water measured in air.

It can be shown that true specific gravity can be computed from different properties:

where g is the local acceleration due to gravity, V is the volume of the sample and of water (the same for both), ρ_sample is the density of the sample, ρ_H2O is the density of water, W_V represents a weight obtained in vacuum, ${\displaystyle {\mathit {m}}_{\mathrm {sample} }}$ is the mass of the sample and ${\displaystyle {\mathit {m}}_{\mathrm {H_{2}O} }}$is the mass of an equal volume of water.

The density of water varies with temperature and pressure as does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined. It is nearly always the case that measurements are made at 1 nominal atmosphere (101.325 kPa ± variations from changing weather patterns). But as specific gravity usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products), variations in density caused by pressure are usually neglected at least where apparent specific gravity is being measured. For true (in vacuo) specific gravity calculations, air pressure must be considered (see below). Temperatures are specified by the notation (T_s/T_r), with T_s representing the temperature at which the sample's density was determined and T_r the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, we note that, while SG_H2O = 1.000000 (20 °C/20 °C), it is also the case that SG_H2O = 0.9982008⁄0.9999720 = 0.9982288 (20 °C/4 °C). Here, temperature is being specified using the current ITS-90 scale and the densities ^[5] used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale, the densities at 20 °C and 4 °C are 0.9982041 and 0.9999720 respectively ^[6], resulting in an SG (20 °C/4 °C) value for water of 0.998232.

As the principal use of specific gravity measurements in industry is determination of the concentrations of substances in aqueous solutions and as these are found in tables of SG versus concentration, it is extremely important that the analyst enter the table with the correct form of specific gravity. For example, in the brewing industry, the Plato table lists sucrose concentration by weight against true SG, and was originally (20 °C/4 °C)^[7] i.e. based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density, ρ_H2O equal to 999.972 kg/m³ in SI units (0.999972 g/cm³ in cgs units or 62.43 lb/cu ft in United States customary units). The ASBC table^[8] in use today in North America for apparent specific gravity measurements at (20 °C/20 °C) is derived from the original Plato table using Plato et al.‘s value for SG(20 °C/4 °C) = 0.9982343. In the sugar, soft drink, honey, fruit juice and related industries, sucrose concentration by weight is taken from a table prepared by A. Brix, which uses SG (17.5 °C/17.5 °C). As a final example, the British SG units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).

Given the specific gravity of a substance, its actual density can be calculated by rearranging the above formula: