Definition of relative density

1) Relative density (also known as specific gravity) is a measure of the density of a material. It is dimensionless, equal to the density of the material divided by the density of water.

Since water's density is 1.0 × 103 kg/m3 in SI units, the relative density of a material is the density of the material measured in kg / m3 divided by 1000 (the density of water). There are no units of measurement.

Water's density can also be measured as one gram per cubic centimetre (under standard conditions) in cgs units. The relative density therefore has the same value as density of the material expressed in grams per cubic centimetre, but without any units of measurement.

Relative density is often used by geologists and mineralogists to help determine the mineral content of a rock or other sample. Gemologists use it as an aid in the identification of gemstones. The reason that relative density is measured in terms of the density of water is because that that is the easiest way to measure it in the field. Basically, density is defined as the mass of a sample divided by its volume. With an irregularly shaped rock, the volume can be very difficult to accurately measure. The most accurate way is to put it in a water-filled graduated cylinder and see how much water it displaces.

Even this method can be rather inaccurate, though, since it is easy to accidentally spill some water. It is far easier to simply suspend the sample from a spring scale and weigh it under water. Solving Isaac Newton's equations yields the following formula for measuring specific gravity:
G = \frac{W}{W - F}
where G is the relative density, W is the weight of the sample (measured in pounds, newtons, or some other unit of force), and F is the force, measured in the same units, while the sample was submerged. Note that it is rather difficult to measure relative densities less than one because in order to do so, the sign of F must change, meaning that you would have to supply a downward force to keep the sample underwater.