How To Calculate Specific Gravity From Density

Pretend that you are an alien who just landed here from a faraway planet and discovered Earthlings discussing a concept called specific gravity. If you had access to a typical Earth dictionary (and if you traveled many trillions of miles to get here, you probably took the time to review the local languages and customs) and looked up each of these words independently, it would be fair of you to assume it had something to do with a particular kind of pull from a massive object.

Instead, you would quickly learn, the term has far more to do with the familiar quantity called density than it does to do with gravity, although there is a non-trivial connection. The reason the term even exists in physical science at all is because of the enormous range of applications of that one liquid resource that is both more plentiful and more vital than any other on Earth: water.

Mass (abbreviated m in physics equations) is a fundamental quantity in physics that denotes the existence of matter. One way to consider matter is that is possesses inertia; another is that gravity acts to accelerate masses, but not massless photons, or "packets" of light (it does a tiny bit, but this is only really noticeable in the vicinity of black holes, where relativistic effects are important). The SI (metric) unit is the kilogram (kg).

Volume (V) represents a quantity of closed three-dimensional space in regular or irregular form. It is based on the fundamental unit of length, the meter (m). Since three dimensions are required, the corresponding standard unit of volume is meters cubed (m³).

You just learned that gravity affects masses. When this happens, it creates a force, which on Earth is referred to as weight. The value of the acceleration of gravity g at Earth's surface is 9.8 m/s², so a mass of 10 kg would have a weight of 10 kg × 9.8 m/s² = 98 kg m/s². This unit is called a newton (N).

When you weigh an object, it returns a number in pounds or kilograms, which represent weight units. In reality, the scale is measuring the weight of the displayed number of kilograms on Earth but telling you the result as a mass. That is, the mass-vs.-weight distinction is factored into the construction of everyday Earth scales.

Density (denoted by ρ, the Greek letter rho) is simply mass divided volume, with corresponding units. In symbols:

\(ρ = \frac{m}{V}\)

Importantly, the unit of mass was originally chosen to correspond to how much of it was possessed by a volume of 1 L (1,000 mL, or equivalently, 1,000 cubic centimeters) of water. Note that 1 L is only 1/1000th of a m³, so the latter unit, while "standard," is not frequently used in lab experiments. Thus 1 kg water = "exactly" 1 L of volume.

The problem with this is that the density of water fluctuates slightly across the range of temperatures between freezing and boiling, so this value is in fact not constant and is only very close to 1.000.

Specific gravity (SG) is a lot simpler than you and your alien friends expected: It's just the ratio of the density of a given object to the density of water at a specific temperature. Specific gravity has no units. Its utility lies in the fact that the density of some objects changes with temperature in a different way than water's does, so using SG allows for a small correction factor.

Example: Say you have a sample of iron, which has a listed density of 7,850 kg/m³. What is the specific gravity of iron in an environment where ρ_water = 997 kg/m³?

To solve , you just divide 7,850 kg/m³ by 997 kg/m³ to get:

\(\begin{aligned}
SG &= \frac{7850 \text{ kg/m}^3}{997 \text{ kg/m}^3} \
&= 7873
\end{aligned}\)

Conversely, if you need a specific gravity to density calculator, you can just multiply the specific gravity by the density of water at the relevant temperature. So now, if you are ever asked to calculate density from specific gravity, your intergalactic trip was worth it!