How to calculate specific gravity?

You need approximately: 10 minutes

Follow the steps and learn how to calculate specific gravity!

1. Understand what specific gravity is

   Although it’s possible to calculate specific gravity (relative density) while having only a vague idea of what it is, it’s obviously better to fully understand it. So, let’s start with a definition and a very brief explanation. Specific gravity is defined as the ratio of the density of a substance to the density of a reference substance.^[1] Very often, that reference substance is water. In that case, specific gravity indicates the density of a substance relative to the density of water.
   
   Keep in mind though that specific gravity itself is not a measure of density! It’s merely a ratio between two densities. As such, we express specific gravity as a number without any units (it’s a dimensionless quantity). And that number can tell us something about the expected behavior of certain objects. If water is the reference substance, an object with specific gravity higher than 1 will sink in water. Conversely, if we find a specific gravity lower than 1, the object will float on water.^[2]

   

2. Be aware that relative density and specific gravity are different terms for the same concept

   We purposely titled this page “How to calculate specific gravity?” even though the term relative density is nowadays often preferred. Why did we do this? Well, to get a chance to clarify the terminology! Specific gravity is a somewhat unfortunate historic choice of wording as the concept is not as strongly related to gravity as this term suggests. It indeed has much more to do with density. And that’s no doubt the reason why many prefer the term relative density.
   
   Some say that specific gravity only concerns cases where water is the reference substance, and that specific gravity is therefore a special case of relative density. They argue that relative density is a more general concept, where the reference substance can be something else than water. In practice though, both terms appear to be used interchangeably and both are also used for situations where the reference substance is not water. Hence, we will continue to use both terms interchangeably in the following steps.

3. Clarify the reference substance

   As mentioned, water is often the reference substance. And, usually that’s water at 4 degrees Celsius (39.2 degrees Fahrenheit). That’s because water is at its maximum density at this temperature.^[3] There are indeed cases though where you need to use a different reference substance! For calculating the specific gravity (relative density) of a gas, the reference substance is usually air (at standard conditions).^[4] So, make sure to use the correct reference substance!

4. Grab the specific gravity formula

   The formula to calculate specific gravity is: $$\text{SG} = \frac{\rho_{\text{substance}}}{\rho_{\text{reference_substance}}}$$The \(\rho\) symbol stands for density. So, \(\rho_{\text{substance}}\) is the density of the substance for which we want to find the specific gravity (relative density). And, \(\rho_{\text{reference_substance}}\) is the density of the reference substance. If we use water as the reference substance, this becomes:$$\text{SG} = \frac{\rho_{\text{substance}}}{\rho_{\text{water}}}$$

5. Obtain the density values

   This step may seem obvious but in some cases this is the hardest part of the whole process! For example, if you first need to make measurements to be able to find a density value. However, the title of this how-to article is “how to calculate specific gravity”, and not “how to measure things”.🙃 Therefore, we assume you don’t need to measure anything or that you have already done so.
   
   Nevertheless, in some cases you may know the total mass of a substance and the volume that it occupies, but not its density. Well, hold on, in reality of course you then do know the density. The following formula allows you to obtain the density value from the mass (M) and volume (V).$$\rho_{\text{substance}} = \frac{M_{\text{substance}}}{V_{\text{substance}}}$$Let’s assume you have determined (or were given) the density of the substance for which you need to calculate the specific gravity. Now you still need to find the density of the reference substance. For the most common case, we just need the value of \(\rho_{\text{water}}\) though. And, that turns out to be really convenient! The value is simply 1 g/cm³ or, equivalently, 1000 kg/m³.

6. Express the density values in the same units

   Once you have the values for \(\rho_{\text{substance}}\) and \(\rho_{\text{reference_substance}}\), please also make sure to express both in the same units. While the standard unit for density is often regarded to be kg/m^3[5][6], it’s very common to use g/cm³ if it’s more convenient.^[7] And for gases, g/L is often a favored unit. Some other examples are g/mL or kg/L. It doesn’t really matter as long as \(\rho_{\text{substance}}\) and \(\rho_{\text{reference_substance}}\) are both expressed using the same units. However, if the units differ, make sure to first convert them accordingly! For example, 1000 kg/m³ is the same as 1 g/cm³, and 1 g/mL equals 1000 g/L or 1 kg/L. And should you come across a quantity expressed in g/cc, it’s good to know that g/cc means exactly the same as g/cm³.

7. Plug the numbers into the equation and find the result

   The calculation is actually very simple. We just have to divide the two density values! Let’s say we want to calculate the specific gravity of gold, using water as the reference substance. We are told, or look up, that gold has a density of 19.32 g/cm³.^[8] Also, we remember from step 5 that the density of water is simply 1 g/cm³ (at 4.0 °C or 39.2 °F). We take the formula from step 4, plug in the numbers, and find:$$\begin{align}\text{SG} & = \frac{\rho_{\text{gold}}}{\rho_{\text{water}}}\\[1ex] & = \frac{19.32\text{ g/cm}^3}{\phantom{9}1.00\text{ g/cm}^3}\\[1ex] & = 19.32\end{align}$$That’s it, we have calculated the specific gravity of gold. As mentioned earlier, we express this value without any units. Again, that’s because it’s simply a ratio between two densities (the relative density). As you can see in the calculation, the units (g/cm³) cancel out in the division.