Math You Need > Calculating Density

How do I Calculate Density?
Density and specific gravity in the geosciences

An introduction to density

Density is the mass of an object divided by its volume.
density equation

Density often has units of grams per cubic centimeter (g/cm3). Remember, grams is a mass and cubic centimeters is a volume (the same volume as 1 milliliter).

density of atoms A box with more particles in it will be more dense than the same box with fewer particles

Density is a fundamental concept in the sciences; you will see it throughout your studies. It is used quite often in identifying rocks and minerals since the density of substances rarely changes significantly. For example, gold will always have a density of 19.3 g/cm3; if a mineral has a density other than that, it isn't gold.

You probably have an intuitive feeling for density in the materials you use often. For example, sponges are low in density; they have a low mass per unit volume. You are not surprised when a large sponge is easy to lift. In contrast, iron is dense. If you pick up an iron skillet, you expect it to be heavy.

Students, and even teachers, often confuse mass and density. The words heavy and light on their own refer to mass, and not density. A very large sponge may weigh a lot (have a high mass), but its density is low because it still weighs very little per unit of volume. For density, you also need to consider the size, or volume, of the object.

How do I determine density?

A concrete cube will weigh more than a cube of air the same size because it is denser
Density is not something that is directly measured. Typically if you want to know the density of something you will weigh it and then measure its volume.

You collect a boulder and take it back to the lab, where you weigh it and find its mass to be 1000 g. You then determine the volume is 400 cm3. What is your boulder's density?
Density is mass divided by volume,
density equation
In this case the mass is 1000g and the volume is 400 cm3, so you divide 1000g by 400 cm3 to get 2.5 g/cm3.

Another tricky thing about density is that you can't add densities. If I have a rock that is made up of two minerals, one with a density of 2.8 g/cm3, and one with a density of 3.5 g/cm3, the rock will have a density between 3.5 and 2.8 g/cm3, not a density of 6.3 g/cm3. This is because both the mass and the volume of the two minerals will be added, and so when they are divided to get the density the result will be between the two.

Typical densities for gasses are on the order of thousandths of grams per cubic centimeter. Liquids often have densities of about 1.0 g/cm3, and indeed, fresh water has a density of 1.0 g/cm3. Rocks often have a density around 3 g/cm3, and metals often have densities above 6 or 7 g/cm3.

How do I calculate specific gravity?

To calculate the specific gravity (SG) of an object, you compare the object's density to the density of water:

specific gravity

Because the density of water in g/cm3 is 1.0, the SG of an object is will be almost the same as its density in g/cm3. However, specific gravity is a unitless number, and is the same in the metric system or any other measurement system. It is very useful when comparing the density of two objects. Since specific gravity is unitless, it doesn't matter whether the density was measured in g/cm3 or in some other units (like lbs/ft3).

You have a sample of basalt with density 210 lbs/ft3. The density of water is 62.4 lbs/ft3. What is the specific gravity of the basalt?
The specific gravity is the density of the substance divided by the density of water, so
specific gravity
So we divide the basalt (210 lbs/ft3) by the density of water (62.4 lbs/ft3), and get S.G.= 3.37.

Why should I calculate density or specific gravity?

Densities are critical for many uses. One of the most critical is that the density of a substance will determine if it will float on another. Less dense substances will float on (or rise through) more dense substances. Here are some examples of how this explains everyday occurrences:

  • Have you wondered why hot air balloons rise? When the air is heated, it becomes less dense until the balloon's total density is less than that of the atmosphere; A hot air balloon is literally floating on the denser, colder air.
  • Have you ever noticed in a lake or the ocean that water is warmer at the surface and colder at the bottom? This is because the warmer water is slightly less dense and, as a result floats on the denser, colder water
  • Do you know why volcanoes erupt?
    A picture of a big boat This huge boat weighs a lot, but it its density must be less than 1.0 g/cm3 because it is floating.
    image from NOAA
    The main reason that magma rises to the surface to erupt at volcanoes is because it is less dense than the rocks that surround it.
A ship floating on water is a great illustration of the difference between mass and density. A ship must have a density of less than 1.0 g/cm3(the density of water), or it will sink. Ships have a large mass, because they are made of steel, but because they have a large volume, their density is less than 1.0 g/cm3. If enough mass is added to them such that their density goes above 1.0 g/cm3, they will sink.

To try some practice problems, go to the sample problem page!

Where is density used in the geosciences?

Galena, a lead ore, is one of the densest common minerals
  • Isostasy - determining how high continents will sit on the mantle
  • Plate tectonics - mechanisms that drive plate tectonics
  • Minerals - determining the name of a mineral through its density
  • Rocks - determining the name and composition of a rock by its density
  • The hypsometric curve - examining the causes of elevation variation on Earth
  • Oceanography - some ocean currents and ocean circulation is controlled by density

Next Steps

I'm ready to practice! (These problems have worked answers.)

I still need more help!
(See the links below for more help with density).

More help with Density

Edinformatics on-line lab on mass, volume and density is put together by NYU. It allows you to look at pictures of measurements and to enter data.

Hyperphysics, at the Georgia State has a page about density and a density converter. This includes several related pages including instructions of measuring density using the Archimedes principle.

Wikipedia's specific gravity page has an explanation of what specific gravity is and how it is used and even discusses its use in the geosciences and mineralogy. However, the content of Wikipedia articles may change and so you may want to be cautious.

Wikipedia's Density page has a general discussion of density and its history, calculation, and units. However, the content of Wikipedia articles may change and so you may want to be cautious.
This page was written and compiled by Dr. Eric M. Baer, Geology Program, Highline Community College, and Dr. Jennifer M. Wenner, Geology Department, University of Wisconsin Oshkosh

      Next Page »