Density – Definition and How to Calculate It

Core Concepts

In this tutorial, you will learn what density is, and how to calculate it. You will also learn the units and you will find out if it is a physical property.

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What is Density? Definition

Density is the measure of how much “stuff” is in a given amount of space. For example, a block of the heavier element lead (Pb) will be denser than the softer, lighter element gold (Au). A block of Styrofoam is less dense than a brick. It is defined as mass per unit volume.

You can therefore think of it as how tightly or loosely packed a substance is or how compact it is. Solids are generally denser than liquids, and liquids denser than gases, but there are many exceptions.

Is Density a Physical Property?

It is a physical property, defined by mass over volume. Physical properties can be observed without changing the chemical makeup of the substance. Other physical properties include melting point and boiling point. Every substance, element and compound has a unique density associated with it.

Density Units

Let’s discuss the “common” units of density, and the “official” units. All units are in some form of weight per a volume. The most common unit for density is grams per cubic centimeter, or $\text{g/cm}^{3}$ . For example, the density of water is one gram per cubic centimeter, and of lead is $3.42 \text{g/cm}^{3}$ . The official units for density, known as SI units (International System of Units) are kilogram per cubic meter ( $\text{kg/cm}^{3}$ ). Other equivalents are grams per milliliter $\text{g/mL}$ and kilograms per liter, $\text{kg/L}$ .

Styrofoam is less dense at about $1\text{g/cm}^{3}$ . It is commonly used as a light material to protect packages during shipment. A brick is about double that of Styrofoam at $2\text{g/cm}^{3}$ . It is therefore hardy enough to withstand the elements as a building material.

How to Calculate Density

To calculate this property, we remember that it is defined as mass per volume. Mass is commonly represented by “ $m$ “, volume by “ $V$ “, and density by either “ $\rho$ “, or uppercase “ $D$ “. The general formula is as follows:

Density Formula / Equation

Measurement	Variable
Density	$\rho$ or $D$
Mass	$m$
Volume	$V$

Variables in the $\rho$ formula

If you know the mass and density of a substance, you can then calculate the volume. If you know the density and volume, you can then calculate the mass. And last but not least, if you know the mass and volume, you can calculate the density.

Density – Fun Facts

The most dense element is osmium.
The least dense element (or any gas) is hydrogen.
One of the most dense astronomical objects known to us is a black hole.
Gold and tungsten, both with a density of $19.3text{g/cm}^{3}$ , are the densest of all easily accessible materials. A small tungsten cube is shockingly heavy.
The world’s least dense solid is a graphene aerogel with a density of $0.16text{mg/cm}^{3}$ developed in a polymer science and engineering lab in China.
Mercury is a liquid metal that is denser than most solids.
The most dense gas, tungsten hexafluoride, is still about 45 times as dense as one of the least denser liquids, isopentane.
An item will only sink in water if it is more dense than water. Try finding a household item more dense than water – it is more difficult than you may think!

Practice Problems

Here are some example calculations, based around some important elements and molecules.

Problem 1

Calculate the density of mercury (Hg) if its mass is $28\text{g}$ and its volume is $2\text{cm}^{3}$ .

Problem 2

If a square block of iron (Fe) with a side length of $2\text{cm}$ weighs $64\text{g}$ . How dense is iron?

Problem 3

Water is approximately $D = 1 \text{g/mL}$ , how much does $5\text{mL}$ of water weigh, in grams?

Practice Problem Solutions

For mercury, $D = 14 \text{g/cm}^{3}$ . To get this value, $28\text{g}$ is divided by $2\text{cm}^{3}$ .
For iron, $D = 8 \text{g/cm}^{3}$ . We already know the weight ( $64 \text{g}$ ). The volume is $2\text{cm} x 2\text{cm} x 2\text{cm}$ because the question says the piece is a square. So the volume is $8\text{cm}^{3}$ . Then $64 \text{g/} 8\text{cm}^{3}$ brings us to the answer of $8 \text{g/cm}^{3}$ .
Five milliliters of water weighs $5 \text{g}$ . To get this answer, we multiply the $1 \text{g/mL}$ times the volume ( $5\text{mL}$ ) that we are interested in.