# A Definition Of Density

It is useful to have a clear definition of density, as this is perhaps not the simplest idea to get your head around. We are all familiar with weight, and we are all familiar with volume, being the amount of space that something takes up. We work with these ideas every day of our lives, yet we spare barely a thought for the density of objects.

## A Definition Of Density

In short, density is **how much something of a set volume weighs**. This is generally measured by taking a cubic centimeter of a substance (cm^-3). If we take a cubic centimeter of some commonly known substances, we can see that they weigh different amounts:

So from the above examples it is easy to see that some of the cubes weigh more than others, even though they all take up the same amount of space. Allotropes and alkenes have different density for example.

This agrees with our experience. We know that a huge block of foam is easier to lift than the same size block of wood or metal. Now we can see that the foam block is ** less dense** than the others, making it easier to lift. We can all imagine lifting a cube of foam, but try lifting the same cube of lead or steel!

## Calculating Density

The best way to calculate the density of any material is to take a cubic centimeter of it and weigh it. That will give you the mass of the substance **per cubic centimeter**. For lead (Pb), each cubic centimeter of it weighs 11.35 grams, making its density 11.35 grams per cubic centimeter, or g / cm^-3 if you’re scientifically minded.

For lead, 1 cubic centimeter weighs 11.35 grams, while 2 grams weighs 22.70 grams and so on; so we see that the ratio of 11.35 grams per cubic centimeter holds fast. The definition of density functions.

## The Formula For Density

“Per” is the maths word for *divided by*. So if we translate the units of density, which are grams per cubic centimeter, into math speak, we get grams / cubic centimeters, or g / cm^3, also written as gcm^-3.

In short, we calculate **density** by dividing **mass** by **volume** as shown to the right. The units can actually be of any kind, as long as they are the same between substances to be compared. We could measure density in milligrams per cubic mile, or kilotons per cubic nanometer, it makes no difference. As long as the units are clearly stated, conversion to standard units is easily achieved.

## Why are some things denser than others?

This is the **big question**. A material that is denser has more matter, or stuff, packed into the same space. To understand this fully, we need to consider matter in terms of the atoms that it is made of. The more stuff that’s in the nuclei of the atoms of the substance, the greater the density will be.

See how this works in the very simplified picture of two atoms to the right.

The mass of the substances is held in the nuclei, and even though the metals take up the same amount of space the one on the left (Lithium) has far less matter in its nucleus than the **lead** on the right. It is because of this, and this alone, that lead is more **dense** than Lithium metal.