Density: Formula and units

In a nutshell

Density is a measure of how heavy $1cm^3$ of a material is. Another way of saying this is that density is the mass per unit volume of a material. Every material has its own density.

Density formula

The density of a material is given as:

$density=\frac{mass}{volume}$

Or, more simply:

$D=\frac{M}{V}$

Units of density, mass and volume

Measurement	Units
Density	kilograms per cubic metre ( $kg/m^3$ ), grams per cubic centimetre ( $g/cm^3$ )
Mass	kilograms ( $kg$ ), grams ( $g$ )
Volume	cubic metres ( $m^3$ ), cubic centimetres ( $cm^3$ )

Solving density problems

To solve problems involving density, follow this procedure:

procedure

1.	Identify what values you have and what variable you want to find.
2.	Rearrange the density formula for the desired variable.
3.	Substitute in known values.
4.	Give the answer with the correct units.

Example 1

The density of gold is $19{,}300kg/m^3$ . A bar of gold weighs $4{,}000kg$ . What is the volume of this bar to two decimal places?

From the given information, identify the density and the mass:

$D=19{,}300kg/m^3,\,M=4{,}000kg$

Write down the density formula:

$D=\frac{M}{V}$

Rearrange the density formula for volume:

$V=\frac{M}{D}$

Substitute in the known values:

$V=\frac{4000kg}{19300kg/m^3}$

Give the answer with the correct units:

$V=0.207253886...m^3$

Round to two decimal places, like the question asks:

$\underline{V=0.21m^3}$ , to two decimal places.