Density
Simple Explanation
Density measures how tightly packed the mass of a substance is: ρ = m/V. A dense material has a lot of mass packed into a small volume; a low-density material has the same mass spread over a much bigger volume.
Why Do We Need It?
Density determines whether an object floats or sinks, and is one of the most useful ways to identify an unknown substance — every pure material has its own characteristic density.
Formula
Density
ρ = m / V
Density measures how tightly packed the mass of a substance is — how much mass is squeezed into each unit of volume.
- ρ
- — density, in kilograms per cubic metre (kg/m³), or grams per cubic centimetre (g/cm³)
- m
- — mass of the substance, in kilograms (kg) or grams (g)
- V
- — volume of the substance, in cubic metres (m³) or cubic centimetres (cm³)
When to use it: Whenever a substance's density needs to be found from its mass and volume (or either of the other two, given the other two).
Worked Example
Find a metal block's density
A metal block has a mass of 540 g and a volume of 60 cm³. Find its density.
Why Does This Work?
Dividing the total mass by the total volume gives exactly how much mass is packed into each unit of volume — the definition of density.
Real-Life Example
Testing gold for purity
A jeweller suspects a "gold" bar might actually be a cheaper metal coated in gold.
By measuring the bar's mass and volume (e.g. by water displacement) and calculating its density, the jeweller can compare it against pure gold's known density (19.3 g/cm³) to check for fakes.
Practice
A liquid has a mass of 250 g and a volume of 200 cm³. Find its density.
EasyA block has a density of 2.7 g/cm³ and a volume of 40 cm³. Find its mass.
MediumCommon mistake
Mixing units — using a mass in grams with a volume in cubic metres (or vice versa) gives a meaningless density; always keep mass and volume in a consistent, matching pair of units.
Quick Review
- ρ = m/V
- Density is measured in kg/m³ or g/cm³.
- Every pure substance has its own characteristic density.