Key takeaways
- Density is ρ = m ÷ V: mass divided by volume, in kg/m³.
- Pure water has a density of about 1,000 kg/m³, a handy benchmark.
- An object floats if its density is lower than the liquid it's in, and sinks if it's higher.
- Volume must be in cubic metres (m³) for the answer to come out in kg/m³.
In this guide
What is density?
Density compares how much mass is squeezed into a given amount of space. Objects with high density feel heavy for their size, like metal. Objects with low density feel light for their size, like foam.
Why does density matter?
Density decides whether an object floats or sinks, which materials feel heavy for their size, and even how engineers pick materials for planes versus buildings.
A steel ship is far denser than water, yet it floats, because its overall shape, including all the air inside it, has a much lower average density than the water it displaces.
The formula
| Symbol | What it means | Example |
|---|---|---|
| ρ | The density, in kilograms per cubic metre (kg/m³) | 1,000 kg/m³ |
| m | The mass of the object, in kilograms (kg) | 5 kg |
| V | The volume of the object, in cubic metres (m³) | 0.005 m³ |
How to calculate density step by step
- 1Weigh the object. Find its mass in kilograms.
- 2Find its volume. Measure it in cubic metres, using the rectangular prism volume calculator for box shapes.
- 3Divide mass by volume.
m ÷ Vgives you the density. - 4Write the answer in kg/m³.
Try the calculator below with your own mass and volume to see the working step by step.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Confusing mass and volume. Mass is how much matter is there; volume is how much space it takes up — density needs both.
- Assuming size equals weight. A large object isn't automatically heavy. A large block of foam can weigh less than a small block of steel.
- Forgetting to convert cm³. 1 cm³ = 0.000001 m³, so small measurements need careful conversion.
Tips and tricks
- To estimate quickly, compare the object to water: does it feel heavier or lighter than an equal volume of water?
- Working backwards from density to volume? Divide mass by density:
V = m ÷ ρ. - Density comparisons work like the reverse of how BMI divides mass by a squared height — a different ratio, but the same idea of relating mass to size.
Where you'll use it in real life
- Engineering: density tells engineers whether a material will float or sink, and how heavy a structure will be.
- Chemistry: density helps identify unknown substances by comparing measured values to known references.
- Shipbuilding: hull design relies on the ship's average density staying below that of water.
- Cooking and household use: oil floats on water because it's less dense, which is why the two separate in a jar.
Quick summary
To find density, divide an object's mass in kilograms by its volume in cubic metres. Compare the result to water's 1,000 kg/m³ to get a quick sense of whether something will float or sink. Use the calculator above to check your own material.
Worked example
You fill a 0.005 m³ (5-litre) container completely with water and find it weighs 5 kg. What is the density of the liquid, and does it match water?
- 01ρ = m / V
- 02ρ = 5 / 0.005
- 03ρ = 1000 kg/m³
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate density?
Divide the mass of an object in kilograms by its volume in cubic metres: ρ = m ÷ V. The result is in kg/m³.
What is the density of water?
Pure water has a density of about 1,000 kg/m³, or 1 gram per cubic centimetre, which is a handy benchmark for comparing other materials.
Why do some objects float and others sink?
An object floats in a liquid if its density is lower than the liquid's density, and sinks if its density is higher.
How do I convert grams per cm³ to kg/m³?
Multiply by 1,000. For example, a density of 2.7 g/cm³ (aluminium) equals 2,700 kg/m³.
