Density — Definition, Formula & Examples
Density is the amount of mass packed into a given volume of an object or substance. It tells you how heavy something is for its size.
Density is the ratio of an object's mass to its volume, expressed as , where has units such as grams per cubic centimeter () or kilograms per cubic meter ().
Key Formula
Where:
- = Density of the object (e.g., g/cm³)
- = Mass of the object (e.g., grams)
- = Volume of the object (e.g., cm³)
How It Works
To find density, measure the mass of an object (using a scale) and its volume (by calculation or water displacement). Then divide mass by volume. A higher density means more mass is squeezed into the same space. You can also rearrange the formula to find mass () or volume () when the other two quantities are known.
Worked Example
Problem: A metal cube has a side length of 5 cm and a mass of 1,000 g. What is its density?
Find the volume: The volume of a cube is side length cubed.
Apply the density formula: Divide the mass by the volume.
Answer: The density of the cube is , which is consistent with iron or steel.
Why It Matters
The high-school modeling standard HSG-MG.A.2 asks you to apply density to estimate masses and volumes in real contexts — for example, deciding whether a piece of jewelry is solid gold or hollow. Engineers and materials scientists choose materials by comparing densities to balance strength against weight.
Common Mistakes
Mistake: Using inconsistent units, such as kilograms for mass but cubic centimeters for volume.
Correction: Always check that your mass and volume units match the density unit you want. If mass is in grams and volume is in cm³, density comes out in g/cm³. Convert units before dividing.