What Is Density in Physics? Formula and Examples

What Is Density?

Density tells you how much mass is packed into a certain amount of space (volume). A dense object has a lot of mass in a small volume; a less dense object has the same mass spread over a larger volume.

Simple analogy: Imagine two boxes the same size. One is filled with feathers, the other with rocks. The box of rocks is denser — it has more mass in the same volume.

The Density Formula

The formula for density is:

ρ = m / V

Where:

• ρ (rho) = density
• m = mass
• V = volume

You can rearrange this to find mass or volume:

• m = ρ × V (to find mass)
• V = m / ρ (to find volume)

Units of Density

The unit depends on what you're measuring:

| System | Density Unit | Common Use | |--------|-------------|------------| | Metric (SI) | kg/m³ | Physics, engineering | | CGS | g/cm³ | Chemistry, everyday use | | Other | g/mL | Liquids |

Useful conversion: 1 g/cm³ = 1,000 kg/m³

The density of pure water is approximately 1 g/cm³ (or 1,000 kg/m³). This makes water a useful reference point.

Worked Examples

Example 1: A block of metal has a mass of 500 g and a volume of 50 cm³. What is its density?

ρ = m / V = 500 g / 50 cm³ = 10 g/cm³

This is the density of silver!

Example 2: A liquid has a density of 0.8 g/cm³ and you have 200 cm³ of it. What is its mass?

m = ρ × V = 0.8 × 200 = 160 g

Example 3: A rock has a mass of 300 g and a density of 2.5 g/cm³. What is its volume?

V = m / ρ = 300 / 2.5 = 120 cm³

Why Things Float or Sink

Density explains why some objects float and others sink:

• If an object is less dense than the fluid it's in → it floats
• If an object is denser than the fluid → it sinks

Examples:

• Wood (density ~0.5 g/cm³) floats on water (1 g/cm³) ✓
• Iron (density ~7.9 g/cm³) sinks in water ✗
• Oil (density ~0.9 g/cm³) floats on water ✓ — that's why oil spills sit on the ocean surface
• Ice (density ~0.92 g/cm³) floats on water ✓ — which is unusual for a solid

Fun fact: Steel ships float because their overall density (including all the air inside) is less than water. The shape matters!

Density of Common Materials

| Material | Density (g/cm³) | |----------|----------------| | Air | 0.001 | | Wood (oak) | 0.6–0.9 | | Ice | 0.92 | | Water | 1.00 | | Aluminum | 2.7 | | Iron | 7.9 | | Gold | 19.3 |

Notice how gold is nearly 20 times denser than water. This is why gold feels so heavy for its size.

Understanding density connects to many physics concepts, including gravity and Newton's laws of motion. In chemistry, density relates to molarity and solution concentration.

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