How Do You Calculate Density?

For IB Physics SL and HL, calculate density by dividing an object's mass by its volume:

$$\rho = \frac{m}{V}$$

Here, $\rho$ is density, $m$ is mass, and $V$ is volume. The SI unit of density is $\text{kg m}^{-3}$.

The Reasoning

Density measures the mass contained per unit volume. A high-density material has more mass packed into the same volume than a low-density material.

The relationship also shows that density is an intrinsic material property when temperature and pressure are fixed. Doubling both mass and volume leaves the ratio unchanged, so two samples of the same uniform material should have the same density.

To calculate it:

1. Measure or determine the object's mass.
2. Measure or calculate its volume.
3. Convert both quantities into compatible units.
4. Substitute them into $\rho = \frac{m}{V}$.

For example, a metal block has a mass of $540\text{ g}$ and a volume of $200\text{ cm}^3$:

$$\rho = \frac{540}{200} = 2.70\text{ g cm}^{-3}$$

Unit conversion is often the main difficulty. Since $1\text{ cm}=10^{-2}\text{ m}$, cubing the conversion gives $1\text{ cm}^3=10^{-6}\text{ m}^3$, while . Therefore, .

Thus, the block's density is $2.70\times10^3\text{ kg m}^{-3}$.

If a question instead asks for mass or volume, rearrange before substituting: $m=\rho V$ or $V=\frac{m}{\rho}$. For example, $0.0150{\text{ m}}^{}$ of oil with density has mass . This rearrangement tests the same proportional relationship and is common in multi-part data-analysis questions.

A common misconception is that a larger object must have a greater density. This is incorrect: density depends on the ratio of mass to volume, not size alone.

Exam Technique

This is part of B.1 Thermal energy transfers for SL and HL. For a Calculate question, show the equation, substitution, unit conversion, and final answer. Check compatible units before dividing, especially when converting $\text{cm}^3$ to $\text{m}^3$.