A material's bulk density is mass divided by the external volume occupied by the specimen:

$$\rho_{\text{bulk}}=\frac{m}{V}.$$

If the specimen contains pores, its bulk density is lower than the density $\rho_s$ of fully dense solid material.

Define porosity as the pore-volume fraction

$$\phi=\frac{V_{\text{pore}}}{V_{\text{total}}}.$$

For a simple two-phase system containing solid and empty pores,

$$\rho_{\text{bulk}}=(1-\phi)\rho_s,$$

so

$$\phi=1-\frac{\rho_{\text{bulk}}}{\rho_s}.$$

The ratio $\rho_{\text{bulk}}/\rho_s$ is the relative density.

Example

A ceramic with theoretical density $3.9,\mathrm{g/cm^3}$ is measured at $3.51,\mathrm{g/cm^3}$. Then

$$\phi=1-\frac{3.51}{3.9}=0.10,$$

so the specimen contains about $10%$ pore volume under the model assumptions.

Porosity changes much more than mass. Pores reduce load-bearing area, concentrate stress, alter thermal and electrical transport, and can provide paths for fluids. In sintered ceramics and powder-metallurgy parts, relative density is therefore a central measure linking processing to performance.