Density

Mass density is mass per unit volume, $\rho =m/V$ for a uniform sample, with SI units $\mathrm{kg}{\mathrm{m}}^{-3}$. For a nonuniform continuum, integrating the local field gives the total mass, $M={\int }_V\rho (\mathbf{x})dV$. The averaging volume must be specified when unresolved grains, pores or multiple phases are present.

For a fixed mass, expansion increases volume and lowers mass density. A material element obeying mass conservation satisfies $D\rho /Dt=-\rho \nabla \cdot \mathbf{v}$, linking that change to the velocity field. Density enters both weight and inertia, but it is different from number density and from relative density. Measuring a sample's mass and external volume can give a different value from measuring the density of its solid grains alone if the sample volume includes void space.

Density is a physical property of matter that describes the mass of an object relative to its volume. It is commonly defined as the mass of an object divided by its volume, and is usually expressed in units such as kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).