The approximation resulting from the assumption that electrons in metals can be analysed using the kinetic theory of gases, without taking the periodic potential of the metal into account. This approximation gives a good qualitative account of some properties of metals, such as their electrical conductivity. At very low temperatures it is necessary to use quantum statistical mechanics rather than classical statistical mechanics. The free-electron approximation does not, however, give an adequate quantitative description of the properties of metals. It can be improved by the nearly free electron approximation, in which the periodic potential is treated as a perturbation on the free electrons.