A simple case of diffusion with time  in one dimension (taken as the -axis) from a boundary located at position , where the concentration is maintained at a value  is
where  is the complementary error function. This is the case when corrosive gases diffuse through the oxidative layer towards the metal surface (if we assume that concentration of gases in the environment is constant and the diffusion space – that is, the corrosion product layer – is semi-infinite, starting at 0 at the surface and spreading infinitely deep in the material). If, in its turn, the diffusion space is infinite (lasting both through the layer with ,  and that with , ), then the solution is amended only with coefficient  in front of  (as the diffusion now occurs in both directions). This case is valid when some solution with concentration  is put in contact with a layer of pure solvent. (Bokstein, 2005) The length  is called the diffusion length and provides a measure of how far the concentration has propagated in the -direction by diffusion in time  (Bird, 1976).
As a quick approximation of the error function, the first two terms of the Taylor series can be used:
If  is time-dependent, the diffusion length becomes
This idea is useful for estimating a diffusion length over a heating and cooling cycle, where  varies with temperature.