A theoretical solution of the concentration distribution in long optical path length thin layer spectroelectrochemical cells is given by a convergent infinite summation of terms. At short times a large number of terms is required to obtain a good approximation. Alternatively, on a timescale at which the boundary of the diffusion layer has not reached the celt wall opposite to the electrode the concentration profile of the thin layer cell is equal to the profile of a semi-infinite bulk electrochemical cell. This profile is described by an error function, for which no analytical solution is available. A new three-parameter exponential approximation for this error function is presented with an accuracy better than 0.05% for all positive values of x. When the diffusion layer boundary reaches the cell wall the semi-infinite bulk model is no longer valid but then the slope of the profile is small enough to he approximated by only the first five terms of the summation.