The diffusion coefficient as well as the dimensionality of the diffusion process can be determined by straightforward and facile data analysis, when fluorescence recovery after photobleaching (FRAP) is measured as a function of time and space by means of confocal laser scanning microscopy. Experiments representing one-dimensional diffusion from a plane source or two-dimensional diffusion from a line source are readily realized. In the data analysis, the deviations of the actual initial conditions from ideal models are consistently taken into account, so that no calibration measurements are needed. The method is applied to FRAP experiments on solutions of Rhodamine B in glycerol and aqueous suspensions of polymethyl methacrylate microspheres.