A general measurement theory for determining the diffusion coefficient D of small molecules in polymer matrices is presented. This theory is applied to an arbitrary geometry of the polymer sample and an arbitrary initial penetrant content in the polymer. It is shown that one does not need to know specifically the dependence of the measured quantity on the concentration of the diffusing species, nor does one need to measure the equilibrium state of the system. By determining the differences Delta M of a measured quantity M, which may be spectroscopic absorption, weight increase or any other concentration-dependent quantity, as a function of time, the diffusion coefficient can be determined. The theory was tested with the results of water diffusion into polyacrylonitrile and poly(vinyl toluene). Diffusion coefficients determined with the general theory agree well with the results achieved by using more complicated conventional calculations. The benefits of the use of the general measurement theory are that one can simplify both measurements and calculations.