A general solution is presented to the problem of finding the minimum fresh gas flow requirements, during spontaneous ventilation, of anaesthetic breathing systems in the Mapleson classification. The solution is applicable to any pattern of breathing, dead space volume and tidal volume. The method is graphical and its use and understanding require no mathematical skills. However, if an analytical form of the respiratory waveform is known, the method is easily extended by use of calculus to obtain a precise analytical solution.