Biogas production in agriculture is processed mostly continuously at mesophilic temperatures in completely stirred tank reactors. Therefore, reactor performance data were studied in long-term semi-continuous laboratory-scale experiments with maize silage, whole-crop rye silage and fodder beet silage as mono-substrate and cattle slurry at mesophilic temperatures. For calculation of biogas yield as function of the organic loading rate, a hyperbolic equation was developed on the base of a first-order reaction rate for substrate degradation. The biogas yield depends also on the maximum biogas yield, the concentration of volatile solids of the input, the density of the effluent, the density of the biogas and the reaction rate constant, which are all substrate- or process-specific. Values of the theoretical maximum biogas yield and the reaction rate constant were observed in the range 0.61-0.93 m3 per kg volatile solids and 0.032-0.316 d(-1), respectively. By means of the hyperbolic equation, the proportion of the biogas yield from the maximum can be calculated for the first and a second reactor which also depends on the volume of each reactor.