Five different two-parameter models were fitted to published data from 30 studies to identify an approximate mathematical form of the relationship between fertility in cattle and the number of inseminated spermatozoa. In all cases, the first parameter defines the maximum attainable fertility, and the second scales the dose according to the percentage of the maximum attained. The best model was the hyperbolic dose-response curve used in pharmacology to analyse the effect of drugs. There is evidence that the semen of individual bulls differs in both parameters of the models and that therefore the viability of semen may be multidimensional. This might explain why measures of semen quality have hitherto been found to correlate poorly with fertility. The hypothesis that spermatozoa are subject to the law of mass action at the ovum predicts these and some other aspects of fertility, and indicates that heterospermic inseminations may provide an efficient way of estimating the parameters of semen.