A basic mathematical relation used in population genetics. It gives the proportion of the various genotypes in a randomly mating population in terms of the frequencies of the genes. The formula was discovered independently in 1908 by G. H. Hardy, a British mathematician, and W. Weinberg, a German physician. Human genetics Population genetics

In its simplest form the Hardy-Weinberg formula may be stated thus: If p is the proportion of gene A in the population and q(= 1 − p) is the proportion of gene a, then after one generation of random mating the three genotypes AA, Aa, and aa will occur in the proportions p², 2pq, and q². In other words the genotypes are given by the appropriate terms in the expansion of the binomial (p + q)². The extension to multiple alleles is direct.

The formula holds only for an infinite population and assumes random mating in the absence of significant mutation pressure or gene transfer between populations. However, it is an accurate approximation in many populations. Genetics