Hardy and Weinberg, together, described a stable, non-evolving population, that is, one in which allelic frequencies do not change.

The Hardy–Weinberg law of genetic equilibrium provides a mathematical model for studying evolutionary changes in allelic frequency within a population. For example, if the frequency of an allele for a particular trait is 0.5 and the population is not evolving, in 1,000 years the frequency of that allele will still be 0.5. The Hardy– Weinberg theorem characterizes the distributions of genotype frequencies in populations that are not evolving, and is thus the fundamental null model for population genetics.

If we put in a simple way, this principle states that both allele and genotype frequencies in a population remain constant – that is, they are in equilibrium – from generation to generation unless specific disturbing influences are introduced. Those disturbing influences include non-random mating, mutations, selection, random genetic drift, gene flow and meiotic drive. It is important to understand that in real populations, one or more of these “disturbing influences” are always in effect. That is, Hardy–Weinberg equilibrium is an ideal state that provides a baseline against which change can be analyzed.

The Hardy–Weinberg principle can be illustrated mathematically with the equation:
p² + 2pq + q² = 1, where ‘p’ and ‘q’ represent the frequencies of alleles. It is important to note that p added to q always equals one (100%).

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