Hardy-Weinberg Equilibrium Calculator

The null hypothesis of population genetics — what happens when nothing is happening.

Homozygous recessive q²0.044%

Dominant allele frequency p0.8

Recessive allele frequency q0.2

Homozygous dominant p²0.6464% of the population

Heterozygous 2pq0.3232% — the carriers

The three frequencies1they sum to exactly one — that is the check

Carriers among the unaffected33.3333%about one in 3

Carriers per affected individual8which is why rare recessives persist

Hardy-Weinberg is the null hypothesis, not a description of any real population. It assumes a large population, random mating, and no selection, mutation or migration — a set of conditions nothing satisfies exactly. Its value is precisely that departures from it point at whichever assumption is failing.

The formula

p + q = 1 ; p^2 + 2pq + q^2 = 1

What equilibrium actually claims

Hardy-Weinberg says that in a large, randomly mating population with no selection, mutation or migration, allele frequencies do not change from one generation to the next, and the genotype frequencies follow directly from them. It is the null hypothesis of population genetics: not a description of any real population, but the baseline against which real ones are measured.

Carriers vastly outnumber sufferers

For a rare recessive disorder the arithmetic is striking. If one person in 10,000 is affected, q is 0.01 and the carrier frequency 2pq is about 0.0198 — roughly one person in fifty. Carriers outnumber affected individuals by about 198 to one, and the rarer the condition the more extreme that ratio becomes. This is why recessive alleles persist: selection barely sees them, because almost every copy is hidden in a heterozygote.

Departure from it is the signal

Because equilibrium is what happens when nothing is going on, a population that departs from it is telling you something is: selection, assortative mating, population structure, or an error in the genotyping. A chi-squared test against the expected frequencies is the standard first check on any genotype dataset.

Ratios are expectations, not promises

Every genetic ratio on these pages is a probability distribution, not a guarantee. A 3:1 cross does not produce three dominant offspring for every recessive one in a litter of four — it produces each offspring independently with a three-quarters chance. Small families depart from the expected ratio routinely, and that is the reason Mendel needed thousands of pea plants rather than dozens.