Hardy–Weinberg Equilibrium Calculator

Testing a sample. 1,000 people are genotyped: 380 AA, 440 Aa and 180 aa. Allele A makes up p = (2 × 380 + 440) ÷ 2,000 = 0.6 of the 2,000 gene copies, so q = 0.4. The expected counts are 1,000 × 0.36 = 360 AA, 1,000 × 0.48 = 480 Aa and 1,000 × 0.16 = 160 aa. χ² = (380 − 360)² ÷ 360 + (440 − 480)² ÷ 480 + (180 − 160)² ÷ 160 = 1.111 + 3.333 + 2.5 = 6.944. With 1 degree of freedom, P = 0.0084, below 0.05: the sample is not in Hardy–Weinberg equilibrium and has too few heterozygotes.

Carriers from incidence. If a recessive condition affects 1 in 2,500 people (an illustrative figure of the size often quoted for cystic fibrosis), q² = 0.0004, q = 0.02, p = 0.98 and carriers are 2pq = 0.0392, about 1 in 25.51.

The common mistake: using the incidence as the allele frequency. Taking q = 0.0004 instead of √0.0004 gives a carrier frequency of 2 × 0.9996 × 0.0004 = 0.0008, about 1 in 1,251, nearly 50 times too low. The incidence is q², the frequency of people with two copies; the allele frequency is its square root.

After Mendel’s work was rediscovered in 1900, some critics argued that a dominant allele ought to spread until three quarters of a population showed the dominant trait. At Cambridge the geneticist Reginald Punnett put the question to the mathematician G. H. Hardy, who answered it in a short letter to Science in 1908, “Mendelian proportions in a mixed population”: without selection, the allele frequencies stay where they are and the genotypes settle at p², 2pq and q² after one generation of random mating.

The German physician Wilhelm Weinberg reached the same result independently in a lecture in Stuttgart the same year, and the principle carries both names. The American geneticist William Castle had described a special case in 1903.

Because the proportions hold only when nothing disturbs them, a departure from Hardy–Weinberg proportions is a signal: inbreeding, selection, migration, a sample drawn from two populations, or, in modern genotyping, errors in the data. The chi-square test on this page is the standard first check.

This calculator estimates allele frequencies from genotype counts, compares the counts with the Hardy–Weinberg expectation using a chi-square goodness-of-fit test with one degree of freedom, and gives the exact p-value from the chi-square distribution together with the observed and expected heterozygosity. It also turns an allele frequency into expected genotype frequencies and numbers, and a recessive-condition incidence into the allele and carrier frequencies. It warns when expected counts are too small for the chi-square approximation.

Everything runs in your browser; nothing you enter is sent anywhere. Disease figures on this page are illustrative, not clinical data.

Related tools: Punnett Square Calculator, Probability Calculator, and Statistics Calculator.