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Hardy–Weinberg Calculator

Find genotype frequencies from an allele frequency.

How it is calculated

The Hardy–Weinberg principle links allele frequencies to genotype frequencies in a population. With two alleles, p is the frequency of the dominant allele and q = 1 − p that of the recessive one. Expected genotype frequencies come from (p + q)2 = p2 + 2pq + q2: homozygous dominant p2, heterozygous 2pq, homozygous recessive q2. The tool takes p as a fraction between 0 and 1 (not a percentage) and shows each genotype as a percentage. The model assumes random mating, a large population, no selection, no mutation and no migration, so real populations may deviate.

Worked example

Take p = 0.7, so q = 1 − 0.7 = 0.30. Homozygous dominant: 0.72 = 49.00%. Heterozygous: 2 × 0.7 × 0.3 = 42.00%. Homozygous recessive: 0.32 = 9.00%. The three add up to 100%. Note that 91% of individuals show the dominant trait (49% + 42%), although the recessive allele itself is 30% of all alleles.

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Common mistakes

  • Entering p as a percentage such as 70 instead of the fraction 0.7.
  • Treating the dominant phenotype frequency as p2; it is p2 + 2pq, because heterozygotes also show the dominant trait.
  • Confusing the recessive phenotype frequency q2 with the allele frequency q; the allele frequency is the square root.
  • Applying the model to a population under strong selection or with non-random mating.

About this calculator

This calculator finds expected genotype frequencies from an allele frequency under the Hardy–Weinberg principle: for a gene with two alleles at frequencies p and q (where p + q = 1), the genotype frequencies in a population at equilibrium are p² (homozygous dominant), 2pq (heterozygous), and q² (homozygous recessive) — the expansion of (p + q)².

Population geneticists use this as a null-hypothesis baseline: real populations are compared against Hardy–Weinberg expectations to detect evolutionary forces like natural selection, genetic drift, non-random mating, or migration, since a population only stays in equilibrium absent these pressures. It's taught in every introductory genetics course as the foundation of population genetics. Enter an allele frequency (p) to get the expected genotype frequencies.

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