Statistical
Hardy-Weinberg Equilibrium formula: allele & heterozygous carrier frequency (2pq)
Explore two-allele genotype proportions under Hardy–Weinberg assumptions using an assumed recessive homozygote frequency.
From an assumed recessive homozygote frequency to allele proportions
For a two-allele autosomal locus in a Hardy–Weinberg model, p+q=1 and genotype proportions are p², 2pq and q². If q²=0.0004, then q=0.02, p=0.98 and 2pq=0.0392. These are population model proportions, not an individual test result or family risk estimate.
The ideal equilibrium assumptions include random mating, a large population and no relevant selection, mutation or migration. Inferring q² from observed disease frequency also requires a matching recessive phenotype model; incomplete penetrance and multiple causal variants can invalidate that inference. A heterozygote is not universally asymptomatic. The labels p and q distinguish alleles rather than normal versus abnormal people.
| Genetic Equilibrium Quantity (Observed q^2 = 0.0004) | Formula | Population Share |
|---|---|---|
| Recessive Allele Frequency (q) | SQRT(q^2) = SQRT(0.0004) | 0.0200 (2.00%) |
| Other allele frequency (p) | 1 - q = 1 - 0.02 | 0.9800 (98.00%) |
| Heterozygous Carrier Frequency (2pq) | 2 * 0.98 * 0.02 | 0.0392 (3.92% — ~1 in 25!) |
| Homozygous Dominant Frequency (p^2) | 0.98 ^ 2 | 0.9604 (96.04%) |
Calculate heterozygous carrier frequency (2pq) from recessive incidence (q^2)
A2 supplies an assumed recessive homozygote proportion q², from 0 to 1. It is not an incidence rate with a time denominator.
=IF(OR(NOT(ISNUMBER(A2)),A2<0,A2>1),"Invalid inputs",LET(q, SQRT(A2), p, 1 - q, ROUND(2 * p * q, 4)))Verify homozygous dominant genotype frequency (p^2)
Unrounded model proportions sum to one. Separately rounded values may differ slightly from one; an arithmetic identity is not evidence that a population satisfies equilibrium.
=IF(OR(NOT(ISNUMBER(A2)),A2<0,A2>1),"Invalid inputs",LET(q, SQRT(A2), ROUND((1 - q) ^ 2, 4)))Try the example
Use the original values or change them to test your understanding.