Hardy–Weinberg equilibrium calculator | Calculator of Alexandria

The formula

p + q = 1

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

$p$ and $q$ are the frequencies of the dominant and recessive alleles of a gene. $p^2$ , $2pq$ and $q^2$ are the frequencies of the three genotypes: homozygous dominant, heterozygous (carriers), and homozygous recessive.

Where it comes from

In 1908, the mathematician G. H. Hardy and the physician Wilhelm Weinberg independently answered a puzzle: why don’t dominant traits take over a population?

Think of each child as drawing two alleles at random from the population’s gene pool, one from each parent. With random mating, the chance of drawing $A$ is $p$ and of drawing $a$ is $q$ . So:

Both $A$ : probability $p \times p = p^2$
Both $a$ : probability $q^2$
One of each, in either order: $pq + qp = 2pq$

These cover every possibility, so they add to $(p + q)^2 = 1$ . In the next generation, the allele frequencies come out as $p$ and $q$ again. Without outside forces, the frequencies stay constant forever, and a dominant allele doesn’t spread just because it’s dominant.

Worked example

A recessive condition affects 1 in 2,500 people, so $q^2 = 0.0004$ :

q = \sqrt{0.0004} = 0.02 \qquad p = 0.98

2pq = 2 \times 0.98 \times 0.02 = 0.0392

About 1 in 26 people is a carrier, around 100 times more common than the condition itself.

Watch out for

The assumptions. Equilibrium needs random mating, a large population, and no selection, mutation or migration. Real populations break these, and departures from Hardy–Weinberg are how geneticists detect those forces.
Start from the recessive phenotype. You can count people with a recessive trait ( $q^2$ ), but carriers look the same as $AA$ people. That’s why calculations usually begin with $q^2$ .

Sources

Last checked November 11, 2026