What is the Hardy-Weinberg equilibrium?

The Hardy-Weinberg equilibrium describes a theoretical population where allele and genotype frequencies remain constant across generations. It requires no mutation, random mating, no gene flow, no genetic drift, and no natural selection.

What do p and q represent?

p is the frequency of the dominant allele (A) and q is the frequency of the recessive allele (a) in the population. By definition, p + q = 1.

What do p², 2pq, and q² mean?

p² is the expected frequency of the homozygous dominant genotype (AA), 2pq is the expected frequency of the heterozygous genotype (Aa), and q² is the expected frequency of the homozygous recessive genotype (aa).

How is the chi-square test used here?

The chi-square test compares observed genotype counts to expected counts (derived from Hardy-Weinberg frequencies). A chi-square value below the critical value (~3.841 at p=0.05, 1 degree of freedom) suggests the population is in equilibrium.

What is the degree of freedom for this test?

With two alleles and three genotype classes, the Hardy-Weinberg chi-square test uses 1 degree of freedom (3 classes minus 1 estimated parameter minus 1).

Can this calculator handle more than two alleles?

This calculator handles the classic two-allele (biallelic) model. For multiple alleles, extend the principle: the sum of all allele frequencies equals 1, and genotype frequencies follow the multinomial expansion.

Hardy Weinberg Calculator

Enter allele frequencies or observed genotype counts to calculate Hardy-Weinberg equilibrium allele and genotype frequencies.

Input Mode

p — Dominant allele frequency (A)

q — Recessive allele frequency (a)

Leave blank to auto-compute q = 1 - p

Enter allele frequencies or genotype counts and click Calculate.

Allele Frequencies

p (dominant, A)

—

q (recessive, a)

—

p + q = —

Expected Genotype Frequencies

AA (p²)

—

Aa (2pq)

—

aa (q²)

—

Chi-Square Test (df = 1)

Genotype	Observed	Expected	(O-E)²/E
Total	—	—	—

Hardy-Weinberg equations: p + q = 1 | p² + 2pq + q² = 1

Summary

The Hardy-Weinberg principle states that allele and genotype frequencies in a population remain constant from generation to generation in the absence of evolutionary influences. Given allele frequencies p and q (where p + q = 1), expected genotype frequencies are: p² (homozygous dominant), 2pq (heterozygous), and q² (homozygous recessive). This calculator also performs a chi-square goodness-of-fit test to determine whether an observed population is in Hardy-Weinberg equilibrium.

How it works

Choose input mode: enter allele frequencies directly, or provide observed genotype counts.
If entering genotype counts, allele frequencies p and q are derived automatically.
Expected genotype frequencies are calculated as p², 2pq, and q².
Expected genotype counts (if sample size is known) are compared to observed counts via chi-square test.
The chi-square statistic and p-value indicate whether the population deviates from equilibrium.
Results update instantly as you type.

Use cases

Genetics coursework and exam preparation.
Estimating carrier frequency for recessive genetic disorders.
Population genetics research and data analysis.
Testing whether a sampled population is in Hardy-Weinberg equilibrium.
Predicting genotype distribution given known allele frequencies.
Biology and bioinformatics teaching demonstrations.
Forensic genetics allele frequency analysis.
Evolutionary biology studies comparing generations.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu