What is the Hardy-Weinberg equilibrium?

Hardy-Weinberg equilibrium describes a theoretical state where allele and genotype frequencies in a population remain stable across generations. It assumes 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), where p + q = 1. p² gives the frequency of homozygous dominant (AA), 2pq gives heterozygous (Aa), and q² gives homozygous recessive (aa).

How is the chi-square test used here?

The chi-square goodness-of-fit test compares observed genotype counts to expected counts (N × p², N × 2pq, N × q²). A chi-square statistic above 3.841 (1 degree of freedom, α = 0.05) indicates significant deviation from HWE.

Why is there only 1 degree of freedom for the chi-square test?

With three genotype classes and one estimated parameter (p), the degrees of freedom are 3 − 1 − 1 = 1.

Can I use this for more than two alleles?

This calculator handles the classic biallelic (two-allele) model. For multi-allelic loci you would need a generalized HWE test, which is beyond the scope of this tool.

What does a significant chi-square result mean?

A p-value below 0.05 suggests the population is NOT in Hardy-Weinberg equilibrium, which may indicate genotyping errors, selection pressure, non-random mating, population stratification, or other evolutionary forces.

Hardy-Weinberg Equilibrium Calculator

Enter allele frequency p to get expected genotype frequencies, then optionally enter observed counts for a chi-square goodness-of-fit test.

Allele Frequency

Frequency of allele A (p)

Enter a decimal value between 0 and 1 (e.g. 0.6)

Derived allele a frequency (q = 1 − p) —

Chi-Square Test (optional)

Enter observed genotype counts to test for deviation from HWE.

Observed AA (homozygous dominant) Observed Aa (heterozygous) Observed aa (homozygous recessive)

Enter allele frequency p and click Calculate to see results.

Allele Frequencies

p (allele A)

—

q (allele a)

—

Expected Genotype Frequencies

AA (homozygous dominant)

p²

—

Aa (heterozygous)

2pq

—

aa (homozygous recessive)

q²

—

Frequency Distribution

AA (p²)—

Aa (2pq)—

aa (q²)—

Chi-Square Goodness-of-Fit Test

χ² statistic

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p-value (df = 1)

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Genotype	Observed	Expected	(O−E)²/E

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Summary

The Hardy-Weinberg Equilibrium (HWE) principle states that allele and genotype frequencies in a population remain constant from generation to generation in the absence of evolutionary influences. Given the dominant allele frequency p, this calculator derives q = 1 − p and computes expected genotype frequencies: p² (homozygous dominant), 2pq (heterozygous), and q² (homozygous recessive). It also supports a chi-square goodness-of-fit test to determine whether an observed sample deviates significantly from HWE.

How it works

Enter the frequency of allele A (dominant) as a decimal between 0 and 1.
The calculator automatically computes q = 1 − p (recessive allele frequency).
Expected genotype frequencies are displayed: p² (AA), 2pq (Aa), and q² (aa).
Optionally enter the total sample size (N) plus observed counts for AA, Aa, and aa genotypes.
The chi-square statistic and p-value are calculated to test for significant deviation from HWE.
A conclusion states whether the population is in Hardy-Weinberg equilibrium at α = 0.05.

Use cases

Estimate genotype frequencies in a population genetics study.
Test whether a SNP dataset deviates from Hardy-Weinberg equilibrium.
Verify population data quality in GWAS pre-processing.
Teach or learn the Hardy-Weinberg principle in genetics courses.
Estimate the frequency of heterozygous carriers of a recessive allele.
Detect non-random mating, selection, or population structure in survey data.
Cross-check manually computed HWE values in lab reports.
Quickly explore how changing p shifts expected genotype proportions.

Frequently Asked Questions

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