What is the Hardy-Weinberg equilibrium equation?

The Hardy-Weinberg equation is p² + 2pq + q² = 1, where p is the frequency of the dominant allele and q is the frequency of the recessive allele (with p + q = 1). The terms p², 2pq, and q² represent the expected frequencies of the homozygous dominant (AA), heterozygous (Aa), and homozygous recessive (aa) genotypes, respectively.

How do I calculate allele frequency from genotype counts?

Given observed counts of AA, Aa, and aa individuals: p = (2×AA + Aa) ÷ (2×N), where N is the total number of individuals (AA + Aa + aa). Then q = 1 − p. For example, if you observe 36 AA, 48 Aa, and 16 aa (N = 100): p = (72 + 48) ÷ 200 = 0.60, and q = 0.40.

How do I calculate carrier frequency from disease prevalence?

If a recessive condition affects q² of the population, the carrier (heterozygous) frequency is 2pq. First find q = √(q²), then p = 1 − q, then carrier frequency = 2pq. For example, if 1 in 2,500 are affected: q² = 0.0004, q = 0.02, p = 0.98, and carrier frequency = 2 × 0.98 × 0.02 ≈ 0.0392 or about 1 in 26.

What is the chi-square test for Hardy-Weinberg equilibrium?

The chi-square goodness-of-fit test compares observed genotype counts to expected counts under Hardy-Weinberg equilibrium. Calculate χ² = Σ (observed − expected)² ÷ expected for each genotype. With 2 alleles, there is 1 degree of freedom. If χ² > 3.841 (p < 0.05), the population significantly deviates from equilibrium.

What are the five conditions for Hardy-Weinberg equilibrium?

Hardy-Weinberg equilibrium requires: (1) no mutation, (2) random mating, (3) no natural selection, (4) infinitely large population size (no genetic drift), and (5) no gene flow (migration). When any of these conditions is violated, allele frequencies can change across generations — which is evolution.

How do you calculate p and q in Hardy-Weinberg?

If you know one allele frequency, the other is simply 1 minus the first (p + q = 1). If you know the frequency of the recessive phenotype (q²), take the square root to get q, then p = 1 − q. From genotype counts: p = (2×AA + Aa) ÷ (2×total individuals).

Can Hardy-Weinberg equilibrium apply to more than two alleles?

Yes. For three alleles (p + q + r = 1), the genotype frequencies expand to p² + q² + r² + 2pq + 2pr + 2qr = 1. The number of possible genotypes for n alleles is n(n+1)/2. This calculator focuses on the two-allele system, which covers most textbook problems and clinical genetics applications.

Why is Hardy-Weinberg equilibrium important in genetics?

Hardy-Weinberg equilibrium serves as the null hypothesis in population genetics — a baseline against which evolution can be detected. It allows geneticists to predict genotype frequencies from allele frequencies, estimate carrier frequencies for genetic diseases, and test whether evolutionary forces are acting on a population.

Hardy Weinberg Equilibrium Calculator

Dominant Allele Frequency (p)

q (recessive) = 0.3000

Population Size (optional)

Used to calculate expected genotype counts

Genotype Frequencies

0.4900

p² (AA)

0.4200

2pq (Aa)

0.0900

q² (aa)

Allele Frequencies

Dominant (p) and recessive (q) allele proportions

p (dominant allele)

0.700000

q (recessive allele)

0.300000

Genotype Distribution

Visual breakdown of population genotypes

AA (p²)

49.00%

Aa (2pq)

42.00%

aa (q²)

9.00%

Carrier Information

Heterozygous carrier statistics

Carrier Frequency

42.00%

Carrier Ratio

1 in 2

Expected Counts

In a population of 1,000

AA (homozygous dominant)

490.0

Aa (heterozygous)

420.0

aa (homozygous recessive)

90.0

How the Hardy-Weinberg Calculator Works

Core equations for population genetics

The Hardy-Weinberg principle describes the relationship between allele frequencies and genotype frequencies in a population that is not evolving. Given two alleles at a single locus with frequencies p (dominant) and q (recessive), the expected genotype frequencies are:

Core Equations

p + q = 1

p² + 2pq + q² = 1

p²

Homozygous Dominant (AA)

2pq

Heterozygous Carrier (Aa)

q²

Homozygous Recessive (aa)

Hardy-Weinberg Assumptions

Five conditions required for equilibrium to hold

The Hardy-Weinberg equilibrium holds when a population meets five key conditions. Violation of any condition drives evolutionary change:

No mutation

Alleles are not changing from one type to another

Random mating

Individuals pair by chance, not by genotype or phenotype

No natural selection

All genotypes are equally fit — no survival or reproduction advantage

Infinitely large population

No genetic drift — small populations experience random frequency changes

No gene flow

No migration of individuals into or out of the population

Worked Example: Cystic Fibrosis

Applying Hardy-Weinberg to a real genetic condition

Cystic fibrosis (CF) is an autosomal recessive disorder affecting about 1 in 2,500 Caucasians. Using Hardy-Weinberg:

Step-by-step Calculation

q²

0.0004

1 / 2500

0.0200

√0.0004

0.9800

1 − 0.02

2pq

0.0392

~1 in 26

This reveals that approximately 1 in 26 people are carriers of the CF allele — far more common than the 1 in 2,500 affected rate might suggest. This is why carrier screening is so important for recessive genetic conditions.

Common Mistakes to Avoid

Frequent errors in Hardy-Weinberg calculations

Confusing allele vs genotype frequency

q is the allele frequency; q² is the genotype frequency. If 4% are affected (q² = 0.04), then q = 0.2, not 0.04.

Forgetting p + q = 1

The two allele frequencies always sum to 1. If you know q, calculate p as 1 − q. Don't treat them as independent.

Using percentages instead of proportions

Hardy-Weinberg uses proportions (0 to 1), not percentages. Convert 4% to 0.04 before calculating.

Assuming equilibrium without testing

Real populations rarely meet all five assumptions. Use the chi-square test to verify whether observed genotype counts match expected frequencies.

Real-World Applications

How Hardy-Weinberg is used in practice

Application	How HWE is Used
Genetic counseling	Estimate carrier probabilities for recessive disorders like CF and sickle cell disease
Forensic genetics	Calculate expected genotype frequencies for DNA profile matching
Evolutionary biology	Detect natural selection by comparing observed vs expected genotype frequencies
GWAS quality control	Filter SNPs deviating from HWE — often signals genotyping error
Conservation biology	Monitor genetic diversity and detect inbreeding in endangered populations

Frequently Asked Questions

Common questions and detailed answers

Embed Hardy Weinberg Equilibrium Calculator

Add this calculator to your website or blog for free.

Related calculators from other categories

Last updated Mar 26, 2026