Hardy-Weinberg Equilibrium Calculator

What Is Hardy-Weinberg Equilibrium?

Hardy-Weinberg equilibrium is a population-genetics model that describes the relationship between allele frequencies and expected genotype frequencies when specified assumptions are met. For a gene with two alleles, the model uses allele frequencies p and q and predicts genotype frequencies p², 2pq, and q².

What Does This Calculator Calculate?

This calculator determines allele frequencies and expected genotype frequencies under the Hardy-Weinberg model. It can start with p, q, or a recessive phenotype frequency interpreted as q².

It also reports the expected heterozygous frequency, often called the carrier frequency when the heterozygous genotype represents a carrier state for a recessive allele, and can estimate expected genotype counts when a population size is supplied.

Hardy-Weinberg Equations

Here, p is the frequency of one allele and q is the frequency of the alternative allele at the same locus.

Worked Example: p = 0.7 and q = 0.3

Using Recessive Phenotype Frequency

If a recessive phenotype is assumed to correspond to the homozygous recessive genotype aa, its frequency is q². The recessive allele frequency can therefore be estimated as:

For example, if the recessive phenotype frequency is 0.09, q = √0.09 = 0.30 and p = 0.70.

What Is a Carrier Frequency?

For a simple autosomal recessive model, heterozygous individuals have genotype Aa and expected frequency 2pq. If Aa represents a carrier state for a particular recessive condition, 2pq is the expected carrier frequency under the model.

The term carrier should not be applied automatically to every heterozygous genotype; it depends on the biological trait and inheritance pattern.

Allele Frequency vs. Genotype Frequency

Hardy-Weinberg Assumptions

The equilibrium model is based on assumptions including a very large population, random mating, no migration, no mutation, no natural selection, and no other forces that systematically alter allele frequencies.

Real populations often violate one or more of these assumptions. Hardy-Weinberg equilibrium is therefore commonly used as a reference model rather than a description that every natural population exactly satisfies.

Why the Genotype Frequencies Sum to 1

The expression p² + 2pq + q² is the expansion of (p + q)². Because p + q = 1, the genotype frequencies must sum to 1 under the model:

Expected Genotype Counts

If a population size N is supplied, expected counts can be estimated by multiplying each genotype frequency by N:

These are expected counts from the model, not guaranteed observed counts.

Common Mistakes

• Confusing allele frequency with genotype frequency.
• Using q² as q without taking the square root.
• Forgetting that p + q must equal 1 for a two-allele locus.
• Entering percentages such as 30 instead of proportions such as 0.30.
• Calling every heterozygote a carrier regardless of the biological trait.
• Assuming Hardy-Weinberg equilibrium automatically applies to every population.
• Treating expected genotype counts as exact observed counts.

Percentage vs. Proportion

The calculator accepts frequencies as proportions between 0 and 1. Convert percentages before entering them: 70% becomes 0.70, 30% becomes 0.30, and 9% becomes 0.09.

When Should You Use This Calculator?

Use it to explore expected allele and genotype frequencies for a two-allele locus under Hardy-Weinberg assumptions, to convert a recessive phenotype frequency into allele frequency, or to estimate expected genotype counts from a population size.

When Hardy-Weinberg Calculations Need Caution

Inference from phenotype frequency can be misleading when penetrance is incomplete, phenocopies occur, multiple genes affect the trait, the inheritance pattern is not simple autosomal recessive, or the population is structured rather than randomly mating.

For real genetic conditions, population-specific data and appropriate statistical or genetic models may be required.

Accuracy and Limitations

The calculations themselves are mathematical and deterministic. The main limitation is model validity: Hardy-Weinberg equations describe expected frequencies only under their stated assumptions.

The calculator does not test whether an observed population is actually in Hardy-Weinberg equilibrium. A formal equilibrium test may require observed genotype counts and a statistical test such as a chi-square analysis.

How to Use the Calculator

1. Enter p, q, or a recessive phenotype frequency.
2. If using q², enter the recessive phenotype frequency as a proportion between 0 and 1.
3. Optionally enter population size to estimate genotype counts.
4. Select Calculate.
5. Review p, q, p², 2pq, q², and the equilibrium check.

Calculation Methodology

The calculator first determines allele frequencies. If p is provided alone, q is calculated as 1 − p. If q is provided alone, p is calculated as 1 − q. If a recessive phenotype frequency q² is supplied, q is estimated as √q² and p as 1 − q.

It then calculates p², 2pq, and q² and verifies that p + q and p² + 2pq + q² equal approximately 1 within normal floating-point rounding.

Frequently Asked Questions

Scientific References

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