Frequency of Allele Formula & How to Use It

This calculator works out the frequency of a specific allele in a population’s gene pool. You enter the number of individuals with each genotype (or the observed genotype counts), and it returns the allele frequency as a proportion (0 to 1) and as a percentage. The core formula is p = (2 × count of homozygous dominant + count of heterozygous) / (2 × total individuals), where p is the frequency of the dominant allele.

Formula

For a single gene with two alleles, A and a, the allele frequency is the proportion of all copies of that gene in the population that are a specific allele. If you have genotype counts:

• N_AA = number of homozygous dominant individuals
• N_Aa = number of heterozygous individuals
• N_aa = number of homozygous recessive individuals
• N = total individuals = N_AA + N_Aa + N_aa

The frequency of allele A is:

p = (2 × N_AA + N_Aa) / (2 × N)

The frequency of allele a is:

q = (2 × N_aa + N_Aa) / (2 × N)

Because every individual carries two copies of the gene, the total number of alleles in the population is 2N. The numerator counts how many of those copies are the allele of interest. Note that p + q = 1 (assuming only two alleles exist at that locus).

Worked Example

Using the calculator defaults: 30 AA, 50 Aa, and 20 aa individuals. Total individuals N = 30 + 50 + 20 = 100.

1. Total allele copies = 2 × 100 = 200.
2. Count of A alleles: each AA has 2 A alleles → 30 × 2 = 60; each Aa has 1 A allele → 50 × 1 = 50; total A = 60 + 50 = 110.
3. Frequency of A (p) = 110 / 200 = 0.55.
4. Count of a alleles: each aa has 2 a alleles → 20 × 2 = 40; each Aa has 1 a allele → 50 × 1 = 50; total a = 40 + 50 = 90.
5. Frequency of a (q) = 90 / 200 = 0.45.
6. Check: p + q = 0.55 + 0.45 = 1.0 ✓

The calculator shows p = 0.550, q = 0.450, and p as 55.0%.

When to Use This Formula

Allele frequency is a central concept in population genetics. You use it whenever you have genotype counts from a sample and want to describe the genetic composition of a population. Common applications include:

• Estimating how common a particular variant is in a population (e.g., a disease-causing allele).
• Comparing genetic diversity between different populations or time points.
• Testing whether a population is in Hardy–Weinberg equilibrium (by comparing observed genotype frequencies to expected ones).
• Calculating carrier frequencies for recessive disorders when you know the frequency of affected individuals.

For a recessive disease, if q² is the frequency of affected individuals (aa), then q = √(q²) and the carrier frequency (heterozygotes) is 2pq. For example, if 1 in 2,500 newborns is affected, q² = 0.0004, so q = 0.02, p = 0.98, and carriers = 2 × 0.98 × 0.02 ≈ 0.0392, or about 1 in 25 people.

How to Read the Result

The result is a proportion between 0 and 1. A frequency of 0.55 means that 55% of all allele copies in the sample are allele A. If you multiply by 100, you get the percentage. The two allele frequencies always sum to 1 (or 100%) if you have accounted for all alleles at that locus. A value close to 0 means the allele is rare; close to 1 means it is nearly fixed in the population.

Keep in mind that this is a sample estimate. The true population frequency may differ due to sampling error. Larger sample sizes give more precise estimates. The formula assumes you have correctly identified the genotypes and that the sample is representative of the population you want to describe.

Common Mistakes and Misconceptions

• Forgetting to multiply by 2: Each individual has two alleles, so the total allele count is 2N, not N. Forgetting this halves the denominator and doubles the frequency.
• Confusing allele frequency with genotype frequency: Genotype frequency is the proportion of individuals with a particular genotype (e.g., AA), while allele frequency is the proportion of allele copies. They are different numbers.
• Assuming Hardy–Weinberg equilibrium: The formula p = 2×AA + Aa / (2N) works regardless of equilibrium. But if you only know the frequency of recessive phenotypes (q²), you can only estimate q if you assume random mating and no selection.
• Using percentages inconsistently: If you enter counts as percentages, the total must be 100, and the result is still a proportion. Mixing raw counts with percentages will give wrong answers.

Limitations of the Formula

This formula is for a single autosomal locus with two alleles. It does not apply directly to:

• X-linked genes (males have one copy, females have two).
• Multiple alleles (e.g., ABO blood type) – you need a generalized formula summing over all alleles.
• Polyploid organisms (more than two chromosome sets).
• Populations with overlapping generations or non-random mating – the formula still computes the observed frequency, but predictions about future generations require additional assumptions.

Also, if your sample is small or biased, the calculated frequency may not reflect the true population. The formula gives a point estimate; confidence intervals require more advanced statistical methods.

Frequently Asked Questions

What is the difference between allele frequency and genotype frequency?

Allele frequency is the proportion of a specific allele among all alleles at that locus in the population. Genotype frequency is the proportion of individuals with a specific genotype (e.g., AA). For example, if 30 out of 100 individuals are AA, the genotype frequency of AA is 0.30, but the allele frequency of A might be 0.55 (as in the example above).

How do I calculate allele frequency from phenotype data?

If the trait is recessive, you can estimate the frequency of the recessive allele (q) by taking the square root of the frequency of affected individuals (q²). For example, if 1% of the population shows the recessive phenotype, q² = 0.01, so q = 0.1 and p = 0.9. This assumes Hardy–Weinberg equilibrium. If the trait is dominant, you cannot directly determine allele frequency from phenotype counts because both AA and Aa look the same.

Why do allele frequencies add up to 1?

Because each individual carries exactly two alleles at a diploid locus, and you are counting all copies. If there are only two alleles, every allele copy is either A or a, so the two proportions must sum to 1. If there are more than two alleles, the sum of all allele frequencies is still 1.

Can I use this formula for X-linked genes?

Not directly. For X-linked genes, males have only one X chromosome (so one allele) and females have two. The total allele count is (number of males) + 2 × (number of females). The frequency of an allele in males equals the frequency of the phenotype in males, while in females you use the same formula as for autosomes. You would need to modify the denominator accordingly.

What if I only know the frequency of homozygous recessive individuals?

Under Hardy–Weinberg equilibrium, you can estimate q as the square root of the recessive genotype frequency (q²). Then p = 1 – q. This is common in medical genetics for autosomal recessive disorders. However, this method is only valid if the population is in equilibrium (random mating, no selection, no mutation, etc.).

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in a | Count of AA (homozygous dominant) | individuals | 30 | 0
in b | Count of Aa (heterozygous) | individuals | 50 | 0
in c | Count of aa (homozygous recessive) | individuals | 20 | 0
out p | Frequency of allele A | - | (2*a + b) / (2*(a+b+c)) | 3
out q | Frequency of allele a | - | (2*c + b) / (2*(a+b+c)) | 3
out p_percent | Allele A frequency (%) | % | ((2*a + b) / (2*(a+b+c))) * 100 | 1