# Hardy-Weinberg Equilibrium Calculator (p² + 2pq + q² = 1) Compute allele and expected genotype frequencies under Hardy-Weinberg equilibrium. Two modes: allele frequency or genotype counts with chi-square test. Derived from Hardy 1908, Weinberg 1908, Wigginton 2005, StatPearls. Educational use only. > Canonical page: https://elysiatools.com/en/tools/hardy-weinberg-equilibrium - **Category:** Education - **Keywords:** hardy-weinberg, hardy weinberg equilibrium, hwe, allele frequency, genotype frequency, p squared, 2pq, population genetics, chi-square test, genetics, biology ## Overview The Hardy-Weinberg Equilibrium Calculator estimates allele and expected genotype frequencies for a biallelic locus using p² + 2pq + q² = 1. Enter a recessive allele frequency or observed AA, Aa, and aa counts to calculate results and, in counts mode, perform a chi-square goodness-of-fit test. Educational use only. ## Inputs - **Input Mode** (select): Choose allele-frequency mode or genotype-counts mode. - **Allele q frequency (recessive)** (number): Frequency of the recessive allele q (0–1). Used in frequency mode only. - **aa count (homozygous recessive)** (number): Observed count of genotype aa. Used in counts mode only. - **Aa count (heterozygous)** (number): Observed count of genotype Aa. Used in counts mode only. - **AA count (homozygous dominant)** (number): Observed count of genotype AA. Used in counts mode only. - **Decimal Places** (number) ## When to use - Calculate AA, Aa, and aa genotype frequencies from a known recessive allele frequency. - Estimate allele frequencies from observed AA, Aa, and aa genotype counts. - Check whether observed genotype counts are consistent with Hardy-Weinberg equilibrium using chi-square. ## How it works - Select Allele Frequency Mode or Genotype Counts Mode. - In frequency mode, enter q, the recessive allele frequency from 0 to 1; the calculator derives p and calculates p², 2pq, and q². - In counts mode, enter the observed AA, Aa, and aa counts; the calculator estimates p and q, then calculates expected genotype counts. - The counts mode reports a chi-square statistic with one degree of freedom and indicates whether the result is significant. ## Use cases - Teaching population genetics and the relationship between allele and genotype frequencies. - Estimating carrier frequency from a recessive allele frequency in genetics exercises. - Comparing observed genotype counts with Hardy-Weinberg expectations in classroom or research practice. ## Frequently asked questions ### What does q represent? q is the frequency of the recessive allele, while p is the frequency of the dominant allele and p + q = 1. ### What do p², 2pq, and q² represent? They are the expected frequencies of AA, Aa, and aa genotypes, respectively. ### What inputs are required in frequency mode? Enter q, the recessive allele frequency, as a value from 0 to 1. ### What inputs are required in counts mode? Enter observed counts for AA, Aa, and aa. ### Is this calculator suitable for clinical decisions? No. It is intended for educational use only. ## Related tools - [Allele Frequency Calculator (p = (2AA + Aa) / 2N)](https://elysiatools.com/en/tools/allele-frequency-calculator): Compute allele frequencies from genotype counts: p = (2AA + Aa) / 2N, q = (2aa + Aa) / 2N. Derived from Hartl & Clark 2007, Griffiths, StatPearls. Educational use only. - [Genotype Frequency Calculator](https://elysiatools.com/en/tools/genotype-frequency-calculator): Compute genotype frequencies from counts: freq = count / N. Also derives allele and phenotypic frequencies. Derived from Hartl & Clark 2007, Griffiths, StatPearls. 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