Use this Hwe Calculator to compare observed AA, Aa, and aa counts with Hardy-Weinberg expected counts. It returns p, q, expected genotypes, chi-square, and HWE status.
This calculator tests whether observed genotype counts fit Hardy-Weinberg equilibrium for a given population. You simply enter the observed numbers for the AA, Aa, and aa genotypes. The tool returns the allele frequencies p and q, the expected genotype counts, the chi-square value, and the final equilibrium status. This tool works for bi-allelic traits only.
What this Hwe Calculator returns
Here is exactly what the calculator determines from your observed genotype counts.
| Output | Meaning | Formula / basis |
|---|---|---|
| Allele frequency p | Frequency of allele A in the sample | $p = \frac{2AA + Aa}{2N}$ |
| Allele frequency q | Frequency of allele a in the sample | $q = 1 – p$ |
| Expected AA | Expected homozygous dominant count under HWE | $p^2 \times N$ |
| Expected Aa | Expected heterozygous count under HWE | $2pq \times N$ |
| Expected aa | Expected homozygous recessive count under HWE | $q^2 \times N$ |
| Chi-square ($\chi^2$) | The statistical difference between observed and expected counts | $\sum \frac{(O-E)^2}{E}$ |
| Equilibrium status | Whether the observed genotype counts are consistent with Hardy-Weinberg equilibrium | Compares $\chi^2$ to the critical value (3.841) |
Inputs required for this Hwe Calculator
To use the tool, you need to provide the actual number of individuals for each genotype in your sample.
| Input | Format | Meaning |
|---|---|---|
| Observed AA | Whole number | Total counted individuals with the homozygous dominant genotype |
| Observed Aa | Whole number | Total counted individuals with the heterozygous genotype |
| Observed aa | Whole number | Total counted individuals with the homozygous recessive genotype |
The calculator accepts whole-number genotype counts only, uses no direct p/q values, allows no percentages, and accepts no multi-allele input.
How this Hwe Calculator works
The tool follows a standard Hardy-Weinberg calculation sequence to compare observed genotype counts with expected genotype counts.
Step 1: Calculate total population size $$N = AA + Aa + aa$$
Step 2: Calculate allele frequencies $p = \frac{2AA + Aa}{2N}$ $q = 1 – p$
Step 3: Calculate expected genotype counts $AA = p^2 \times N$ $Aa = 2pq \times N$ $aa = q^2 \times N$
Step 4: Calculate chi-square $$\chi^2 = \sum \frac{(O-E)^2}{E}$$
Step 5: Determine equilibrium status The tool checks the final chi-square value against the critical threshold. It returns “consistent with HWE” if the number is low, or “deviates from HWE” if the difference is statistically significant. A warning appears when any expected counts fall below 5, as small theoretical groups can make the statistical test less reliable.
Hardy-Weinberg formulas used in this calculator
These are the core mathematical expressions the tool relies on to process your inputs.
| Formula | Meaning | Used for |
|---|---|---|
| $p + q = 1$ | Total allele frequency across the two alleles | Finding the second allele frequency once the first is known |
| $p^2$ | The frequency of the homozygous dominant genotype | Predicting the expected AA population fraction |
| $2pq$ | The frequency of the heterozygous genotype | Predicting the expected Aa population fraction |
| $q^2$ | The frequency of the homozygous recessive genotype | Predicting the expected aa population fraction |
| $p = \frac{2AA + Aa}{2N}$ | Allele A frequency from observed counts | Finding the exact starting p value from observed counts |
| $\chi^2 = \sum \frac{(O-E)^2}{E}$ | The sum of squared differences divided by expected values | Measuring how far observed counts drift from expected counts |
Example calculation from observed AA, Aa, and aa counts
Here is how the calculator processes a sample population of 100 individuals.
Observed counts: AA = 36 Aa = 48 aa = 16
1. Total population $N = 36 + 48 + 16 = 100$
2. Allele frequencies $p = \frac{2(36) + 48}{2(100)} = \frac{120}{200} = 0.6$ $q = 1 – 0.6 = 0.4$
3. Expected genotype counts Expected AA $= 0.6^2 \times 100 = 36$ Expected Aa $= 2(0.6)(0.4) \times 100 = 48$ Expected aa $= 0.4^2 \times 100 = 16$
4. Chi-square $$\chi^2 = \frac{(36-36)^2}{36} + \frac{(48-48)^2}{48} + \frac{(16-16)^2}{16} = 0 + 0 + 0 = 0$$
5. Final result Because the chi-square value is below 3.841, the population is consistent with Hardy-Weinberg equilibrium.
Interpreting p, q, expected counts, and chi-square
These outputs show how the observed genotype counts compare with Hardy-Weinberg expectations.
| Result | What it indicates | How to read it |
|---|---|---|
| $p > q$ | The dominant allele is more common | Allele A is more common in the sample |
| $q > p$ | The recessive allele is more common | Allele a is more common in the sample |
| observed counts close to expected | Observed counts are close to Hardy-Weinberg expectations | The sample is consistent with Hardy-Weinberg equilibrium |
| large $\chi^2$ | The population deviates from equilibrium | Observed genotype counts differ more strongly from Hardy-Weinberg expectations |
| expected count warning below 5 | The statistical test might be inaccurate | The sample size is too small for a highly reliable chi-square result |
| fixed allele / no variation detected | One allele frequency is 1.0 (100%) | Every individual in the population has the exact same genotype for this trait |
Limits of this Hwe Calculator
This tool is built strictly for standard Hardy-Weinberg testing and has a few specific boundaries.
| Limitation | What it means here |
|---|---|
| bi-allelic only | The tool only works for genes with exactly two alleles |
| observed genotype counts only | You cannot enter allele frequencies directly to work backward |
| whole-number counts required | The calculator does not process decimals or fractions as inputs |
| small expected counts can weaken chi-square | If any expected group falls below 5, the math becomes less trustworthy |
| fixed allele edge case | If a population has only one genotype, the equilibrium test becomes unnecessary |
| not for offspring cross prediction | This measures an existing population, it does not act as a Punnett square |
Choosing the right calculator depends on the exact genetics problem you need to solve.
| Tool | Use it when | Do not use it when |
|---|---|---|
| Hwe Calculator | Testing whether observed genotype counts are consistent with Hardy-Weinberg equilibrium | Predicting the exact traits of a single offspring |
| Punnett square calculator | Finding genotype probabilities for a specific mating cross | Testing whether observed population counts are consistent with Hardy-Weinberg equilibrium |
| Mendelian chi-square calculator | Checking if offspring match standard inheritance ratios | Testing for Hardy-Weinberg equilibrium in a random mating population |
Related Tools & Calculators: