Enter your observed phenotype counts (up to four) and your expected Mendelian ratio — or plug in a custom ratio — and this Chi-Square Goodness of Fit calculator computes your χ² value, degrees of freedom, p-value, and critical value to tell you whether your cross results support or reject the expected genetic ratio.
Chi-Square Value (χ²)
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Degrees of Freedom
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P-value
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Critical Value
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Hypothesis Test Result
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Total Observed
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A chi-square goodness of fit test determines whether observed genetic ratios from crosses significantly differ from expected Mendelian ratios. It helps geneticists validate inheritance patterns and hypotheses.
If p-value < 0.05 (or your chosen significance level), reject the null hypothesis - your observed data significantly differs from expected ratios. If p-value ≥ 0.05, fail to reject the null hypothesis - your data supports the expected Mendelian ratio.
Degrees of freedom equals the number of phenotype categories minus one (n-1). For a 3:1 ratio, df = 1; for 1:2:1 ratio, df = 2; for 9:3:3:1 ratio, df = 3.
Use 3:1 for monohybrid crosses with complete dominance, 1:1 for test crosses, 1:2:1 for incomplete dominance or codominance, and 9:3:3:1 for dihybrid crosses involving two traits.
Key assumptions include: independent observations, expected frequency of at least 5 in each category, random sampling, and that the data represents actual counts (not percentages or proportions).
Multiply the total number of offspring by the proportion for each phenotype in the expected ratio. For example, with 160 total offspring and a 3:1 ratio: expected dominant = 160 × (3/4) = 120, expected recessive = 160 × (1/4) = 40.
A very high chi-square value indicates large deviations from expected ratios, suggesting the observed data doesn't fit the hypothesized Mendelian pattern. This might indicate linkage, epistasis, or other genetic factors affecting inheritance.
While this calculator handles up to 4 categories (sufficient for most Mendelian ratios), chi-square tests can theoretically handle any number of categories. For complex genetic analyses, consult specialized statistical software.