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Chi-Square Test for Genetic Ratios Calculator

Test observed offspring counts against an expected Mendelian ratio (3:1, 1:2:1, 9:3:3:1, 1:1 or custom) — χ², degrees of freedom and p-value.

Observed counts (in ratio order)

Expected ratio

Custom ratio (e.g. 9:7)

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How it works

χ² = Σ (O − E)² ÷ E, E = total × ratio share; df = classes − 1

A goodness-of-fit chi-square asks whether the gap between observed and Mendelian-expected counts is bigger than chance sampling would produce. A high p-value (above 0.05) means the hypothesis survives; it never proves the ratio. Mendel’s own pea data — 315:108:101:32 — fit 9:3:3:1 with χ² = 0.47.

Worked example

315, 108, 101, 32 against 9:3:3:1 (n = 556): expected 312.75, 104.25, 104.25, 34.75 → χ² = 0.470, df 3, p = 0.93.

Frequently asked questions

What does rejecting the ratio mean biologically?

Linkage, lethal genotypes, epistasis (e.g. 9:7 or 12:3:1), incomplete penetrance or simply misclassification.

Can I use it with small samples?

Expected counts should be at least 5 in every class; otherwise use an exact binomial or multinomial test.

Related calculators

Chi-Square Goodness-of-Fit Calculator

Test whether observed counts match an expected distribution with the chi-square goodness-of-fit statistic, degrees of freedom and p-value.

Dihybrid Cross Calculator

Cross two parents across two independent genes and get the phenotype ratio, the probability of each of the four trait combinations and the expected offspring counts for a chosen brood size.

Punnett Square Calculator

Cross two parent genotypes for a single gene and get the offspring genotype ratio, phenotype ratio and the odds of dominant versus recessive traits.

For teaching and planning — verify against your lab protocol and instrument documentation.