Test observed offspring counts against expected Mendelian ratios for monohybrid, dihybrid, test cross, incomplete dominance, or any custom ratio with chi-square goodness-of-fit.
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Classic 3:1 dominant : recessive ratio for one segregating gene.
In the same order as the expected ratio categories.
| Category | Observed | Expected | (O−E)²/E |
|---|---|---|---|
| Dominant | 75 | 75 | 0 |
| Recessive | 25 | 25 | 0 |
When to use
Do not use for
A monohybrid 3:1 expects [dominant, recessive]. If you flip the order, the test still runs but the result is meaningless.
Categories with expected counts below 5 distort the chi-square distribution. Pool them with the nearest larger category before computing.
It only fails to reject it. A larger sample might still find a significant deviation. Treat "consistent with Mendelian" as "no evidence against," not as "confirmed."
Reviewers need all three to evaluate the test. Reporting only "p<0.05" hides whether the deviation is biologically meaningful or just a tiny p-value from a huge sample.
Expected counts = total observed (ratio_i / sum(ratio)). Chi-square = Σ((O−E)²/E). df = categories − 1. p-value computed from the regularized lower incomplete gamma function P(df/2, χ²/2) using a Lanczos-approximation log-gamma — accurate to 1e-12. Significance threshold = 0.05. Warns when any expected count is below 5 (chi-square approximation invalid).
Last validated 2026-04-06. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.
ConductScience Mendelian Ratio + Chi-Square Calculator (v1.0.0). ConductScience, Inc. 2026. Available at: https://conductscience.com/tools/mendelian-ratio-calculator
Pearson K. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine. 1900;50(302):157-175.
Mendel G. Experiments in plant hybridization. Verh. Naturforsch. Ver. Brünn. 1866.
Two heterozygotes for a single gene. Three dominant phenotypes for every one recessive. The classic Mendel pea cross: tall tall → 75% tall, 25% dwarf.
Two heterozygotes for two unlinked genes. Nine show both dominants, three show one dominant + one recessive (each way), one shows both recessives. Mendel's second law of independent assortment.
A heterozygote crossed with a homozygous recessive. Used to confirm whether a dominant-phenotype individual is heterozygous (1:1 expected) or homozygous (no recessives).
When the heterozygote shows an intermediate phenotype (e.g., red white snapdragons → pink). Three distinguishable categories instead of two.
Most chi-square deviations are not random noise — they're the start of an interesting biological story. The five most common explanations:
Two genes on the same chromosome don't segregate independently. A dihybrid cross will deviate from 9:3:3:1 toward the parental combinations. Use a recombination frequency calculator to estimate the genetic distance.
Some genotypes die in utero or during development. A 1:2:1 incomplete dominance cross becomes 0:2:1 (or 2:1) if the homozygous dominants are lethal. Yellow mouse coat color is the classic example.
Genes on the X or Y chromosome give sex-specific ratios. A monohybrid for an X-linked recessive shows 50% affected males but 0% affected females in the F1 of a heterozygous mother wild-type father.
Some genotypes don't always express the expected phenotype. The cross deviates from the Mendelian ratio in a consistent direction.
Always rule this out first. If your deviation is huge and unexpected, audit the scoring before invoking biology.
Tracks every breeding pair, litter, and weanling with genotype rolls forward through generations so cross categories are always correct.
Open app EquipmentPair this calculator with sample-size planning to detect ratio deviations at 80% power
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