Trihybrid Cross Calculator

Background.

"What fraction of the offspring of AaBbCc × AaBbCc show all three dominant traits?" Drawing the answer is a poor way to find it. Each triple heterozygote makes eight kinds of gamete, so the full Punnett square has 64 boxes. The product rule gets there in a line instead. Crossed heterozygote by heterozygote, each gene gives the dominant phenotype three times in four, and because the genes assort independently the three chances multiply: (3/4)³ = 27/64, or 42.1875%.

Set the phenotype you want at each gene, dominant or recessive, and enter both parents as six-letter genotypes. You get the probability of that exact combination, the same figure as a reduced fraction, the two extreme classes (dominant at every gene and recessive at every gene), the distinct gametes each parent makes, the smallest grid in which every cell is equally likely, the number of phenotype and genotype classes that can occur, and the full phenotype series, largest class first.

All 64 combinations are counted rather than the textbook ratio assumed, so crosses that are not triple heterozygotes come out right too. AABbCc × AaBbcc, for example, yields only four phenotype classes, and its all-dominant class is 3/8 rather than 27/64. Crossing against aabbcc, the three-point testcross, flattens all eight classes to 1/8 each.

Everything rests on complete dominance at each gene and on all three genes assorting independently. That second condition is not automatic: later mapping found two of Mendel's seven pea traits on the same chromosome about 12.6 map units apart, and the three-point testcross became the standard way of measuring how far real genes depart from independence.

What is trihybrid cross calculator?

A trihybrid cross follows three genes through one mating. Under independent assortment, a parent heterozygous at all three genes makes 2³ = 8 gamete types in equal numbers, so two such parents fill 4³ = 64 equally likely cells, producing 3³ = 27 possible genotypes and, with complete dominance, 2³ = 8 visible phenotype classes. The underscore notation groups genotypes that look alike: A_ means AA or Aa, both showing the dominant trait, while aa is written in full because a recessive phenotype fixes the genotype. That is why aabbcc is the one phenotype class that corresponds to a single genotype.

How to use this calculator.

1. 01Type each parent as six letters: positions 1–2 are gene 1, 3–4 gene 2, 5–6 gene 3. Uppercase means the dominant allele and lowercase the recessive one; the three genes need three different letters, used in the same order for both parents.
2. 02Choose dominant or recessive for each gene to pick which of the eight phenotype classes you are asking about.
3. 03Read the probability and the exact fraction beside it. A combination that cannot occur shows 0% and 0/1 rather than an error.
4. 04Check the setup against the counts: a triple heterozygote should make 8 gametes, and a triple-heterozygote cross should give 64 cells, 27 genotype classes and 8 phenotype classes.
5. 05For a three-point testcross, enter aabbcc as the second parent; every class should then sit at 12.5%.

The formula.

The product rule: P(class) = P₁ × P₂ × P₃, where each Pᵢ is the chance of the wanted phenotype at gene i, worked out as a one-gene cross. For the dominant phenotype, Aa × Aa gives 3/4, Aa × aa gives 1/2, any cross involving AA gives 1, and aa × aa gives 0; the recessive chance is one minus each of those. Multiplying is valid only because the three genes are assumed to assort independently, so the outcome at one gene says nothing about the others. Rather than relying on the shortcut, every parent's eight gametes (repeats included) are paired with the other parent's eight, and the 64 cells are counted; each probability is therefore a whole number of cells out of 64, reduced to lowest terms for the fraction. The other counts follow the same logic: a parent heterozygous at h genes makes 2ʰ distinct gametes, the smallest equally likely grid is the product of the two parents' gamete types, and the genotype and phenotype class counts are whatever actually occurs in the 64 cells. Linkage between any of the three gene pairs, epistasis, lethal genotypes or incomplete penetrance would all make real progeny depart from these figures.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Abbott S. & Fairbanks D. J. (2016). Experiments on Plant Hybrids by Gregor Mendel. Genetics 204(2):407–422. doi:10.1534/genetics.116.195198. Peer-reviewed English translation of Mendel (1866). Source for the trifactorial experiment — 639 plants resolved into 27 classes, with the printed class averages of 10, 19, 43 and 78 — and for the 2ⁿ gamete / 3ⁿ genotype / 4ⁿ combination series. Open access. Retrieved 2026-07-29.
2. [2]OpenStax, Biology 2e, section 12.3 'Laws of Inheritance'. Rice University, 2018, CC BY 4.0. Source for the forked-line method — 'create rows equal to the number of genes being considered, and then segregate the alleles in each row on forked lines' — and for the trihybrid result 'the probability of F2 offspring having yellow, round, and tall traits is 3 × 3 × 3, or 27'. Free, openly licensed. Retrieved 2026-07-29.
3. [3]Biology LibreTexts, Map: Raven Biology 12th Edition, section 12.03 'Dihybrid Crosses and Mendel's Law of Independent Assortment'. Independent-publisher statement of the general multi-locus product rule — 'the probability of the desired genotype at the first locus multiplied by the probability of the desired genotype at the other loci' — worked through to a tetrahybrid case: '(1/4) × (1/4) × (1/4) × (1/4), we determine that 1/256 of the offspring will be quadruply homozygous recessive'. Free. Retrieved 2026-07-29.
4. [4]Reid J. B. & Ross J. J. (2011). Mendel's genes: toward a full molecular characterization. Genetics 189(1):3–10. doi:10.1534/genetics.111.132118. Source for the linkage caveat: Mendel's seven traits occupy only five of the seven pea linkage groups, with le and v about 12.6 map units apart, so 'an element of luck was involved with his choice of characters'. Open access via PMC. Retrieved 2026-07-29.
5. [5]MedlinePlus Genetics, US National Library of Medicine. Inheritance Patterns, page last updated 19 April 2021. Source for the classical single-gene inheritance definitions and for the position that most visible human traits are not governed by one or a few genes. Free. Retrieved 2026-07-29.