About the Trihybrid Cross Punnett Square Calculator
A trihybrid cross tracks three genes at once — for example AaBbCc × AaBbCc. Because a Punnett square for three heterozygous genes has 8 gamete types on each side, drawing it by hand means filling in an 8 × 8 grid of 64 boxes and tallying each genotype. This calculator skips the grid: it computes the probability for each gene separately, then multiplies those probabilities together, which gives exactly the same answer with far less counting.
Why you can multiply instead of drawing 64 boxes
Mendel's Law of Independent Assortment says that genes on different chromosomes (or far apart on the same chromosome) are inherited independently of one another. When events are independent, their probabilities multiply. So the chance an offspring is dominant for gene A and gene B and gene C is simply P(A dominant) × P(B dominant) × P(C dominant). The 64-box grid is just the visual bookkeeping of that same multiplication.
The single-gene building block
Every trihybrid result is built from three one-gene crosses. For a single gene, the two most common cases are:
- Aa × Aa → 1/4 AA, 1/2 Aa, 1/4 aa. Phenotype: 3/4 dominant, 1/4 recessive (the classic 3:1 ratio).
- Aa × aa (a test cross) → 1/2 Aa, 1/2 aa. Phenotype: 1/2 dominant, 1/2 recessive.
- AA × aa → all Aa. Phenotype: 100% dominant, all heterozygous.
The calculator lets you set each of the six parental gene states (Parent 1 and Parent 2, for genes A, B, and C) so you can model any trihybrid cross, not just the textbook all-heterozygous one.
The classic AaBbCc × AaBbCc result
When both parents are heterozygous for all three genes, each gene contributes 3/4 dominant and 1/4 recessive. The full phenotype ratio across the 64 boxes is 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1, where:
- 27/64 (≈ 42.19%) show all three dominant traits — that's (3/4)³.
- 9/64 each show two dominant and one recessive trait (three such categories).
- 3/64 each show one dominant and two recessive traits (three such categories).
- 1/64 (≈ 1.56%) is recessive for all three traits — the aabbcc genotype, which is (1/4)³.
Those eight numbers add to 64, which is a quick way to confirm you have not miscounted. Note that only 1 in 64 offspring is the fully homozygous dominant AABBCC genotype, even though 27 in 64 look fully dominant — genotype and phenotype are not the same thing.
Genotype counts vs. phenotype counts
An AaBbCc × AaBbCc cross produces 3 × 3 × 3 = 27 distinct genotypes (each gene can be AA, Aa, or aa) but only 2 × 2 × 2 = 8 phenotype classes under simple dominance. This is why the trihybrid is a favorite exam problem: the genotype ratio (from 1:2:1 per gene) and the phenotype ratio (from 3:1 per gene) are different, and mixing them up is the most common mistake.