This trihybrid cross calculator works out the classic three-gene cross — AaBbCc × AaBbCc by default, any heterozygous parents you enter — returning the 27:9:9:9:3:3:3:1 phenotype ratio, the full genotype probability table, and the probability of any specific offspring genotype you specify.

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Three Genes: Multiplication Replaces the 64-Box Square

A trihybrid cross has 8 gamete types per parent and a 64-cell Punnett square — drawable once, as a rite of passage, and never again, because independent assortment lets probability do the work. Each heterozygous gene independently deals offspring genotypes ¼ AA : ½ Aa : ¼ aa and phenotypes ¾ dominant : ¼ recessive; the three genes multiply. The phenotype ledger of AaBbCc × AaBbCc is the famous 27:9:9:9:3:3:3:1: dominant-at-all-three 27/64, the three "two dominant, one recessive" classes at 9/64 each, the three "one dominant" classes at 3/64, and the triple recessive at 1/64. Genotypes fan out to 27 classes, the likeliest single one being the all-heterozygote AaBbCc at (½)³ = 12.5% — which is why the calculator's target-pricing defaults to it: in 640 offspring, expect ≈ 80 triple heterozygotes, 270 all-dominant phenotypes, and just 10 triple recessives.

The assumptions deserve their usual bold type: complete dominance at each locus, independent assortment (genes unlinked — on different chromosomes or distant on the same one), no epistasis (genes not masking each other), equal viability. Mendel's own peas obeyed them closely enough to found a science; real loci negotiate. When observed counts deviate from 27:9:9:9:3:3:3:1 beyond chi-square tolerance, the deviation itself is the discovery — linkage or epistasis announcing itself in the residuals. For crosses where parents aren't all heterozygous (testcrosses, AAbbCc × aaBbCc and friends), the same forked-line multiplication applies gene by gene: price each locus from its own monohybrid ratio (the Punnett Square page handles the one- and two-gene cases with full grids) and multiply the three.

Worked Examples (Verified)

  • AaBbCc offspring: (½)³ = 12.50% (8/64); ≈80 in 640.
  • All-dominant phenotype: (¾)³ = 42.19% (27/64).
  • Triple recessive aabbcc: (¼)³ = 1.56% (1/64); ≈10 in 640.
  • AABbCc: ¼ × ½ × ½ = 6.25% (4/64).

Trihybrid Discipline

  • Forked-line over grid: price each gene separately (1:2:1 or 3:1) and multiply — 64 boxes are for learning, not for working.
  • Ratios presume unlinked genes; parental-type excess in real data is the fingerprint of linkage.
  • Epistasis rewrites phenotype ratios (9:7, 15:1, 12:3:1...) while genotype probabilities stand — check which layer a question asks about.
  • Expected counts need big litters to resemble ratios: 64 offspring expect 1 triple recessive, but P(zero in 64) ≈ e⁻¹ ≈ 37% — absence in a small sample proves nothing.
  • Order of alleles in a genotype string is display convention; AABbCC and CCAABb are the same genotype — the calculator prices per-gene pairs in the order you type them (A-pair, B-pair, C-pair).

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Frequently Asked Questions

What is the phenotypic ratio of a trihybrid cross?

For AaBbCc × AaBbCc with complete dominance and independent assortment: 27:9:9:9:3:3:3:1 — 27/64 showing all three dominant traits, 9/64 in each of the three classes dominant at exactly two loci, 3/64 in each class dominant at exactly one, and 1/64 recessive at all three. It is (3:1)³ expanded, which is also how to reconstruct it if you ever forget: cube the monohybrid phenotype ratio.

How many genotypes does a trihybrid cross produce?

27 distinct genotype classes (3 per gene, multiplied: 3³), spread over the 64 equally likely zygote combinations. The most probable single genotype is AaBbCc at 8/64 = 12.5%; the least probable are the eight "corner" genotypes (all-homozygous combinations like AABBCC and aabbcc) at 1/64 each. This calculator prices any specific genotype you type and gives expected counts for your planned offspring number.

How do I find the probability of a specific offspring?

Multiply the per-gene probabilities: from Aa × Aa, P(AA) = ¼, P(Aa) = ½, P(aa) = ¼. For AaBbCc: ½ × ½ × ½ = ⅛. For AABbCc: ¼ × ½ × ½ = 1/16. The forked-line (branch diagram) method is exactly this, and it's what the calculator automates for the standard trihybrid parents. Other parental combinations work the same way once you take each gene's ratio from its own monohybrid cross.

Why not just draw the 64-box Punnett square?

You can — it contains no different information. But with 8 gametes per side it invites bookkeeping errors, and it collapses entirely at four genes (256 boxes) where multiplication still takes seconds. The square's real value is pedagogical (it PROVES the gamete frequencies); working geneticists use forked-line multiplication, and exam boards accept either. Our Punnett Square page draws the mono- and dihybrid grids where they're practical.

What if the three genes are linked?

Then independent assortment fails and these ratios distort: parental allele combinations appear in offspring more often than recombinant ones, by an amount set by the recombination frequency between the loci. The 27:9:9:9:3:3:3:1 expectation becomes the null hypothesis you test against — significant deviation in a chi-square test is evidence FOR linkage. Three-point testcrosses (the classic mapping experiment) exploit exactly this distortion to order genes and measure map distances.

What is epistasis and how does it change the ratios?

Epistasis is one gene masking or modifying another's expression — the genotype probabilities (this calculator's layer) are unchanged, but phenotype classes merge, morphing 27:9:9:9:3:3:3:1 into signatures like 36:9:9:9:... rescaled versions of classic dihybrid epistatic ratios (9:7 complementary, 15:1 duplicate, 12:3:1 dominant epistasis). If phenotype counts refuse the standard ratio while genotype-level markers fit, epistasis is the first hypothesis.

How many offspring do I need to see the triple recessive?

Expectation says 1 in 64, but probability runs the waiting room: P(at least one aabbcc in n offspring) = 1 − (63/64)ⁿ — about 63% by n = 64, 95% only near n ≈ 190. Breeders planning around rare recessive combinations size litters/clutches with this math, and its mirror image sizes backcross and testcross programs. Enter your planned count in the calculator to see expected numbers per class.

Is this trihybrid cross calculator free?

Yes — free, instant, no sign-up. Enter any target genotype for its probability and expected count, with the full 27:9:9:9:3:3:3:1 ratio explained.