Trihybrid Cross Calculator
Enter the genotype at each of three gene loci for both parents. The calculator generates the full 8x8 Punnett square (64 offspring combinations), then tallies every genotype frequency, the eight phenotype classes, and the classic 27:9:9:9:3:3:3:1 ratio when both parents are AaBbCc. Results update as you type.
What is a trihybrid cross?
A trihybrid cross is a genetic experiment that simultaneously tracks the inheritance of three independent traits, each controlled by a single gene with two alleles: a dominant allele (capital letter) and a recessive allele (lowercase letter). The term "trihybrid" refers to an organism that is heterozygous at all three loci, such as AaBbCc. When two trihybrid individuals mate, Mendel's Law of Independent Assortment predicts that each gene sorts into gametes independently of the others, producing eight gamete types and 64 possible offspring genotype combinations in a full 8x8 Punnett square.
The product rule: why independent assortment simplifies the math
Instead of drawing all 64 cells of the Punnett square by hand, geneticists use the product rule: because the three loci assort independently, the probability of any three-locus genotype or phenotype combination equals the product of the individual one-locus probabilities. For example, in an AaBbCc x AaBbCc cross, each locus independently gives a 3/4 chance of a dominant phenotype and a 1/4 chance of a recessive phenotype. The probability of showing dominant at all three loci is 3/4 x 3/4 x 3/4 = 27/64, which matches the first number in the classic 27:9:9:9:3:3:3:1 ratio. This calculator applies the product rule across all eight phenotype classes automatically.
Reading the 27:9:9:9:3:3:3:1 phenotype ratio
When both parents are AaBbCc, the offspring distribute across eight phenotype classes in the ratio 27:9:9:9:3:3:3:1 (out of 64 total). The 27 represents offspring showing all three dominant traits (A_ B_ C_). The three groups of 9 each show two dominant and one recessive trait. The three groups of 3 each show one dominant and two recessive traits. The single group of 1 (aabbcc) shows all three recessive traits. This ratio is one of Mendel's most cited results and a cornerstone of classical genetics. It only holds when the three genes are on different chromosomes (or far apart on the same chromosome) so they sort independently, and when dominance at each locus is complete.
Testcrosses, pure lines and other common crosses
A testcross (AaBbCc x aabbcc) reveals an organism's genotype: because the recessive parent contributes only recessive alleles, every offspring phenotype directly reflects a gamete type from the heterozygous parent. With three heterozygous loci the testcross produces eight equally frequent phenotype classes in a 1:1:1:1:1:1:1:1 ratio, confirming that eight distinct gamete types were produced. A pure-line cross (AABBCC x aabbcc) yields an F1 generation that is entirely AaBbCc - all offspring show all three dominant phenotypes - and the 64-cell Punnett square is only needed in the F2 generation from F1 x F1 parents.
Limitations of this model
This calculator assumes complete dominance at every locus, meaning one copy of the dominant allele fully masks the recessive allele. It also assumes independent assortment, which requires the three gene loci to be on different chromosomes or separated by enough distance that recombination effectively randomizes allele combinations. Genes that are close together on the same chromosome show linkage and do not assort independently, breaking the product rule. Other complications include incomplete dominance (where heterozygotes show an intermediate phenotype), codominance, epistasis (where one gene masks another), and pleiotropy (where one gene affects multiple traits). For any of these situations, a full gamete-by-gamete Punnett square and knowledge of the specific inheritance pattern are required.
Common trihybrid cross phenotype ratios
| Cross | Ratio (8 classes) | Grid size |
|---|---|---|
| AaBbCc x AaBbCc | 27:9:9:9:3:3:3:1 | 8 x 8 = 64 |
| AaBbCc x aabbcc (testcross) | 1:1:1:1:1:1:1:1 | 8 x 1 = 8 |
| AABBCC x aabbcc (F1 = AaBbCc) | All A_ B_ C_ (F1) | 1 x 1 = 1 |
| AABBCc x aabbcc | 1:1:0:0:0:0:0:0 | 2 x 1 = 2 |
| AaBBCC x AaBBCC | 3:0:0:0:0:0:0:1 (at A; B,C fixed) | 2 x 2 = 4 |
Expected phenotype ratios for selected crosses of three independently assorting loci under complete dominance.
Frequently asked questions
What is the classic phenotype ratio for a trihybrid cross?
When both parents are heterozygous at all three loci (AaBbCc x AaBbCc), the offspring show the classic 27:9:9:9:3:3:3:1 phenotype ratio across eight classes. Out of 64 offspring, 27 express all three dominant traits, three groups of 9 each express two dominant and one recessive, three groups of 3 each express one dominant and two recessive, and 1 expresses all three recessive traits.
How many gamete types can a trihybrid parent produce?
A parent that is heterozygous at all three loci (AaBbCc) can produce 2^3 = 8 distinct gamete types: ABC, ABc, AbC, Abc, aBC, aBc, abC, and abc. A parent that is homozygous at one locus produces only 2^2 = 4 types, and a parent homozygous at all three loci produces only one gamete type. The size of the Punnett square equals (Parent 1 gamete types) x (Parent 2 gamete types).
Why does independent assortment let us use the product rule?
Independent assortment means the allele a gamete receives at one locus has no effect on which allele it receives at another locus. Because the events are statistically independent, the probability of inheriting a specific combination of alleles is simply the product of the individual probabilities at each locus. This is equivalent to multiplying the separate 2x2 Punnett square results for each gene - there is no need to draw out all 64 cells of the full square.
What happens if the parents are not both triply heterozygous?
If any locus is homozygous in one or both parents, that locus contributes fewer gamete types, and the Punnett square shrinks. For example, if Parent 1 is AA at locus A (homozygous dominant), every offspring inherits at least one A allele, so all offspring are phenotypically dominant at that locus regardless of what Parent 2 contributes. The phenotype ratio for the other two loci is then determined independently by the remaining heterozygous loci.
Does this calculator work for genes that are linked?
No. This calculator assumes complete independent assortment. For linked genes (on the same chromosome and close together), the frequency of recombinant gametes is less than 50%, so offspring phenotype ratios deviate from what the product rule predicts. Calculating outcomes for linked genes requires knowledge of the recombination frequency between the loci.
What does a testcross tell a geneticist?
A testcross pairs an organism of unknown genotype with a fully homozygous recessive parent (aabbcc). Because the recessive parent can only contribute recessive alleles, the phenotype of each offspring directly reveals which gamete type the unknown parent contributed. If 8 equally frequent phenotype classes appear, the unknown parent must have been AaBbCc - producing all 8 gamete types in equal proportions.