Advanced Punnett Square Calculator
Calculate offspring probabilities for single or two-locus Punnett squares.
Why Multiplication Beats Drawing the Grid
A dihybrid cross needs a 4×4 grid; a trihybrid needs 8×8 with 64 boxes. Beyond two genes, drawing the square becomes impractical — but the product rule handles any number of independently assorting genes.
For AaBbCc × AaBbCc, the probability of A_B_C_ is simply (3/4)³ = 27/64. No grid required. The classic 9:3:3:1 dihybrid ratio is just (3/4, 1/4) applied twice and multiplied out.
| Genes heterozygous | Gamete types | Grid size | Phenotype classes |
|---|---|---|---|
| 1 | 2 | 4 | 2 |
| 2 | 4 | 16 | 4 |
| 3 | 8 | 64 | 8 |
| 4 | 16 | 256 | 16 |
When Independent Assortment Fails
The product rule requires genes to assort independently, which holds only when they are on different chromosomes or far apart on the same one. Linked genes violate it, producing an excess of parental combinations and a deficit of recombinants.
A dihybrid testcross giving anything other than 1:1:1:1 indicates linkage, and the deviation quantifies the map distance directly.
Epistasis Changes the Ratio, Not the Genotypes
| Interaction | Phenotype ratio | Example |
|---|---|---|
| Independent | 9:3:3:1 | Standard dihybrid |
| Recessive epistasis | 9:3:4 | Coat colour in mice |
| Dominant epistasis | 12:3:1 | Squash fruit colour |
| Duplicate genes | 15:1 | Wheat kernel colour |
| Complementary genes | 9:7 | Flower pigment pathway |
Every one of these is still a 9:3:3:1 genotypic outcome. What changes is which genotype classes look alike. In recessive epistasis the 3 and 1 classes merge into a single phenotype, giving 9:3:4 — the underlying Mendelian ratios are intact, but one gene masks the other's expression.
Recognising these modified ratios is how gene interactions were mapped before molecular methods, and the numbers still identify the interaction type from breeding data alone.
Worked Examples
Common Mistakes
A trihybrid square has 64 boxes. Multiplying single-gene probabilities gives the same answer in one line.
Independent assortment is required. Linked genes give an excess of parental combinations, and a testcross ratio other than 1:1:1:1 reveals it.
Ratios such as 9:3:4 and 12:3:1 are still 9:3:3:1 genotypically. Epistasis merges phenotype classes without altering inheritance.
These are probabilities. Human pedigrees rarely have enough offspring for observed ratios to approach expectation.