Dihybrid cross calculator

Two genes, four gametes per parent, sixteen cells: this page opens the calculator on the classic dihybrid cross AaBb × AaBb and shows the 4 × 4 Punnett square with its 9:3:3:1 phenotypic ratio already worked out. Edit either parent, for example AaBb × aabb or AABb × AaBB, and every cell, ratio and probability updates immediately.

How the 4 × 4 square is built

A parent that is heterozygous for two genes makes four gamete types, because either allele of the first gene can travel with either allele of the second: AB, Ab, aB and ab, each with probability 1/4. Write one parent’s four gametes across the top and the other’s down the side, and the 16 cells hold every possible combination. The calculator does this for you and colours the cells by outcome, so the nine genotypes are easy to spot: AABB once, AaBb four times, aabb once, and the six remaining genotypes twice each. That is the full genotypic ratio, 1:2:1:2:4:2:1:2:1.

Where 9:3:3:1 comes from

Under complete dominance the sixteen cells fall into four phenotypes. Nine cells carry at least one A and one B (dominant for both traits), three carry A with bb, three carry aa with B, and a single cell is aabb. This 9:3:3:1 pattern is the product of two independent 3:1 ratios: 3/4 × 3/4 = 9/16 for the double dominant, 3/4 × 1/4 = 3/16 for each single recessive, and 1/4 × 1/4 = 1/16 for the double recessive. Mendel’s own count of 556 seeds, 315 : 108 : 101 : 32, matches it closely. The pattern relies on the two genes assorting independently, which holds for genes on different chromosomes or far apart on the same one; tightly linked genes give different numbers.

Using the calculator

• Presets under the parents switch between the P cross (AABB × aabb), the F1 × F1 cross shown here and the dihybrid test cross.
• Phenotype view merges cells that look alike, so the square itself displays the 9:3:3:1 grouping; the Genotype view shows all nine genotypes.
• Analysis lists both ratios, the four gametes of each parent, the split between homozygous and heterozygous offspring (4 of 16 are homozygous at both genes) and every outcome with its probability. Type a pattern such as A_bb into the finder to get the chance of one particular result.
• Dominance modes recompute the square for incomplete dominance or codominance, where the nine genotypes become nine distinguishable phenotypes in a 1:2:1:2:4:2:1:2:1 ratio.

Beyond two genes

Slide the gene count to three and the same tool draws the 64-cell trihybrid square with its 27:9:9:9:3:3:3:1 ratio; four genes give 256 cells and five give 1,024. For crosses where you only want the simplified ratios, the genotype and phenotype ratio calculator opens on a trihybrid cross; for the pea version of this square with Mendel’s yellow and round traits, see the pea plant Punnett square.

Frequently asked questions