Punnett Square Calculator (monohybrid & dihybrid)

Understanding the Punnett square calculator — concept and principle

A Punnett square lists every combination of gametes from two parents and shows the expected genotype and phenotype ratios of their offspring. This calculator handles monohybrid crosses (one gene, such as Aa × Aa), dihybrid crosses (AaBb × AaBb) and more genes in the same format, with uppercase letters as dominant alleles.

How it is calculated

1. Each genotype is read in pairs of letters, one pair per gene (Aa, then Bb).
2. Gametes: each parent passes on one letter from every pair, so a parent with n heterozygous genes makes 2ⁿ gamete types in equal proportions (AaBb gives AB, Ab, aB, ab).
3. Every gamete of parent 1 is combined with every gamete of parent 2; the total number of cells is gametes₁ × gametes₂.
4. Genotypes are counted after sorting each pair (Aa and aA are the same).
5. Phenotypes: any uppercase letter in a pair shows the dominant form, written A_; only a lowercase pair, aa, shows the recessive form.

The principle

Mendel's law of segregation says the two alleles of a gene separate during meiosis, so each gamete carries one, with equal probability. The law of independent assortment says genes on different chromosomes segregate independently, so the probabilities for each gene multiply. For one heterozygous gene the offspring ratio is 1 AA : 2 Aa : 1 aa, which with complete dominance is a 3 : 1 phenotype ratio. Two independent genes give (3 : 1) × (3 : 1) = 9 : 3 : 3 : 1.

Worked example

1. Parents: AaBb × AaBb. Each makes four gametes (AB, Ab, aB, ab), so the square has 4 × 4 = 16 cells.
2. Gene A alone gives AA 1/4, Aa 2/4, aa 1/4; gene B is the same.
3. Multiply: AaBb = 2/4 × 2/4 = 4/16; AABb = 1/4 × 2/4 = 2/16; AABB = 1/16, and so on for all nine genotypes.
4. Phenotypes: A_ = 3/4 and B_ = 3/4, so A_B_ = 9/16, A_bb = 3/16, aaB_ = 3/16, aabb = 1/16.

How to read the result

Each fraction is a probability for one offspring, not a guaranteed count. With 16 offspring you expect about 9 : 3 : 3 : 1, but random variation is normal.

Common mistakes

• Writing parents in different gene orders (AaBb and BbAa); keep the same order for both.
• Expecting the predicted ratio exactly in a small number of offspring.
• Applying independent assortment to genes that are linked on the same chromosome.
• Forgetting that incomplete dominance or codominance make Aa a distinct phenotype.

Frequently asked questions

What is a test cross?

Crossing an individual showing the dominant phenotype with a homozygous recessive (aa). If any offspring are recessive, the parent was Aa.

Why is the dihybrid phenotype ratio 9:3:3:1?

Because each gene alone gives 3:1, and independent genes multiply: 3×3, 3×1, 1×3 and 1×1.

What is the chance two carriers have an affected child?

Aa × Aa gives aa with probability 1/4 for each child, independently of earlier children.

Sources: G. Mendel, "Versuche über Pflanzen-Hybriden", Verhandlungen des naturforschenden Vereines in Brünn 4 (1866) · R. C. Punnett, Mendelism, Macmillan (1905 and later editions)