Punnett square calculator

How it works

Write each parent as letter pairs, one pair per gene: Aa for one gene, AaBb for two. Upper case is the dominant allele and lower case the recessive one. The calculator assumes complete dominance, so a single capital letter is enough to show the dominant trait.

It follows Mendel's two laws: each parent passes on one allele of every gene (segregation), and different genes sort into eggs or sperm independently (independent assortment). The tool lists every combination each parent can pass on, one parent along the top and the other down the side, and fills each cell by joining the two.

gametes per parent = 2^n      cells = 2^n × 2^n      (n = number of genes)

Four genes give a 16 by 16 square of 256 cells. A homozygous gene such as AA still contributes both of its identical alleles, so the square keeps its textbook size and every cell is equally likely. Both parents must carry the same genes, written in any order. In the results, A_ means "at least one A", so A_ bb covers any offspring with the dominant form of the first trait and the recessive form of the second.

Three other modes change the rules:

• ABO blood groups. Pick each parent from AA, AO, BB, BO, AB and OO. A and B are codominant, so AB is a blood group of its own, and O is recessive.
• X-linked traits. Write the mother as XAXa and the father as XAY or XaY. A father passes his X only to daughters and his Y only to sons, so the tool reports daughters and sons separately.
• Gene drive note. A homing gene drive copies itself onto the partner chromosome in the germline. If a share e of the wild-type copies gets converted, a heterozygous carrier crossed with a wild type passes the drive to (1 + e) / 2 of its offspring. At e = 0 that is Mendel's 50%; at e = 0.9 it is 95%.

Worked example

The tool opens on Aa × Aa. Each parent makes A and a gametes, and the four cells read AA, Aa, Aa and aa: a genotype ratio of 1 AA : 2 Aa : 1 aa. Three of the four cells hold at least one A, so the phenotypes split 3 dominant to 1 recessive, the ratio Mendel counted in his second-generation peas.

Two genes: AaBb × AaBb. Each parent makes four kinds of gamete (AB, Ab, aB, ab), so the square has 16 cells holding nine different genotypes. Grouped by appearance, they give the classic 9:3:3:1: nine A_ B_, three A_ bb, three aa B_ and one aa bb.

Blood groups: AO × BO fills its four cells with AB, AO, BO and OO. The children's blood groups are A, B, AB and O in equal shares, a quarter each, including O children from an A parent and a B parent.

X-linked: XHXh × XHY, the textbook pattern for a recessive trait on the X. Half of the sons get the mother's Xh and show the recessive trait. Half of the daughters are carriers who show the dominant trait, and none shows the recessive one, because every daughter gets her father's XH.

The same arithmetic explains why seed saved from an F1 hybrid does not come true: the hybrid is heterozygous at many genes, so its offspring segregate like the Aa × Aa cross. If you save seed anyway, the seed viability calculator helps with the sowing.

What it can't tell you

A Punnett square gives probabilities, not outcomes. A 3:1 ratio means each child has a three in four chance of the dominant trait, not that a family of four will split three and one.

Genes close together on one chromosome tend to be inherited together (linkage), which breaks the independent sorting the calculator assumes. The letter mode also assumes simple dominance, so incomplete dominance and genes that mask one another (epistasis) need working out by hand.

Most traits people ask about, from eye color to height to many disease risks, depend on several genes plus environment, and a square cannot predict them. The ABO mode leaves out the separate Rh factor (model it in the one-gene mode as D for positive and d for negative, a textbook simplification). Rare blood group variants also mean blood type alone never settles parentage. For questions about a real family's health, a genetic counselor is the person to ask.

The gene drive note covers a single generation. It ignores resistance alleles, fitness costs and population dynamics, which decide whether a real drive spreads. Our piece on gene drives and the case for caution explains why those matter.

Sources

• Gregor Mendel, Experiments on Plant Hybridization (1866), the pea crosses behind segregation and independent assortment.
• Reginald C. Punnett, the British geneticist who introduced the square in the early 1900s.
• Karl Landsteiner's description of the ABO blood groups (1901), plus any introductory genetics textbook on codominance and X-linkage.
• Austin Burt's 2003 paper in Proceedings of the Royal Society B, which proposed homing genes as a tool for controlling wild populations.

Questions

How do you do a Punnett square?

Write the alleles each parent can pass on along the top and down the side of a grid. Fill each cell with one allele from its row and one from its column, then count the cells of each genotype and divide by the total.

What is the 9:3:3:1 ratio?

It is the result of crossing two parents heterozygous for two genes (AaBb × AaBb). Out of 16 offspring, nine show both dominant traits, three and three show one of each, and one shows both recessive traits.

Can two type O parents have a type A child?

Under the simple ABO model, no: OO × OO gives only OO children. Rare genetic variants do exist, so any real case is a question for a blood group laboratory or a genetic counselor.

Why are X-linked recessive traits more common in males?

A son has one X chromosome, from his mother, so a single recessive allele is enough to show the trait. A daughter needs a recessive allele from both parents, which is less likely.

Can a Punnett square predict eye color?

Not reliably. Eye color depends on several genes, so the old model of brown dominant over blue is a simplification that real families break.