Punnett Squares Explained: Predict Genes Step by Step

What is a Punnett square?

A Punnett square is a diagram, named after the geneticist Reginald Punnett, that predicts the offspring of a genetic cross. You write one parent's gametes (egg or sperm cells, each carrying one allele) along the top and the other parent's down the side. Every box is a possible child.

Some words you need:

• Gene: a section of DNA that codes for a trait, such as seed shape.
• Allele: one version of a gene. A capital letter (R) is the dominant allele and a lower-case letter (r) is the recessive one.
• Genotype: the pair of alleles an organism has, such as Rr.
• Phenotype: the trait you can see, such as round seeds.
• Homozygous: two identical alleles (RR or rr). Heterozygous: two different alleles (Rr), also called a hybrid.

A dominant allele shows in the phenotype even when only one copy is present. A recessive allele only shows when there are two copies.

How to do a Punnett square step by step

Use these steps for a monohybrid cross, which follows one gene:

1. Write each parent's genotype, for example Rr × Rr.
2. Split each parent into gametes: Rr gives R or r.
3. Draw a 2 × 2 grid. Put one parent's gametes across the top and the other's down the side.
4. Fill each box with the allele from its column and the allele from its row.
5. Count the genotypes (RR, Rr, rr) and then the phenotypes.

For Rr × Rr the four boxes are RR, Rr, Rr, rr. That is 1 : 2 : 1 for genotypes. Because R is dominant, RR and Rr both look round, so the phenotype ratio is 3 round : 1 wrinkled.

Why does the Punnett square 3:1 ratio appear?

Two hybrid parents each make two kinds of gamete in equal numbers. That makes four equally likely pairings. Three of them contain at least one dominant allele, so three quarters (75%) of children show the dominant trait and one quarter (25%) show the recessive trait.

This was first found by Gregor Mendel, who crossed pea plants in the 1860s and counted about 3 round seeds for every 1 wrinkled seed in the second generation. A 3:1 ratio is a probability, not a promise. A family with four children can easily have two, or none, with the recessive trait. Only a large sample, such as hundreds of offspring, comes close to 3:1.

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

A dihybrid cross follows two genes at once, for example seed shape (R/r) and seed colour (Y/y). Cross two parents that are both RrYy. Each parent now makes four gamete types: RY, Ry, rY, ry. The grid is 4 × 4, which has 16 boxes.

The phenotype ratio is:

• 9 round and yellow
• 3 round and green
• 3 wrinkled and yellow
• 1 wrinkled and green

That is the 9:3:3:1 ratio. It only works when the two genes sit on different chromosomes and are inherited independently, which Mendel called the law of independent assortment.

What about incomplete dominance and sex-linked traits?

Not every trait is simple dominant and recessive.

• Incomplete dominance: neither allele wins. A red snapdragon (RR) crossed with a white one (WW) gives pink (RW) flowers. Crossing two pink plants gives 1 red : 2 pink : 1 white, so the phenotype ratio matches the genotype ratio.
• Sex-linked traits: the gene sits on the X chromosome. Females are XX and males are XY, so a male with one faulty X allele shows the trait because he has no second X to cover it. Red-green colour blindness and haemophilia work this way, and they are more common in males.

Common mistakes with Punnett squares

• Writing the same allele twice for a pure parent. An RR parent makes only R gametes, so the grid has repeated columns.
• Mixing up genotype and phenotype. Rr is a genotype. "Round" is a phenotype.
• Reading 3:1 as a guarantee. Each child is an independent 75% / 25% chance, whatever the older children are like.
• Forgetting that a hybrid parent makes two gamete types. Rr makes R and r, not Rr.
• Using a dihybrid grid with only 4 boxes. A dihybrid cross needs 16.

Frequently asked questions

What does a Punnett square show?

A Punnett square shows every possible allele combination that two parents can pass to their children, and how likely each one is. From the boxes you can read the chance of each genotype and each phenotype, such as a one in four chance of a recessive trait.

What is the difference between genotype and phenotype?

Genotype is the pair of alleles an organism carries, such as Rr. Phenotype is the trait you can observe as a result, such as round seeds. Two organisms with different genotypes (RR and Rr) can share the same phenotype when one allele is dominant.

How many boxes does a dihybrid Punnett square have?

A dihybrid Punnett square has 16 boxes. Each parent heterozygous for two genes makes four gamete types, and 4 × 4 = 16 pairings. A monohybrid square has only 4 boxes because each parent makes two gamete types.

Why is the 3:1 ratio not exact in real families?

Each child is an independent chance event, like a coin toss. The 3:1 ratio is the probability for each child, not the exact number in a small family. The ratio only appears reliably when you count a large number of offspring.

Can a Punnett square predict everything about a child?

No. It works for single genes with clear inheritance patterns. Many human traits, such as height, depend on many genes and on the environment, so a Punnett square can only give rough odds for them.

Try it yourself

Open the Punnett Square tool and pick Monohybrid. Set both parents to Hybrid and press Watch it fertilise to see the 3:1 ratio build up. Then switch to Dihybrid to see all 16 boxes and the 9:3:3:1 ratio, and drag the Offspring sampled slider up to 400 to watch a small sample settle towards the true ratio. To see where alleles come from, read how DNA makes a protein and how natural selection works.