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How to Read a Punnett Square

A Punnett square is a probability table. Each parent's possible alleles go along an edge, every box is one equally likely combination, and the ratios you read off it are the probabilities for each offspring.

Setting one up

  • Write one parent's two alleles along the top, one per column.
  • Write the other parent's two alleles down the side, one per row.
  • Fill each box by combining its row and column allele.
  • Write the dominant allele first in each box, so Aa rather than aA.

Genotype versus phenotype

The genotype is the allele pair, such as Aa. The phenotype is the visible trait it produces. A dominant allele masks a recessive one, so AA and Aa look the same, which is why a 1:2:1 genotype ratio shows up as a 3:1 phenotype ratio.

Each offspring is independent

The square gives probabilities, not a guaranteed distribution. A 1 in 4 chance means each child independently has that chance. Three unaffected children do not make the fourth more likely to be affected.

Worked examples

Example 1

Question

Two heterozygous parents (Aa x Aa) have a child. What are the genotype and phenotype ratios?

Answer

Genotypes 1 AA : 2 Aa : 1 aa; phenotypes 3 dominant : 1 recessive

Steps

  1. 1Put A and a along the top, and A and a down the side.
  2. 2The four boxes come out as AA, Aa, Aa, and aa.
  3. 3Genotype ratio: 1 AA to 2 Aa to 1 aa.
  4. 4AA and Aa both show the dominant trait, so three boxes look dominant.
  5. 5Only aa shows the recessive trait, giving a 3:1 phenotype ratio, or a 25% chance of the recessive trait.

Example 2

Question

A heterozygous parent is crossed with a homozygous recessive one (Aa x aa). What fraction of offspring show the recessive trait?

Answer

One half, 50%

Steps

  1. 1Top edge: A and a from the heterozygous parent.
  2. 2Side edge: a and a from the homozygous recessive parent.
  3. 3The four boxes are Aa, aa, Aa, aa.
  4. 4Two of the four are aa, so 50% show the recessive trait.
  5. 5This is a test cross: the 50-50 split reveals that the dominant-looking parent was heterozygous.

If the dominant parent had been AA, no offspring would show the recessive trait. That is exactly what a test cross is for.

Example 3

Question

A carrier mother (X^H X^h) and an unaffected father (X^H Y) have children. What proportion of sons are affected?

Answer

Half of the sons, which is one quarter of all children

Steps

  1. 1Mother's gametes: X^H and X^h. Father's gametes: X^H and Y.
  2. 2The four boxes are X^H X^H, X^H Y, X^H X^h, and X^h Y.
  3. 3Daughters are X^H X^H and X^H X^h: unaffected, though one is a carrier.
  4. 4Sons are X^H Y and X^h Y: one unaffected, one affected.
  5. 5So half the sons are affected, and a quarter of all the children.

Common mistakes

Reading the genotype ratio when the question asked for phenotypes.

1:2:1 is genotypes; 3:1 is phenotypes. Read which one the question wants before answering.

Putting both alleles of one parent on the same side.

One parent per edge. Both parents' alleles on one axis produces nonsense boxes.

Assuming a 3:1 ratio guarantees three dominant children in four.

It is a probability for each child independently, not a quota to be filled.

Treating a sex-linked cross like an ordinary one.

Track the X and Y explicitly. Males have only one X, so a single recessive allele shows.

Practice it

Work these out first, then open the answer. Stuck halfway? Select the problem and ask Solvecoon for the step you are missing.

  • 1. Bb x bb. What percentage of offspring show the recessive trait?

    Show answer

    50%. Two of the four boxes are bb.

  • 2. Two brown-eyed parents have a blue-eyed child, where blue is recessive. What are the parents' genotypes?

    Show answer

    Both are heterozygous, Bb. Each must have passed on a recessive allele.

  • 3. AA x aa. What are the offspring genotypes?

    Show answer

    All four boxes are Aa, so every offspring is heterozygous and shows the dominant trait.

Questions people ask

What do the capital and lowercase letters mean?
Capital is the dominant allele, lowercase the recessive one, and both use the same letter so the pairing is obvious.
How do I do a cross with two traits?
Use a four by four square with each parent's four possible gamete combinations, which gives the classic 9:3:3:1 phenotype ratio for a dihybrid cross.
What is a carrier?
Someone heterozygous for a recessive condition. They do not show it, but they can pass the allele on.
Why do sex-linked conditions affect males more?
Males have one X chromosome, so a single recessive allele on it is expressed with no second copy to mask it.
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