# How to do Punnett squares

Canonical: https://duckyhelper.com/learn/biology/punnett-squares/
Updated: 2026-10-01

A Punnett square is a grid that shows every way two parents' alleles can combine in their offspring. Write one parent's possible gametes across the top and the other's down the side, then fill each box with one allele from each. Count the boxes to get the expected genotype and phenotype ratios. For example, Aa × Aa gives 1 AA : 2 Aa : 1 aa, which is a 3 : 1 phenotype ratio when A is dominant.

## Key ideas

- **Gene and allele.** A gene is a stretch of DNA for a trait. Alleles are its versions, such as violet (P) or white (p) flowers in peas.
- **Genotype and phenotype.** The genotype is the pair of alleles (PP, Pp or pp). The phenotype is the trait you see (violet or white).
- **Dominant and recessive.** A dominant allele (capital letter) shows up whenever it is present. A recessive allele (lowercase) shows only in a homozygous individual (pp).
- **Homozygous and heterozygous.** Two of the same allele is homozygous (PP or pp). Two different alleles is heterozygous (Pp).
- **Law of segregation.** Each parent passes on exactly one of its two alleles for a gene, chosen at random.

Each box in a 2 × 2 square has a \(\tfrac{1}{4}\) chance. For genes on different chromosomes (independent assortment), multiply probabilities:

$$
P(\text{A and B}) = P(\text{A}) \times P(\text{B})
$$

## Worked examples

**Example 1: a monohybrid cross**

Problem: In peas, violet flowers (P) are dominant over white (p). Cross two heterozygous plants, Pp × Pp. Give the genotype and phenotype ratios.

1. Each parent makes two kinds of gametes: P and p.
2. Fill the 4 boxes: PP, Pp, pP (same as Pp) and pp.
3. Genotypes: 1 PP, 2 Pp, 1 pp. Phenotypes: PP and Pp are violet (3 boxes), pp is white (1 box).

Answer: Genotypes 1 PP : 2 Pp : 1 pp; phenotypes 3 violet : 1 white

**The Pp × Pp square**

|  | P | p |
| --- | --- | --- |
| **P** | PP | Pp |
| **p** | Pp | pp |

**Example 2: a test cross**

Problem: A violet plant could be PP or Pp. You cross it with a white plant (pp) and get 52 violet and 48 white offspring. What is its genotype?

1. If it were PP, every offspring would be Pp: 100% violet.
2. If it were Pp, the square gives 2 Pp and 2 pp: a 1 : 1 ratio of violet to white.
3. 52 : 48 is close to 1 : 1, and any white offspring at all means the parent carries p.

Answer: The violet parent is heterozygous, Pp

**Example 3: a dihybrid cross**

Problem: In peas, round seeds (R) are dominant over wrinkled (r), and yellow (Y) over green (y). Cross RrYy × RrYy. What fraction of offspring are wrinkled and green?

1. Each parent makes 4 gametes in equal amounts: RY, Ry, rY, ry. That makes a 4 × 4 square with 16 boxes.
2. Faster: treat each gene on its own. \(P(\text{rr}) = \tfrac{1}{4}\) and \(P(\text{yy}) = \tfrac{1}{4}\).
3. Multiply.

   $$
   P(\text{rryy}) = \tfrac{1}{4} \times \tfrac{1}{4} = \tfrac{1}{16}
   $$
4. The full phenotype ratio is 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green.

Answer: 1/16 of the offspring (the 9 : 3 : 3 : 1 ratio)

**Example 4: a sex-linked trait**

Problem: Red-green color blindness is recessive and on the X chromosome. A carrier mother (\(X^B X^b\)) and a father with normal vision (\(X^B Y\)) have children. What fraction of their sons are color blind?

1. Mother's gametes: \(X^B\) or \(X^b\). Father's gametes: \(X^B\) or Y.
2. Sons get Y from the father, so a son is \(X^B Y\) or \(X^b Y\), each with a \(\tfrac{1}{2}\) chance.
3. \(X^b Y\) has no second X to cover the recessive allele, so he is color blind. Daughters get the father's \(X^B\), so none are color blind.

Answer: 1/2 of the sons

## Common mistakes and how to fix them

- **Putting both alleles on one side.** Each gamete gets one allele per gene. Fix: write each parent's single-allele gametes on the edges.
- **Confusing genotype and phenotype ratios.** 1 : 2 : 1 is genotypes, 3 : 1 is phenotypes. Fix: read the question for which one it asks.
- **Treating the ratio as a promise.** A 3 : 1 ratio is a probability for each child. Four children could all be violet.
- **Writing dihybrid gametes wrong.** RrYy makes RY, Ry, rY and ry, never Rr or Yy. Fix: each gamete has one letter of each gene.

**Practice questions**

1. Cross Tt × tt. What is the chance that an offspring is tt?
   A. 0%
   B. 25%
   C. 50%
   D. 75%

   Answer: 50%. Tt makes T or t, and tt makes only t. The boxes are Tt, Tt, tt, tt: 2 of 4 are tt.

2. What genotype ratio does Aa × Aa give?
   A. 3 AA : 1 aa
   B. 1 AA : 2 Aa : 1 aa
   C. 1 AA : 1 aa
   D. All Aa

   Answer: 1 AA : 2 Aa : 1 aa. The four boxes are AA, Aa, aA and aa, and Aa and aA are the same genotype.

3. Two parents are both Dd. What fraction of their children are expected to be DD?

   Answer: 1/4. Only one of the four boxes is DD, so the chance is \(\tfrac{1}{4}\), or 25%.

4. Cross AaBb × aabb (a dihybrid test cross). What fraction of offspring is aabb?

   Answer: 1/4. \(P(\text{aa}) = \tfrac{1}{2}\) from Aa × aa, and \(P(\text{bb}) = \tfrac{1}{2}\) from Bb × bb. Multiply: \(\tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{4}\).

5. In snapdragons, flower color shows incomplete dominance: RR is red, RW is pink and WW is white. Two pink plants are crossed. What fraction of the offspring are pink?
   A. 1/4
   B. 1/2
   C. 3/4
   D. All of them

   Answer: 1/2. RW × RW gives 1 RR : 2 RW : 1 WW. With incomplete dominance, each genotype has its own color, so 2 of 4 are pink.

## Frequently asked questions

### Why do Punnett square ratios not match real families exactly?

Each child is a separate random event, like a coin flip. A 1/4 chance does not mean exactly one in four children. Ratios match better in large numbers, which is why Mendel counted thousands of pea plants.

### Do I have to draw a 16-box square for a dihybrid cross?

No. If the two genes assort independently, solve each gene with a small 2 × 2 square and multiply the probabilities. That is faster and makes fewer mistakes. Draw the 16-box square when your teacher asks for it or to check the 9 : 3 : 3 : 1 pattern.

### What is the difference between incomplete dominance and codominance?

In incomplete dominance the heterozygote is a blend, like pink snapdragons from red and white. In codominance both alleles show fully, like AB blood type, where both A and B markers are on the red blood cells.

## Sources

- [OpenStax Biology 2e, 12.2 Characteristics and Traits](https://openstax.org/books/biology-2e/pages/12-2-characteristics-and-traits), accessed 2026-10-01
- [OpenStax Biology 2e, 12.3 Laws of Inheritance](https://openstax.org/books/biology-2e/pages/12-3-laws-of-inheritance), accessed 2026-10-01

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## Try asking Ducky

- "Check my Punnett square. Did I set up the gametes right for RrYy?"
- "I got 3:1 but the answer key says 1:2:1. Which one did the question ask for?"
- "Give me a sex-linked cross to try, and let me fill in the square first."

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