What Is a Punnett Square?

A Punnett square is a simple grid used to predict the possible genotypes — and therefore phenotypes — of offspring from two parent organisms. It was devised by British geneticist Reginald Crundall Punnett in the early 1900s, after he and William Bateson were working through Mendel’s rediscovered laws of inheritance.

The grid works because of Mendel’s Law of Segregation: during the formation of gametes (egg and sperm), the two alleles for any given gene separate so that each gamete carries only one allele. A Punnett square models all the possible combinations when those gametes fuse at fertilization.

You’ll encounter Punnett squares in virtually every genetics unit — from AP Biology free-response questions to college-level genetics exams and MCAT biochemistry passages. Understanding them deeply (not just mechanically) will save you many points.

Key Terms You Must Know

Before filling in your first grid, make sure these definitions are solid in your memory:

Allele
One of two or more versions of a gene. Represented by a letter (e.g., A or a).
Dominant allele
Masks the effect of the recessive allele when present. Written as a capital letter (e.g., A).
Recessive allele
Only expressed when no dominant allele is present. Written as a lowercase letter (e.g., a).
Genotype
The actual allele combination an organism has (e.g., AA, Aa, aa).
Phenotype
The observable trait expressed (e.g., “tall” or “short,” “purple flower” or “white flower”).
Homozygous
Two identical alleles: AA (homozygous dominant) or aa (homozygous recessive).
Heterozygous
Two different alleles: Aa. Sometimes called a “carrier” for recessive traits.
Gamete
A reproductive cell (sperm or egg) that carries one allele per gene.
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AP Bio exam tip: In free-response questions, always define your symbols (e.g., “Let T = tall allele, t = short allele”) before drawing your Punnett square. You lose points if the grader can’t follow your logic.

Monohybrid Cross: Step-by-Step

A monohybrid cross looks at the inheritance of a single gene with two alleles. The most classic example is Mendel’s pea plant height: the tall allele (T) is dominant over the short allele (t).

Example: Aa × Aa (heterozygous × heterozygous)

This is the most common exam cross — two heterozygous parents. Follow these steps:

1
Identify the parent genotypes. Parent 1: Aa — Parent 2: Aa. Both are heterozygous; both have one dominant and one recessive allele.
2
List each parent’s possible gametes. Each parent can produce two types of gametes: A or a. Place Parent 1’s gametes across the top of the grid. Place Parent 2’s gametes down the left side.
3
Fill in the four cells. Each cell combines the column header (one gamete) with the row header (other gamete). Read column-first, then row: the column allele always goes first.
4
Count genotypes and determine phenotypes. Count how many of each genotype appear, then classify phenotypes using the dominance rule.

Here is the completed Punnett square for Aa × Aa:

A a
A AA Aa
a Aa aa

Genotype & Phenotype Ratios for Aa × Aa

Genotypic Ratio
1 AA — Homozygous dominant (25%)
2 Aa — Heterozygous (50%)
1 aa — Homozygous recessive (25%)
Phenotypic Ratio
3 Dominant phenotype — AA and Aa both express the dominant trait (75%)
1 Recessive phenotype — aa expresses the recessive trait (25%)

The classic result: 3:1 phenotypic ratio. This is Mendel’s famous ratio — 3 tall : 1 short pea plants — and it appears on nearly every genetics exam.

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Common mistake: Students often confuse genotypic and phenotypic ratios. Remember — Aa and AA look the same on the outside (same phenotype) even though their genotypes are different. The phenotypic ratio (3:1) collapses two genotypes into one phenotype class.

Other Common Monohybrid Crosses

CrossGenotypic RatioPhenotypic RatioExam tip
AA × aaAll AaAll dominantAll offspring look like the dominant parent
Aa × aa1 Aa : 1 aa1 dominant : 1 recessiveTest cross! Used to find unknown genotype
AA × AAAll AAAll dominantNo variation in offspring
AA × Aa1 AA : 1 AaAll dominantAll dominant phenotype, but ½ are heterozygous
Aa × Aa1 AA : 2 Aa : 1 aa3 dominant : 1 recessiveThe classic Mendel ratio ★
aa × aaAll aaAll recessiveOnly recessive offspring

Dihybrid Cross: Step-by-Step

A dihybrid cross tracks the inheritance of two genes simultaneously. This is where most students get confused — but the logic is the same as a monohybrid cross, just scaled up.

The key insight is Mendel’s Law of Independent Assortment: genes on different chromosomes are inherited independently of each other. This is what makes the dihybrid cross work the way it does.

Example: AaBb × AaBb

Both parents are heterozygous for two genes: A/a and B/b. Let’s say A = round seed (dominant), a = wrinkled seed; B = yellow seed (dominant), b = green seed.

1
Find all possible gametes using FOIL. An AaBb parent can make 4 types of gametes: AB, Ab, aB, ab. Use the FOIL method — combine each A allele with each B allele: (A or a) × (B or b) → AB, Ab, aB, ab.
2
Build a 4×4 grid. Place one parent’s 4 gametes across the top, the other parent’s 4 gametes down the left side. This creates 16 possible combinations.
3
Fill in all 16 cells. Each cell = column gamete + row gamete. Alphabetize within each gene pair: if column is aB and row is Ab, the offspring genotype is AaBb (not aAbB).
4
Classify each cell by phenotype. An offspring shows the dominant trait for gene A if it has at least one A. Same rule for gene B. Count how many cells fall into each of the four phenotype classes.

The completed 4×4 Punnett square for AaBb × AaBb:

AB Ab aB ab
AB AABB AABb AaBB AaBb
Ab AABb AAbb AaBb Aabb
aB AaBB AaBb aaBB aaBb
ab AaBb Aabb aaBb aabb

The 9:3:3:1 Ratio Explained

Counting the 16 cells by phenotype class gives the famous 9:3:3:1 ratio:

Dihybrid Cross Phenotypic Ratio (AaBb × AaBb)
9 A_B_ — Dominant for both traits (round yellow) — 9/16
3 A_bb — Dominant for A, recessive for B (round green) — 3/16
3 aaB_ — Recessive for A, dominant for B (wrinkled yellow) — 3/16
1 aabb — Recessive for both traits (wrinkled green) — 1/16

The underscore notation (A_) means “at least one dominant allele here” — it includes both AA and Aa genotypes. In phenotype terms, you can’t tell them apart by looking.

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Shortcut: multiply monohybrid results. The 9:3:3:1 ratio is actually just the 3:1 ratio multiplied by itself. (3:1) × (3:1) = 9:3:3:1. This multiplication shortcut works for any dihybrid cross where both genes show simple dominance. On time-limited exams, use it instead of drawing the full 4×4 grid.

Special Cases & Exceptions

Not all genes follow simple Mendelian dominance. AP Biology and MCAT both test these extensions of Mendelian genetics:

Incomplete Dominance

Neither allele is fully dominant. Heterozygotes show a blended phenotype. Classic example: red flower (RR) × white flower (r’r’) → pink flower (Rr’). The phenotypic ratio for Rr’ × Rr’ is 1 red : 2 pink : 1 white — genotypic and phenotypic ratios are the same (1:2:1), unlike in simple dominance.

Codominance

Both alleles are fully expressed simultaneously. Example: blood type A (IAIA) × blood type B (IBIB) → all offspring are blood type AB (IAIB). Both the A and B antigens appear on red blood cells at the same time.

Sex-Linked Traits

Genes located on the X chromosome. Males (XY) have only one X chromosome, so they can’t be “carriers” of recessive X-linked traits — they either have it or they don’t. The Punnett square setup differs: you’ll write gametes as XA, Xa, and Y. Classic examples: color blindness, hemophilia.

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When the 9:3:3:1 ratio doesn’t appear: If a dihybrid cross produces a ratio like 9:7, 9:3:4, or 15:1, the two genes are likely showing gene interaction (epistasis) — where one gene masks or modifies the expression of another. Epistasis questions appear regularly in AP Bio FRQ.

Struggling with a specific Punnett square?

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Practice Problems

Test your understanding with these classic genetics crosses. Try to work through each one before checking your answer with the solver.

Monohybrid Crosses
  1. A homozygous dominant tall plant (TT) is crossed with a homozygous recessive short plant (tt). What are the genotypic and phenotypic ratios of the offspring?
  2. A heterozygous tall plant (Tt) is crossed with a short plant (tt). What fraction of offspring will be tall?
  3. Two parents each have genotype Bb, where B = black fur and b = brown fur. B is dominant. What percentage of offspring will have brown fur?
  4. In humans, freckles (F) is dominant over no freckles (f). A person with freckles whose parent had no freckles is crossed with a person without freckles. What are the possible genotypes and phenotypes?
Dihybrid Crosses
  1. In pea plants: R = round (dominant), r = wrinkled; Y = yellow (dominant), y = green. Cross RrYy × RrYy. How many of 160 offspring would you expect to be round and green?
  2. Cross AaBb × aabb. What are the four possible phenotype classes and their expected frequencies?
  3. Two genes assort independently. One gene shows incomplete dominance: RR = red, Rr = pink, rr = white. The other shows simple dominance: TT or Tt = tall, tt = short. Cross RrTt × RrTt. How many phenotypic classes are there?

Frequently Asked Questions

What is a Punnett square and when was it invented?

A Punnett square is a predictive grid that shows all possible genotypic outcomes of a genetic cross between two parents. It was developed by British geneticist Reginald Crundall Punnett around 1905, building on Gregor Mendel’s foundational work on pea plant inheritance from the 1860s.

What is the genotypic ratio for Aa × Aa?

For an Aa × Aa cross, the genotypic ratio is 1 AA : 2 Aa : 1 aa. This means 25% of offspring are homozygous dominant, 50% are heterozygous, and 25% are homozygous recessive. The phenotypic ratio (assuming simple dominance) is 3 dominant : 1 recessive.

How do you find gametes for a dihybrid parent?

For a parent with genotype AaBb, list all combinations of one allele from each gene: AB, Ab, aB, ab. A quick way is the FOIL method: treat each gene separately, then combine. A dihybrid heterozygote always produces 4 gamete types in equal proportions.

Why does a dihybrid cross give a 9:3:3:1 ratio?

The 9:3:3:1 ratio results from independent assortment of two genes. Each gene independently follows the 3:1 phenotypic ratio, and (3:1) × (3:1) = 9:3:3:1. The “9” represents offspring dominant for both traits; the two “3s” represent offspring dominant for one trait but recessive for the other; the “1” represents offspring recessive for both.

What is a test cross in genetics?

A test cross is a cross between an organism of unknown genotype (showing the dominant phenotype) and a homozygous recessive individual (aa). If any offspring show the recessive phenotype, the unknown parent must be heterozygous (Aa). If all offspring show the dominant phenotype, the unknown parent is likely homozygous dominant (AA). Test crosses are how Mendel figured out his crosses, and they appear frequently on AP Bio exams.

Can I solve Punnett squares online for free?

Yes — our Punnett Square Solver is completely free and requires no account. Enter any parent genotypes (monohybrid or dihybrid) and get the completed grid, genotype frequencies, and phenotype ratios with full explanations instantly.

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