This Punnett square calculator builds the grid for a monohybrid (2×2), dihybrid (4×4) or trihybrid (8×8) cross and gives the genotype and phenotype ratios and the probability of each outcome. Choose each parent's genotype for up to three genes, and set each gene to complete dominance, incomplete dominance or codominance. You can also switch to an X-linked cross to see results for daughters and sons separately. The coloured boxes group offspring by phenotype, so you can use it as a Punnett square maker or generator for homework and check your own grid box by box.
How to use the Punnett square generator
- Pick autosomal genes or an X-linked (sex-linked) trait.
- Choose how many genes to follow. One gene gives a 2×2 square, two genes a 4×4 square and three genes an 8×8 square.
- For each gene, set the letter and each parent's genotype: homozygous dominant (AA), heterozygous (Aa) or homozygous recessive (aa).
- Choose the inheritance pattern for each gene. The phenotype groups change to match.
- Read the square, the ratios, the probability tables and the chart. Hover over a box to see its phenotype. Copy the link to share the exact cross.
Key terms
NHGRI's Talking Glossary defines an allele as one of two or more versions of a DNA sequence at a given location. You inherit one allele from each parent: two identical alleles make you homozygous, two different ones make you heterozygous. When the alleles differ and only one is expressed, that one is dominant and the masked one is recessive. A recessive trait appears only when both alleles are recessive. By convention the dominant allele takes a capital letter (A) and the recessive allele the lower case of the same letter (a). The genotype is the pair of alleles, such as Aa, and the phenotype is the observable trait.
Monohybrid cross: the 2×2 Punnett square
Each parent passes on one of its two alleles, so a heterozygote Aa makes A and a gametes in equal numbers. Put one parent's gametes on top and the other's down the side, then fill each box with the alleles from its row and column. For Aa × Aa the boxes are AA, Aa, Aa and aa. OpenStax Biology 2e gives the expected results for Mendel's pea colour cross, Yy × Yy: a 1 YY : 2 Yy : 1 yy genotype ratio and a phenotype ratio of 3 yellow : 1 green. Each box is a 1-in-4 (25%) chance for each offspring.
Test cross
An organism showing a dominant trait could be AA or Aa. To tell which, cross it with a homozygous recessive (aa). OpenStax notes that an AA parent gives all heterozygous, dominant-looking offspring, while an Aa parent gives a 1:1 ratio of heterozygotes and recessive homozygotes. Set parent 2 to aa in the calculator to see both outcomes.
Punnett square for a dihybrid cross (4×4)
With two genes, each gamete carries one allele of each. By Mendel's law of independent assortment, as OpenStax puts it, every combination of alleles is equally likely to end up in a gamete. An AaBb parent therefore makes four gamete types in equal proportion: AB, Ab, aB and ab. The square is 4×4 = 16 boxes, and for AaBb × AaBb OpenStax reports the classic 9:3:3:1 phenotype ratio: 9 showing both dominant traits, 3 dominant for the first gene only, 3 dominant for the second only, and 1 recessive for both. There are 9 distinct genotypes in a 1 : 2 : 1 : 2 : 4 : 2 : 1 : 2 : 1 ratio.
To list gametes without missing any, use the FOIL pattern for AaBb: first (AB), outer (Ab), inner (aB), last (ab). A parent that is homozygous for a gene, such as AABb, makes only two gamete types (AB and Ab). A 4×4 grid still works, with the repeated gametes filling duplicate rows.
Trihybrid crosses and the product rule
A parent heterozygous for n genes makes 2ⁿ kinds of gamete (the formula in OpenStax's Table 12.5), so a trihybrid AaBbCc makes 8 and the full square has 64 boxes. The calculator draws all 64 and counts them for you. OpenStax gives the trihybrid F₂ phenotype ratio as 27:9:9:9:3:3:3:1.
By hand, the forked-line method is quicker. Because the genes assort independently, work out each gene on its own, then multiply. That is the product rule. For AaBbCc × AaBbCc the chance of an aabbcc offspring is ¼ × ¼ × ¼ = 1/64. The chance of an offspring dominant for all three traits is ¾ × ¾ × ¾ = 27/64. The chance of the exact genotype AaBbCc is ½ × ½ × ½ = 1/8, or 8 of the 64 boxes.
| Cross | Boxes | Genotypes | Genotype ratio | Phenotype ratio |
|---|---|---|---|---|
| Aa × Aa (monohybrid) | 4 | 3 | 1 : 2 : 1 | 3 : 1 |
| Aa × aa (test cross) | 4 | 2 | 1 : 1 | 1 : 1 |
| AA × aa | 4 | 1 | 1 | 1 |
| Aa × Aa, incomplete dominance | 4 | 3 | 1 : 2 : 1 | 1 : 2 : 1 |
| AaBb × AaBb (dihybrid) | 16 | 9 | 1 : 2 : 1 : 2 : 4 : 2 : 1 : 2 : 1 | 9 : 3 : 3 : 1 |
| AaBb × aabb (dihybrid test cross) | 16 | 4 | 1 : 1 : 1 : 1 | 1 : 1 : 1 : 1 |
| AaBb × Aabb | 16 | 6 | 1 : 1 : 2 : 2 : 1 : 1 | 3 : 3 : 1 : 1 |
| AaBbCc × AaBbCc (trihybrid) | 64 | 27 | see calculator | 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1 |
Genotype ratios are listed in the textbook order, homozygous dominant first (AA : Aa : aa, or AABB : AABb : AAbb and so on). Phenotype ratios are listed largest group first under complete dominance, and in the same AA : Aa : aa order when a gene shows incomplete dominance or codominance.
Incomplete dominance and codominance
Not every heterozygote looks like the dominant parent. In incomplete dominance it has an intermediate phenotype. OpenStax's example is the snapdragon: a red parent (CᴿCᴿ) crossed with a white parent (CᵂCᵂ) gives pink offspring (CᴿCᵂ), and crossing two pinks gives a 1 red : 2 pink : 1 white ratio. In codominance both alleles are fully expressed together. NHGRI's glossary uses the AB blood type, where the A and B alleles both show, and OpenStax uses the human MN blood groups. In both patterns the heterozygote is its own phenotype, so the phenotype ratio matches the genotype ratio. Choose either option for a gene and the calculator splits Aa into its own colour.
X-linked (sex-linked) Punnett squares
NHGRI describes X-linked traits as those influenced by genes on the X chromosome. Females (XX) carry two copies of such a gene. OpenStax explains that males (XY) are hemizygous, with only one allele for any X-linked characteristic, so a single recessive allele shows in a son. In the square, the mother's two X chromosomes go down the side and the father's X and Y across the top. Daughters always receive their father's X, and sons always receive his Y. That is why, as MedlinePlus notes, fathers cannot pass X-linked traits to their sons.
For a carrier mother (XᴬXᵃ) and an unaffected father (XᴬY), the four boxes are XᴬXᴬ, XᴬXᵃ, XᴬY and XᵃY. Among daughters, half are unaffected and half are carriers; among sons, half are unaffected and half show the trait. The calculator reports these by sex, because the overall 3:1 ratio hides the difference. MedlinePlus also notes that males are affected by X-linked recessive disorders much more often than females, and the square shows why.
How to read the results
- Box count over the total is the probability for each offspring. 4 of 16 boxes is 25%.
- Ratios are simplified. 12:4 out of 16 is shown as 3:1.
- Every birth is independent. A 1-in-4 chance does not mean exactly one child in four will be affected.
- Colours are phenotypes, not genotypes. AA and Aa share a colour under complete dominance because they look the same.
Common mistakes
- Putting both alleles of a gene in one gamete. A gamete carries one allele per gene: A or a, never Aa.
- Missing gamete combinations. AaBb makes four types. Using only AB and ab (two gametes) gives the wrong ratio.
- Treating linked genes as independent. The 9:3:3:1 ratio assumes the genes assort independently. OpenStax notes that genes close together on the same chromosome are linked and break this rule.
- Forgetting the Y in sex-linked crosses. Sons get no X from their father.
- Mixing letters. Use the same letter for the two alleles of a gene (A and a), and different letters for different genes.
Punnett squares turn genetics into probability. For related maths try the mixed fraction calculator for multiplying fractions like ¾ × ¾, or the z-score calculator for traits that vary continuously. Biology students may also want the AP Biology score calculator.
Frequently asked questions
What is a Punnett square?
A grid that lists one parent's possible gametes along the top and the other parent's down the side. Each box combines one gamete from each parent, and because every gamete is equally likely, each box is an equally likely offspring genotype. Counting boxes gives the genotype and phenotype ratios.
How do you do a Punnett square for a dihybrid cross?
Write each parent's four gamete types, such as AB, Ab, aB and ab for AaBb. Put one set along the top and the other down the side of a 4×4 grid, and fill each of the 16 boxes with the combined alleles. For AaBb × AaBb you get 9 genotypes and the 9 : 3 : 3 : 1 phenotype ratio that OpenStax Biology 2e describes for Mendel's peas.
What is a 4x4 Punnett square used for?
A 4×4 square is the standard layout for a dihybrid cross, two genes at once, where each parent is heterozygous for both and makes four kinds of gamete. It also works when only one parent is a double heterozygote, though some rows or columns then repeat.
What is the phenotypic ratio of a monohybrid cross?
For two heterozygotes (Aa × Aa) with complete dominance, 3 dominant : 1 recessive. The genotype ratio is 1 AA : 2 Aa : 1 aa. With incomplete dominance or codominance the heterozygote looks different, so the phenotype ratio becomes 1 : 2 : 1, the same as the genotype ratio.
What is a trihybrid Punnett square?
A cross of three genes. A parent heterozygous for all three (AaBbCc) makes 2³ = 8 kinds of gamete, so the full square is 8×8 = 64 boxes. For AaBbCc × AaBbCc there are 27 genotypes and a 27:9:9:9:3:3:3:1 phenotype ratio, as OpenStax Biology 2e states.
How do you do a Punnett square for sex-linked (X-linked) traits?
Write the mother's two X chromosomes down the side (for example Xᴬ and Xᵃ) and the father's X and Y across the top. Daughters get an X from each parent; sons get the mother's X and the father's Y. For a carrier mother and an unaffected father, half the sons are expected to be affected and half the daughters to be carriers.
What is the difference between incomplete dominance and codominance?
In incomplete dominance the heterozygote is intermediate, like OpenStax's pink snapdragons from red × white parents. In codominance both alleles show in full at the same time. NHGRI's example is AB blood type, and OpenStax's is the human MN blood group.
What is a test cross?
Crossing an individual that shows the dominant trait with a homozygous recessive one. If all offspring show the dominant trait, the unknown parent was probably homozygous dominant. A 1:1 split means it was heterozygous.
Are Punnett square results guaranteed?
No. Each box is a probability for each child independently, not a count for a family. Two heterozygous parents have a 25% chance of a homozygous recessive child at every birth, whatever earlier children were like. Real families of a few children often differ from the ratio by chance.
When does a Punnett square give the wrong answer?
When its assumptions fail. Genes close together on the same chromosome are linked and don't assort independently, as OpenStax notes. Traits controlled by many genes, affected by the environment, or showing lethal alleles or incomplete penetrance also depart from the simple ratios.
Sources & method
- OpenStax Biology 2e, §12.2 Characteristics and Traits — monohybrid ratios, test cross, incomplete dominance, codominance, X-linked traits
- OpenStax Biology 2e, §12.3 Laws of Inheritance — dihybrid 9:3:3:1, independent assortment, forked-line method, trihybrid 27:9:9:9:3:3:3:1, linkage
- NIH NHGRI Talking Glossary — Allele
- NIH NHGRI Talking Glossary — Dominant
- NIH NHGRI Talking Glossary — Recessive
- NIH NHGRI Talking Glossary — Codominance
- NIH NHGRI Talking Glossary — X-Linked
- NIH MedlinePlus Genetics — What are the different ways a genetic condition can be inherited?
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