Punnett Square Calculator
Any cross from Aa × Aa to a 256-square tetrahybrid, with ratios and a χ² test.
Phenotypes
| Phenotype | Squares | Fraction | Probability |
|---|
Punnett square
Genotypes
| Genotype | Phenotype | Squares | Fraction | Probability |
|---|
Forked-line method
Each gene on its own, then the products of its probabilities — the same answer without drawing the square.
χ² test of your counts
Type how many offspring of each phenotype you counted, to test them against the expected ratio.
| Phenotype | Observed | Expected | (O − E)² ÷ E |
|---|
About the Punnett Square Calculator
A Punnett square lists every way the gametes of two parents can combine, so you can read off the genotypes and phenotypes of their offspring and how likely each is. This calculator draws the square for crosses of one to four genes: monohybrid (2 × 2), dihybrid (4 × 4), trihybrid (8 × 8) and tetrahybrid (16 × 16, 256 squares). It handles several kinds of inheritance:
- complete, incomplete and codominance;
- multiple alleles, from the ABO blood groups to any allelic series you type;
- X-linked traits, with results for daughters and sons.
You get the genotype and phenotype ratios with fractions and probabilities, a colour-coded square, and the forked-line (branch) breakdown. A χ² test compares offspring you have counted with the expected ratio. Type a cross such as AaBb × aabb, or start from an example — Mendel’s peas, snapdragons, blood groups or fruit-fly eye colour.
How to use it
- Type the cross in letter notation — one letter per gene, capital for the dominant allele, such as AaBb × aabb (write X-linked genes as XAXa × XAY) — or press an example.
- For each gene, choose the kind of inheritance (complete, incomplete or codominance, ABO, or a custom series of alleles), add trait names if you like (tall/short), and check both parents’ genotypes.
- Read the phenotype and genotype ratios, then the square itself. Press a phenotype under the square to outline its squares. The forked-line list shows the same probabilities gene by gene.
- To test real data, type the number of offspring you counted in each class: the χ² test gives the p-value and says whether the counts fit the expected ratio.
Examples
Pp × Pp, violet dominant over white
3 violet : 1 white; genotypes 1 PP : 2 Pp : 1 pp
Mendel counted 705 violet and 224 white: χ² = 0.39, p = 0.53, consistent with 3 : 1.
RrYy × RrYy, round/wrinkled and yellow/green
9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green
Mendel’s 315, 108, 101 and 32 seeds give χ² = 0.47, p = 0.93.
Snapdragons CᴿCᵂ × CᴿCᵂ
1 red : 2 pink : 1 white
Blood groups Iᴬi × Iᴮi
A, B, AB and O, each with probability 1/4
Fruit-fly eyes XᵂXʷ × XᵂY (red dominant)
All daughters red-eyed; sons half red-eyed, half white-eyed
AaBbCc × AaBbCc
64 squares; 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1
Common uses
- Genetics homework and exam practice, from simple monohybrid crosses to trihybrid and tetrahybrid problems.
- Checking a hand-drawn Punnett square, or using the forked-line method when a square would be too big.
- Testing lab or classroom counts (fruit flies, Wisconsin Fast Plants, maize ears) against a Mendelian ratio with χ².
- Explaining blood-group inheritance or X-linked traits such as fruit-fly eye colour.
How the square works
Each parent passes on one allele of every gene, and the two alleles separate with equal chance — Mendel’s law of segregation. Different genes on different chromosomes are inherited independently — the law of independent assortment. So a parent heterozygous for n genes makes 2ⁿ kinds of gamete in equal numbers (AaBb makes AB, Ab, aB and ab), while a homozygous gene adds only one kind. Crossing two such parents gives 3ⁿ genotypes and, with complete dominance, 2ⁿ phenotypes (OpenStax Table 12.5) — 81 and 16 for a tetrahybrid cross. The square crosses the gametes of the two parents, and every square is equally likely. A phenotype that fills 9 of 16 squares therefore has a probability of 9/16 = 56.25 %.
Dominance, multiple alleles and X-linked genes
The kinds of inheritance are those described in OpenStax Biology 2e (ch. 12):
- Complete dominance: heterozygotes look like the dominant homozygote (A_ means AA or Aa).
- Incomplete dominance: heterozygotes are intermediate — snapdragons CᴿCᵂ are pink.
- Codominance: both alleles show, as in the MN blood groups (LᴹLᴺ).
- Multiple alleles: a gene can have more than two alleles in a population, ranked in an allelic series. The ABO blood groups have Iᴬ and Iᴮ codominant and both dominant over i. You can type any series with > (dominant over), = (codominant) and ~ (incomplete), such as the rabbit coat-colour series C > c^ch > c^h > c.
- X-linked genes are carried on the X chromosome. A father (XY) has only one copy, and gives his X to daughters and his Y to sons, so the results are given separately for daughters and sons.
Forked-line method and χ² test
With independent assortment, the probability of a combination is the product of each gene’s own probabilities: 3/4 round × 3/4 yellow = 9/16 round and yellow. The forked-line list shows this for every combination. It is the quick way to answer questions about trihybrid and larger crosses.
Pearson’s χ² goodness-of-fit test compares observed counts O with expected counts E = n × expected proportion: χ² = Σ (O − E)² ÷ E, with k − 1 degrees of freedom for k phenotype classes. The p-value is the chance of a deviation at least that large if the ratio is right. If it is below the significance level you choose (usually 0.05), the counts do not fit. The p-value comes from the regularised incomplete gamma function (Abramowitz & Stegun §6.5). NIST notes the approximation needs every expected count to be at least 5, and the calculator warns when one is not.
What a Punnett square cannot predict
Many familiar traits are polygenic: they depend on many genes and on the environment. MedlinePlus Genetics explains that eye colour was once thought to follow a single brown-over-blue gene, but that model is too simple. Several genes are involved, and two blue-eyed parents can have a brown-eyed child. Height and skin colour are similar. A one- or two-gene Punnett square gives falsely precise answers for such traits. Use it for single-gene traits, or for textbook models labelled as such.
Sources
- OpenStax, Biology 2e: 12.1 Mendel’s Experiments, 12.2 Characteristics and Traits, 12.3 Laws of Inheritance.
- G. Mendel, Experiments in Plant Hybridisation, in an English translation at the Internet Archive — the 705 : 224 and 315 : 108 : 101 : 32 counts (the first pair is also in OpenStax 12.1).
- MedlinePlus Genetics (US National Library of Medicine): Is eye color determined by genetics? and inheritance patterns (ABO is codominant).
- NIST/SEMATECH e-Handbook of Statistical Methods: chi-square goodness-of-fit test and critical values.
Limitations
- Genes are assumed to be unlinked (independent assortment). Genes close together on a chromosome, and crossing over, give other ratios.
- Only one gene can be X-linked, and the XY system is assumed. In birds the female has the two different sex chromosomes, so their sex-linked crosses are the other way round.
- Epistasis (genes that change each other’s effect), lethal genotypes, incomplete penetrance and environmental effects are not modelled; for interacting genes, group the phenotype classes yourself.
- Up to 4 genes and up to 6 alleles per gene; the χ² test needs at least two phenotype classes.
Privacy
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Frequently asked questions
How do you make a Punnett square?
List each parent’s possible gametes — one allele of each gene, every combination — along the top and the side. Fill each square with the alleles from its row and column. For Aa × Aa the gametes are A and a for both parents, giving AA, Aa, Aa and aa: 1 : 2 : 1 genotypes and 3 : 1 phenotypes with complete dominance.
What is the ratio of a dihybrid cross?
Crossing two double heterozygotes (AaBb × AaBb) with complete dominance gives 9 A_B_ : 3 A_bb : 3 aaB_ : 1 aabb phenotypes in 16 squares, and nine genotypes in the ratio 1 : 2 : 1 : 2 : 4 : 2 : 1 : 2 : 1. A test cross AaBb × aabb gives 1 : 1 : 1 : 1.
What is the difference between the genotype ratio and the phenotype ratio?
The genotype ratio counts allele combinations (AA, Aa, aa); the phenotype ratio counts what you can see. With complete dominance AA and Aa look the same, so 1 : 2 : 1 genotypes become 3 : 1 phenotypes. With incomplete dominance or codominance each genotype has its own phenotype, so the two ratios are the same.
Can a Punnett square predict my child’s eye colour?
Not reliably. Eye colour is polygenic: MedlinePlus Genetics notes that the old single-gene brown-over-blue model is too simple, and that two blue-eyed parents can have a brown-eyed child. The same applies to height and skin colour. Punnett squares work for single-gene traits such as the ABO blood groups.
How do I use the χ² test for a genetics cross?
Count the offspring in each phenotype class and type the counts. The calculator works out the expected numbers from the ratio, χ² = Σ (O − E)² ÷ E, and the p-value with k − 1 degrees of freedom. For Mendel’s 705 violet and 224 white flowers against 3 : 1, χ² = 0.39 and p = 0.53, so the data fit. A p-value below 0.05 would mean the counts are unlikely under that ratio.
Why are X-linked results different for sons and daughters?
Sons get their only X from their mother and a Y from their father, so a son shows whichever X allele his mother passed on. Daughters get one X from each parent. In XᵂXʷ × XᵂY fruit flies, every daughter is red-eyed, while half the sons are white-eyed.