Punnett Square Calculator
Enter two parent genotypes and get the completed square, the genotypic and phenotypic ratios, and the percentage chance of every offspring outcome.
Write each parent's genotype, one letter per allele
A capital letter is the dominant allele, the same letter in lower case is the recessive one. Aa is a single trait, AaBb is two traits, AaBbCc is three — the grid resizes itself to match.
How the Punnett square calculator works
A Punnett square calculator predicts the possible genotypes and traits of offspring from parental genes. Enter each parent’s alleles to calculate inheritance probabilities. For a simple heterozygous cross such as Aa × Aa, the expected genotype ratio is 25% AA, 50% Aa, and 25% aa.
Those three percentages come from counting boxes rather than from a formula. The grid sets every allele one parent can pass on against every allele the other can pass on, so each box is one equally likely combination an offspring could inherit — and with four boxes, one AA, two Aa and one aa, the genotypic ratio 1:2:1 is simply those counts written out. Group the boxes by appearance instead of by alleles and the same square gives the phenotypic ratio, 3:1, because a single dominant allele is enough to hide the recessive one.
The calculator above does the counting for you, and it does not stop at the classic two-by-two grid. Give it one trait and you get a 4-box square; give it two and it builds the 16-box dihybrid grid; give it three and it fills all 64 boxes of a trihybrid cross, which is where doing it by hand stops being reasonable. You can also switch off complete dominance — with incomplete dominance or codominance nothing is masked, and the phenotypic ratio collapses onto the genotypic one.
A parent with the genotype Aa makes two kinds of gamete, A and a, in equal numbers.
One parent's gametes head the columns, the other's the rows, and every box is the pair that meets there.
Identical boxes are added together and the totals are reduced — 4 boxes of Aa × Aa give 1:2:1 and 3:1.
The four words you need
Allele
A or a
One version of a gene. A capital letter marks the dominant allele, the same letter in lower case the recessive one — a convention, not a rule of nature.
Gamete
A · a
An egg or sperm cell, carrying one allele per gene. A parent with n heterozygous traits makes 2ⁿ kinds of gamete in equal proportions.
Genotype
AA · Aa · aa
The pair of alleles an offspring actually inherits — what is written inside each box of the square.
Phenotype
A– or aa
What that genotype looks like. Under complete dominance AA and Aa are indistinguishable, which is why 1:2:1 becomes 3:1.
Why the grid is always a square of 2ⁿ: each parent contributes one allele per gene, so a one-gene cross is 2 × 2 = 4 boxes, a two-gene cross 4 × 4 = 16, and a three-gene cross 8 × 8 = 64. Beyond that the grid stops being a teaching aid and the same answer is quicker to reach by multiplying the probabilities of each gene separately.
Method reference: the monohybrid layout and the genotypic and phenotypic ratios follow Omni Calculator's Punnett Square Calculator.
Every possibility
The six monohybrid crosses
With one gene and two alleles there are only three genotypes, so there are only six crosses in existence. Everything a monohybrid Punnett square can ever tell you is in this table — under complete dominance, where the capital allele masks the lower-case one.
| Cross | Genotypic ratio | Phenotypic ratio | Recessive offspring | Known as |
|---|---|---|---|---|
| AA × AA | all AA | all dominant | 0% | True-breeding dominant |
| AA × Aa | 1 AA : 1 Aa | all dominant | 0% | Half the offspring carry |
| AA × aa | all Aa | all dominant | 0% | The F1 generation |
| Aa × Aa | 1 : 2 : 1 | 3 : 1 | 25% | The classic monohybrid cross |
| Aa × aa | 1 Aa : 1 aa | 1 : 1 | 50% | The test cross |
| aa × aa | all aa | all recessive | 100% | True-breeding recessive |
The test cross earns its name here. A plant showing the dominant trait could be AA or Aa and you cannot tell by looking. Cross it with aa: if any offspring comes out recessive, the parent was heterozygous.
Ratio reference: the 3:1 phenotypic and 1:2:1 genotypic results, and the test-cross logic, are set out in Khan Academy's Mendel's law of segregation.
Reading a genotype
Homozygous, heterozygous, and the carriers in between
Two identical alleles make a genotype homozygous; two different ones make it heterozygous. That single distinction is what separates the genotypic ratio from the phenotypic one, and it is where most of the useful information in a Punnett square hides. In an Aa × Aa cross, three of the four boxes look the same from the outside, but only one of those three will breed true.
AA — homozygous dominant
Two dominant alleles. Shows the dominant trait and can only pass on a dominant allele.
Aa — heterozygous
One of each. Looks dominant under complete dominance, but carries the recessive allele and passes it on half the time.
aa — homozygous recessive
Two recessive alleles. The only genotype that shows the recessive trait, which is why it can be read directly off the offspring.
The two-thirds rule: in the offspring of Aa × Aa, three boxes show the dominant trait and two of those three are heterozygous. So a randomly chosen dominant-looking offspring has a 2 in 3 chance of carrying the recessive allele — not 1 in 2, which is the answer people reach for. The calculator reports this as the hidden-carrier share.
Definitions reference: heterozygous, homozygous, allele and genotype are defined in the National Human Genome Research Institute's Talking Glossary of Genomic and Genetic Terms.
Beyond the two-by-two
Types of Punnett square, and when each applies
Mendel's two laws are what make the grid work. Segregation says the two alleles of a gene separate cleanly into different gametes; independent assortment says one gene's alleles are dealt out without regard to another's. The first justifies the 2 × 2 square, the second justifies extending it to 4 × 4 and 8 × 8.
Monohybrid — 4 boxes
One gene. Aa × Aa gives 1:2:1 genotypes and 3:1 phenotypes. This is the square everyone draws first.
Dihybrid — 16 boxes
Two genes. AaBb × AaBb gives the famous 9:3:3:1, the result that revealed independent assortment.
Trihybrid — 64 boxes
Three genes, 27:9:9:9:3:3:3:1 phenotypes. Correct, complete, and a poor use of an afternoon by hand.
Incomplete dominance and codominance
The heterozygote shows an intermediate form, or both alleles at once. Three genotypes, three appearances, and a 1:2:1 phenotypic ratio.
Sex-linked traits
Genes on the X chromosome are written XAXa and XAY, so sons and daughters get different ratios from the same cross.
Multiple alleles
Human ABO blood group needs three alleles — IA, IB and i — with codominance between the first two.
Inheritance-pattern reference: autosomal dominant, autosomal recessive, X-linked, codominant and mitochondrial inheritance are described in MedlinePlus's Inheritance Patterns, from the U.S. National Library of Medicine.
Where the grid misleads
Three things a Punnett square cannot tell you
The square is exactly right about a model of inheritance that most real traits do not obey.
Linked genes break it
Two genes close together on the same chromosome travel together. The dihybrid grid assumes they do not, so its 9:3:3:1 quietly stops being true.
Most traits are polygenic
Height, skin colour and nearly every disease risk involve many genes and the environment. No square with two letters in it describes them.
Probability is not a quota
A 25% chance applies afresh to each offspring. Four children of Aa × Aa parents can all show the recessive trait, or none can.
Interesting fact
The man who drew the square also found the exception to it
Reginald Punnett was a Cambridge zoologist who took up Mendel's rediscovered work with William Bateson in the early 1900s, and the diagram that carries his name appeared in his own textbook as a way of showing students where the ratios came from. In the same years, breeding sweet peas, the two men kept finding results that the diagram could not explain: flower colour and pollen shape turned up together far more often than independent assortment allowed. They had stumbled on genetic linkage — genes riding on the same chromosome — without being able to name it, and it took Thomas Hunt Morgan's fruit flies to explain why. The tidiest teaching tool in genetics and the first solid evidence against its central assumption came out of the same laboratory, within a year or two of each other.
In practice
Turning a ratio into an answer
Most exam questions and most breeding decisions are one of three shapes, and each one is read off a different part of the square.
Working forwards
You know both parents and want the odds for the offspring. Fill the square and read the phenotypic ratio — this is what the calculator does by default.
Working backwards
You know the offspring and want a parent's genotype. A single recessive offspring proves both parents carried a recessive allele, whatever they look like.
Two traits at once
You want the chance of a specific combination. Multiply: a 3/4 chance for one trait and a 1/4 for another gives 3/16 for both together — the shortcut behind 9:3:3:1.
Repeated offspring
The chance of three recessive offspring in a row from Aa × Aa is 1/4 × 1/4 × 1/4 = 1/64, because each birth is independent of the last.
Worked example: AaBb × AaBb, complete dominance · each parent makes 4 gametes (AB, Ab, aB, ab) · 4 × 4 = 16 boxes · 9 boxes dominant for both traits, 3 dominant for A only, 3 dominant for B only, 1 recessive for both · phenotypic ratio 9:3:3:1, so a 6.25% chance of the double recessive aabb.
Common mistakes to avoid
Confusing the two ratios. 1:2:1 is genotypes and 3:1 is phenotypes. They describe the same four boxes, and a question asking for one will not accept the other.
Treating the ratio as a headcount. Four offspring from Aa × Aa will not politely arrive as three dominant and one recessive. The ratio is a probability per birth.
Listing gametes wrongly for a dihybrid. AaBb makes AB, Ab, aB and ab — one allele from each gene, never AA or Bb.
Forgetting that a homozygous parent still fills the grid. AA makes only one kind of gamete, so every column is identical — the square is still drawn, it just has repeated headings.
Frequently Asked Questions
How do you use a Punnett square for a genetic cross?
Write one parent's possible gametes along the top of the grid and the other parent's down the side, then fill each box with the pair of alleles that meet there. A parent with the genotype Aa contributes A to half its gametes and a to the other half — Mendel's law of segregation at work, with the two alleles of a gene separating cleanly before either is passed on. A cross of Aa with Aa therefore needs a two-by-two grid and produces four equally likely boxes: AA, Aa, Aa and aa. Counting those boxes gives the genotypic ratio of 1:2:1, and grouping them by appearance gives the phenotypic ratio of 3:1. A single-gene cross of this kind is called a monohybrid cross, and it is the one almost everyone draws first. The calculator above does the same steps and shows the completed square, so you can check a grid you have drawn by hand.
What is the difference between genotype and phenotype?
The genotype is the pair of alleles an individual carries — AA, Aa or aa — and the phenotype is the trait those alleles produce, such as purple or white flowers. They are not the same list, because under complete dominance a single dominant allele is enough to mask the recessive one: AA and Aa look identical, so three genotypes collapse into two phenotypes. That is exactly why the genotypic ratio 1:2:1 and the phenotypic ratio 3:1 describe the same four boxes of the same Punnett square. When the alleles show incomplete dominance or codominance instead, nothing is masked and the two ratios become the same. The distinction sits at the heart of heredity: what passes from one generation to the next is the genotype, and the phenotype is only what that inheritance happens to look like from the outside.
How do you tell heterozygous from homozygous?
Look at whether the two alleles match. They occupy the same position on a matching pair of chromosomes, one chromosome inherited from each parent, so every individual holds exactly two copies of the gene. Homozygous means both copies are the same version — AA is homozygous dominant and aa is homozygous recessive — while heterozygous means they differ, as in Aa. From the outside you often cannot tell: a heterozygous individual and a homozygous dominant one look identical whenever the trait shows complete dominance. The way to separate them is a test cross against a homozygous recessive partner. If any offspring shows the recessive trait the parent must have been heterozygous, because it could only have passed on the recessive allele it was carrying.
What is the purpose of a Punnett square?
It converts a question about inheritance into a question about counting. By laying out every gamete one parent can make against every gamete the other can make, the square guarantees that no combination is missed and that each box carries the same probability, so the chance of any outcome is simply the number of boxes showing it divided by the total. Breeders use it to plan crosses, students use it to work out ratios, and genetic counsellors use the same arithmetic when a condition follows a single-gene pattern. Its value is that it makes the reasoning visible rather than asking you to trust a formula — it is the everyday tool of Mendelian genetics for putting a number on a genetic outcome before that outcome exists.
How do you do a dihybrid cross?
Track two genes at once. Each parent with the genotype AaBb produces four kinds of gamete — AB, Ab, aB and ab — taking one allele from each gene, so the grid becomes four by four and holds sixteen boxes. Fill it the same way and the phenotypes come out in the ratio 9:3:3:1: nine offspring dominant for both traits, three dominant for the first only, three for the second only and one recessive for both. That result holds only while the two genes sit on different chromosomes, or far enough apart on the same chromosome to be dealt out independently — genes that travel together give quite different counts. The same answer can be reached by multiplying the two single-gene probabilities together, which is quicker for three genes or more. The calculator handles monohybrid, dihybrid and trihybrid crosses and resizes the square to match.
What does a 3:1 ratio actually mean?
It means that for every offspring showing the recessive trait, three are expected to show the dominant one — a 75% chance against a 25% chance, applied independently to each individual offspring. It does not promise that four offspring will divide neatly three to one, any more than four coin tosses must give two heads; the ratio describes what to expect across a whole generation, not inside any one family. The monohybrid cross that produces it also hides a useful detail: of those three dominant-looking offspring, only one is homozygous dominant and two are heterozygous carriers, so a dominant-looking individual from this cross has a two-in-three chance of carrying the recessive allele.
Can a Punnett square predict a child's eye colour?
Only roughly, and only for the simplified version of the trait taught in classrooms. Eye colour is polygenic — several genes contribute, with OCA2 and HERC2 doing most of the work — so the one-gene brown-over-blue square is a teaching model rather than a description of human genetics. Punnett squares are reliable where a trait really does follow a single gene with clear dominance, which covers many inherited conditions but few ordinary appearance traits. A new mutation widens the gap further: a change arising fresh in an egg or sperm cell was in neither parent's genotype, so no square drawn from the parents can anticipate it. For questions about a real pregnancy or family history, the square is a starting point for a conversation with a genetic counsellor, not a substitute for one.
Before you trust the square
- Both parent genotypes written with the same letters
- Gametes listed with one allele per gene, not two
- The dominance pattern matched to the trait
- Genotypic and phenotypic ratios kept apart
- Genes assumed to assort independently, and that assumption checked
- Results read as probabilities per offspring, not as a headcount
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Disclaimer
This calculator is an educational tool. It applies the standard Mendelian model — one gene, two alleles, clean segregation and independent assortment — and reports the ratios that model produces. Real inheritance departs from it more often than the model admits.
Nothing here is medical or genetic advice. Questions about an inherited condition, a family history, carrier status or a current or planned pregnancy belong with a qualified clinician or a certified genetic counsellor, who can take account of family structure, population carrier frequencies, penetrance, and testing that no grid can substitute for.
The independent assortment assumption is the most important limitation. Genes lying close together on the same chromosome are inherited as a unit, so a dihybrid or trihybrid square will overstate how often the non-parental combinations appear. The calculator flags this whenever more than one gene is entered, but it cannot know which genes you have in mind or how far apart they sit.
Most traits people are curious about are not single-gene traits at all. Height, skin and eye colour, intelligence, body shape and the great majority of disease risks are polygenic and shaped by environment as well; the classroom versions of these traits — one gene, brown over blue — are simplifications kept for teaching, and a Punnett square built on them will produce a confident number that means very little.
The results are probabilities, not counts. A 25% chance is renewed in full for every offspring, so a family of four can contain no recessive individuals or four of them without anything having gone wrong with the genetics. Ratios describe expectations across large numbers, and small families are not large numbers.
Finally, the notation is a convention rather than a fact about the gene. Capital letters for dominant alleles and lower-case for recessive ones is a bookkeeping habit that breaks down for codominant systems such as ABO blood groups, for X-linked traits where the sexes must be handled separately, and for alleles that are neither cleanly dominant nor recessive. Where your source uses a different notation, follow the source and treat this page as a cross-check.
Last updated
Ratios, definitions, and references checked on this date.