Audited —·Last updated 29 Jul 2026·6 citations·Tier 1·0 uses

Punnett Square Calculator

Free Punnett square calculator for a one-gene cross. Enter two parent genotypes, pick complete, incomplete or codominant expression, get exact ratios.

Punnett Square Calculator

Two allele letters for ONE gene, e.g. Aa, AA or aa. UPPERCASE is the dominant allele, lowercase the recessive one. Any letter works (Tt, Bb, Rr). For two genes use the dihybrid cross calculator.
Same gene letter as parent 1, e.g. Aa. The cross is symmetric — swapping the two parents cannot change the answer, only the orientation of the grid.
How is the heterozygote expressed?
Dominant phenotype
75.00
Percentage of offspring showing the dominant phenotype. Under complete dominance this is the dominant homozygote PLUS the heterozygote (AA + Aa). Under incomplete dominance and codominance the heterozygote has its own class, so this counts the dominant homozygote (AA) only. Exact, not an estimate — but it is the expected proportion over many offspring, not a prediction about one child.
Heterozygote phenotype
0.00
Recessive phenotype
25.00
Homozygous dominant (AA)
25.00
Heterozygous (Aa)
50.00
Homozygous recessive (aa)
25.00
Genotype ratio
1 AA : 2 Aa : 1 aa
Phenotype ratio
3 dominant (A_) : 1 recessive (aa)
Punnett square
[AA · Aa] [Aa · aa]

Background.

A Punnett square is the small grid that turns Mendel's law of segregation into arithmetic you can check by eye. Enter the two parents' genotypes for a single gene, choose how the heterozygote is expressed, and this calculator returns the exact genotype and phenotype probabilities for one offspring, the reduced integer ratios that textbooks and exam papers ask for, and the grid itself.

The logic is one sentence long. A diploid parent carries two alleles at the gene in question, and meiosis puts exactly one of them into each gamete, with equal probability. Line parent 1's two possible gametes down the side of a two-by-two grid and parent 2's two possible gametes across the top, fill each cell with the pair that would result, and every cell is equally likely. Counting the cells is the whole calculation. For the classic heterozygote cross Aa × Aa the four cells are AA, Aa, Aa and aa, so a quarter of offspring are AA, half are Aa and a quarter are aa — the 1 : 2 : 1 genotype ratio. If the dominant allele completely masks the recessive one, the AA and Aa offspring look identical and the visible ratio collapses to 3 dominant : 1 recessive, which is 75 % against 25 %.

That collapse is why the dominance selector matters more than it looks. The genotype numbers never change — 25 % / 50 % / 25 % for Aa × Aa in all three modes — because dominance describes how alleles are *expressed*, not which alleles are *inherited*. What changes is how many visible classes exist. Under complete dominance there are two, and the heterozygote is hidden inside the dominant one. Under incomplete dominance the heterozygote is an intermediate blend and gets its own class, so the phenotype ratio stays 1 : 2 : 1 — a pink snapdragon from a red and a white parent is the standard illustration. Under codominance both allele products appear separately rather than blending, as in the AB blood group where the A and B sugars are both present on the red cell surface; the arithmetic is identical to incomplete dominance but the biology, and the class label, are not.

The numbers this page returns are exact ratios for an idealised cross, and it is worth being blunt about what that does and does not mean. They are not a personal risk figure. Each conception is an independent draw from the same distribution: if two carriers have three unaffected children, the fourth pregnancy still carries the same 25 % chance, because probability has no memory and the earlier outcomes did not use anything up. The model also assumes one autosomal gene with exactly two alleles, equal survival of every genotype, and full penetrance — everyone with the affected genotype shows the trait. Real inheritance bends all three. Lethal alleles kill one genotype class outright and turn 3 : 1 into 2 : 1. Reduced penetrance and variable expressivity mean a genotype does not guarantee a phenotype. Epistasis lets a second gene override the first. Genes with three or more alleles, like ABO, need a different grid, and genes on the X chromosome need results split by sex. For a real family and a real condition, a clinical geneticist or a certified genetic counsellor is the right source of a risk figure; a Punnett square is a teaching device and a first approximation, not a diagnosis.

Within those limits the tool is exact rather than approximate. There is no fitted constant, no measured parameter and no rounding to argue about: every probability is a count out of four, so the only values it can ever return are 0 %, 25 %, 50 %, 75 % and 100 %. Below the widget you will find the derivation from the law of segregation, a step-by-step walk through the worked example, the difference between the three dominance models with real examples of each, what a carrier actually is, why the sum rule and the product rule give the same answer as counting cells, and where the model stops being trustworthy.

What is punnett square calculator?

A Punnett square is a grid, devised by the British geneticist Reginald Punnett in the early 1900s, that enumerates every equally likely combination of parental gametes for one or more genes. For a single gene it is a 2×2 table: parent 1's two possible gametes label the rows, parent 2's two possible gametes label the columns, and each of the four cells holds the genotype a zygote would receive from that particular pairing. Because meiosis segregates the two alleles of a gene into gametes with equal probability — Mendel's first law, the law of segregation — all four cells are equally likely, so the probability of any genotype is simply the number of cells containing it divided by four.

The vocabulary matters. An allele is one version of a gene. A genotype is the pair of alleles an individual carries; a phenotype is what you can observe. Homozygous means the two alleles are the same (AA or aa); heterozygous means they differ (Aa). By universal convention the dominant allele is written with a capital letter and the recessive allele with the same letter in lowercase, which is why this calculator reads case as the dominance signal and refuses a genotype like Ab that mixes two different gene letters. A carrier is a heterozygote for a recessive condition: unaffected, because the working allele is enough, but able to pass the non-working allele to half of their children.

Dominance is a statement about the heterozygote, and it comes in three flavours that this calculator treats as separate modes. Complete dominance means the heterozygote is phenotypically indistinguishable from the dominant homozygote, so two genotype classes share one phenotype and 1 : 2 : 1 becomes 3 : 1. Incomplete dominance means the heterozygote is intermediate — neither parent's phenotype, but something between them. Codominance means both alleles are fully and separately expressed in the heterozygote, so you can see both products at once; the ABO blood group's AB phenotype is the textbook case. Incomplete dominance and codominance produce identical numbers, because in both the heterozygote is its own visible class; they differ in mechanism, and the page keeps them apart so the label on the result is honest.

How to use this calculator.

  1. Write the two parents' genotypes for a single gene using one letter. Uppercase is the dominant allele, lowercase the recessive one: AA, Aa and aa are the three possibilities. Any letter works — Tt for tall/short peas, Bb for coat colour, Rr for flower colour.
  2. Enter parent 1's genotype and parent 2's genotype. Both must use the same letter, because a Punnett square of this size follows one gene at a time. Order does not matter: the cross is symmetric, and swapping the parents only transposes the grid.
  3. Choose how the heterozygote is expressed. Pick complete dominance for a normal dominant/recessive trait, incomplete dominance when the heterozygote is an intermediate blend, and codominance when both allele products are separately visible.
  4. Read the three phenotype percentages first — they answer 'what fraction of offspring will look like what'. The three genotype percentages below them answer 'what fraction will carry which alleles', which is the question that matters for carrier status.
  5. Use the genotype and phenotype ratio strings for homework and exam answers; they are already reduced to the smallest whole numbers, with impossible classes dropped rather than shown as zero.
  6. Check the grid string against your own hand-drawn square. Each bracket is one row of the 2×2 table, and the two entries inside a bracket are the two columns.
  7. If your problem involves two genes, use the dihybrid cross calculator; three genes, the trihybrid cross calculator; a gene on the X chromosome, the sex-linked inheritance calculator; and blood groups, the blood type inheritance calculator, because ABO has three alleles rather than two.

The formula.

P(genotype) = (cells containing it) ⁄ 4
rows · parent 1's two gametescolumns · parent 2's two gametes4 · total cells, all equally likelyA · dominant allele (uppercase)a · recessive allele (lowercase)

The calculation rests on one biological fact and one counting argument.

The biological fact is Mendel's law of segregation: the two alleles a diploid individual carries at a gene separate during meiosis so that each gamete receives exactly one of them, and each of the two is equally likely. A parent with genotype Aa therefore makes A gametes and a gametes in equal numbers; a parent with genotype AA makes only A gametes; aa makes only a.

The counting argument is that fertilisation pairs one gamete from each parent independently. Build the 2×2 grid with parent 1's two alleles as rows and parent 2's two alleles as columns and every cell is an equally likely fertilisation event, so

P(genotype g) = (number of the 4 cells equal to g) ⁄ 4

For Aa × Aa the cells are AA, Aa, Aa, aa. That gives P(AA) = 1/4 = 25 %, P(Aa) = 2/4 = 50 %, P(aa) = 1/4 = 25 %, which is the 1 AA : 2 Aa : 1 aa genotype ratio.

Mapping genotypes onto phenotypes is where the dominance model enters, and it only ever regroups those same numbers:

complete dominance → dominant class = AA + Aa = 25 % + 50 % = 75 %; recessive class = aa = 25 %. Ratio 3 : 1. incomplete dominance → three classes, 25 % / 50 % / 25 %. Ratio 1 : 2 : 1. codominance → three classes, 25 % / 50 % / 25 %. Ratio 1 : 2 : 1, different labels.

So complete dominance is the only model that changes the visible ratio, and it does so by merging two genotype classes rather than by altering any probability. Notice the direction: complete dominance always makes the dominant phenotype MORE common than the dominant genotype (75 % versus 25 %), never less, because it moves the heterozygotes into the dominant column.

The same answer falls out of probability rules without drawing anything, which is the check worth knowing. By the product rule, P(AA) = P(A from parent 1) × P(A from parent 2) = ½ × ½ = ¼. By the sum rule, the chance of showing the dominant phenotype under complete dominance is P(AA) + P(Aa) = ¼ + ½ = ¾. Cell counting and the probability rules are the same calculation written two ways, and this page agrees with both.

ROUNDING STAGE. Every quantity here is an exact rational number with denominator 4. The arithmetic is carried in arbitrary-precision Decimal and rounded exactly once, at the return boundary, to ten decimal places — a rounding that can never change anything, because the only reachable percentages are 0, 25, 50, 75 and 100. There is no intermediate rounding, no threshold and no accumulation of error.

INVALID DOMAIN. There is no singularity: the denominator is the constant 4, never a user value, so no input can make the result blow up. What the calculator does reject, field by field, is a genotype that is not exactly two letters, a genotype mixing two different gene letters such as Ab, a non-letter character, two parents described with different gene letters, and an unrecognised dominance model.

A worked example.

Example

Two heterozygous parents, one gene, complete dominance — the single most common genetics question there is, and the one behind every 'both parents are carriers' counselling scenario. Parent 1 is Aa, so it makes A gametes and a gametes in equal numbers. Parent 2 is Aa and does the same. The 2×2 grid is therefore [AA · Aa] on the first row and [Aa · aa] on the second, which the calculator prints as its Punnett square output. Four cells, all equally likely: one AA, two Aa, one aa. The genotype results follow by counting. Homozygous dominant AA is 1 cell of 4, so 25 %. Heterozygous Aa is 2 cells of 4, so 50 %. Homozygous recessive aa is 1 cell of 4, so 25 %. The reduced genotype ratio is 1 AA : 2 Aa : 1 aa. Because complete dominance was selected, the AA and Aa offspring are visually identical, so they merge: the dominant phenotype comes out at 25 % + 50 % = 75 %, the heterozygote phenotype at 0 % (it has no separate class in this model), and the recessive phenotype at 25 %. The reduced phenotype ratio is 3 dominant (A_) : 1 recessive (aa). The three phenotype percentages add to exactly 100, as do the three genotype percentages. Read as a carrier problem, the same four numbers say: if both parents carry one copy of a recessive variant, each child has a 25 % chance of inheriting two copies and being affected, a 50 % chance of being an unaffected carrier like the parents, and a 25 % chance of inheriting neither copy. That is exactly the figure the US National Library of Medicine's StatPearls entry on autosomal recessive inheritance gives, and it derives it the other way round — 50 % × 50 % = 25 % by the product rule — which is a useful independent check on the grid. Switch the dominance selector to incomplete dominance without changing anything else and the genotype numbers stay at 25 / 50 / 25, but the heterozygote stops hiding: the phenotype output becomes 25 % dominant homozygote, 50 % intermediate, 25 % recessive homozygote, and the phenotype ratio becomes 1 : 2 : 1. Nothing about inheritance changed — only what you can see. One caution that belongs next to the number rather than at the bottom of the page: 25 % is a per-conception expectation, not a quota. Three unaffected children do not make the fourth safe, and they do not make it more likely to be affected either. Each pregnancy is an independent draw.

parent2 GenotypeAa
dominance Modelcomplete
parent1 GenotypeAa

Frequently asked questions.

What is a Punnett square and who invented it?
A Punnett square is a grid that lists every equally likely combination of gametes from two parents, so you can read genotype probabilities off it by counting cells. It is named after Reginald Crundall Punnett, the British geneticist who popularised the layout in the first decade of the twentieth century while working with William Bateson on the newly rediscovered Mendelian rules. For a single gene the square is 2×2: each parent contributes one of two possible gametes, giving four equally likely fertilisation outcomes. The device does not add any biology of its own — it is a bookkeeping tool for Mendel's law of segregation, and it gives exactly the same answers as multiplying probabilities directly. Its value is that it makes the enumeration visible, which is why it survives in classrooms a century after the algebra caught up with it.
Why does Aa × Aa give a 3:1 ratio and not 1:2:1?
It gives both, at different levels of description. The genotype ratio really is 1 AA : 2 Aa : 1 aa — 25 %, 50 %, 25 % — and this calculator always reports those three numbers. The 3 : 1 you remember is the phenotype ratio, and it only appears under complete dominance, where the heterozygote looks exactly like the dominant homozygote. Merging those two genotype classes into one visible class gives 1 + 2 = 3 parts dominant against 1 part recessive, so 75 % against 25 %. Change the dominance model to incomplete dominance or codominance and the phenotype ratio reverts to 1 : 2 : 1, because the heterozygote becomes visible in its own right. Nothing about the inheritance changed between the two cases — only what an observer can distinguish.
Does a 25 % chance mean one in every four children will be affected?
No, and this is the single most consequential misreading of a Punnett square. Twenty-five percent is the probability for each pregnancy considered separately, not a quota that gets filled. Each conception is an independent draw from the same distribution, so two carrier parents can have four affected children in a row, or four unaffected ones, and neither outcome is evidence that the model is wrong. Concretely, the chance that all four of four children are unaffected is 0.75⁴ ≈ 31.6 %, and the chance that exactly one of four is affected — the 'textbook' outcome — is only about 42 %. Probability has no memory: three unaffected children neither use up the risk nor increase it for the fourth.
What is the difference between incomplete dominance and codominance?
The arithmetic is identical; the biology is not. In both cases the heterozygote is its own visible class, so the phenotype ratio for Aa × Aa is 1 : 2 : 1 rather than 3 : 1. The difference is what the heterozygote looks like. Under incomplete dominance the two allele products blend into something intermediate that neither homozygote shows — a red-flowered and a white-flowered snapdragon crossing to give pink is the standard example, and the pink arises because one working copy of the pigment gene makes roughly half as much pigment. Under codominance both allele products are made in full and are separately detectable, with no blending: a person with ABO genotype AB carries both the A sugar and the B sugar on their red cells, and a laboratory can see each one. The NLM's MedlinePlus Genetics defines codominant inheritance as two alleles both being expressed with each making a slightly different protein, which is exactly that distinction.
What does 'carrier' mean, and how do I read carrier status off this calculator?
For a recessive condition, a carrier is a heterozygote: someone with one working allele and one non-working allele who is themselves unaffected, because one working copy is enough, but who can pass the non-working copy to half of their children. On this page the carrier figure is the 'Heterozygous (Aa)' output. For a carrier × carrier cross that is 50 %, alongside 25 % affected and 25 % who inherit neither copy. Note that under complete dominance you cannot tell a carrier from a non-carrier by looking — both are in the 75 % dominant-phenotype group — which is why carrier status is established by genetic testing or by pedigree inference rather than by inspection. That inference is what the pedigree probability calculator does: among the unaffected children of two carriers, two thirds rather than one half are carriers, because the affected quarter has been excluded by observation.
When does a Punnett square give the wrong answer?
Whenever one of its assumptions fails, and several fail routinely. Lethal alleles remove a whole genotype class before birth — homozygotes for the yellow-coat allele in mice die in utero, so a yellow × yellow cross gives a 2 : 1 live ratio, not 3 : 1. Reduced penetrance means some individuals with the affected genotype never show the trait, so the phenotype fraction is lower than the genotype fraction. Variable expressivity means the trait appears at different severities. Epistasis means a second gene can mask the first entirely, converting a 9 : 3 : 3 : 1 dihybrid ratio into 9 : 7 or 12 : 3 : 1. Genes with more than two alleles need a larger grid. Genes on the X chromosome need results split by sex. Mitochondrial genes are not inherited by this model at all. And imprinting makes the answer depend on which parent an allele came from, which a Punnett square cannot represent.
Can I use a Punnett square to work out my own family's risk?
Only as a rough teaching illustration, never as a clinical number. A Punnett square gives exact ratios for an idealised single-gene cross with known genotypes and full penetrance. A real family risk calculation has to handle unknown genotypes, population carrier frequencies specific to the condition and ancestry, the sensitivity and residual risk of whatever test was done, age-dependent penetrance, and any information the pedigree already contains about unaffected relatives. Those elements combine through Bayesian updating, not through cell counting, and they routinely move a figure by a factor of two or more. If a real decision hangs on the number, the correct source is a clinical geneticist or a certified genetic counsellor, who will also know whether the condition in question actually follows a simple Mendelian pattern.
Why does the calculator reject a genotype like Ab?
Because Ab describes two different genes, not one, and a 2×2 square cannot represent two genes. In standard notation the capital and lowercase forms of the same letter are the two alleles of one gene: A and a are alternatives at the same locus, while A and b belong to different loci. If your problem really does involve two genes — seed shape and seed colour, say — the correct tool is a 4×4 dihybrid square with sixteen cells, which is what the dihybrid cross calculator builds. Three genes need 64 cells and are usually solved by multiplying single-gene probabilities instead, which is what the trihybrid cross calculator does. The calculator also rejects a single character, three or more characters, and any non-letter, so that a typo produces a clear error under the field rather than a plausible-looking wrong answer.
Do the genotype percentages change when I switch dominance models?
No, and that is the point of keeping them on screen. Dominance describes how alleles are expressed, not which alleles are transmitted, so the 25 % / 50 % / 25 % genotype split for Aa × Aa is identical under complete dominance, incomplete dominance and codominance. Only the phenotype grouping changes: complete dominance merges the homozygous dominant and heterozygous classes into a single 75 % visible class, while the other two models keep three classes of 25 %, 50 % and 25 %. If you ever see a tool change the genotype numbers when you change the dominance setting, something is wrong with it.
How do the product rule and the sum rule relate to the grid?
They are the same calculation without the drawing. The product rule says the probability of two independent events both happening is the product of their probabilities, so the chance of inheriting A from an Aa parent and A from another Aa parent is ½ × ½ = ¼ — the AA cell. The sum rule says the probability of either of two mutually exclusive outcomes is their sum, so the chance of showing the dominant phenotype under complete dominance is P(AA) + P(Aa) = ¼ + ½ = ¾. OpenStax's Biology 2e states exactly that sum in its Laws of Inheritance section, and it matches the 75 % this page returns by counting three of four cells. For one or two genes the grid is quicker to see; for three or more genes the probability rules are quicker to compute, which is why trihybrid problems are almost always solved by multiplication rather than by drawing 64 boxes.

References& sources.

  1. [1]Abbott S. & Fairbanks D. J. (2016). Experiments on Plant Hybrids by Gregor Mendel. Genetics 204(2):407–422. doi:10.1534/genetics.116.195198. A peer-reviewed modern English translation of Mendel's 1866 Versuche über Pflanzen-Hybriden, published by the Genetics Society of America. Contains Mendel's single-character series (the 1:2:1 genotype series) and the statement that for n differing characters there are 2ⁿ gamete types, 3ⁿ genotype classes and 4ⁿ combinations. Open access, not paywalled. Retrieved 2026-07-29.
  2. [2]Gulani A. & Weiler T. Genetics, Autosomal Recessive. StatPearls, NCBI Bookshelf ID NBK546620, last update 1 May 2023. States the carrier × carrier outcome verbatim — 'a 25% chance that the child will be affected, a 50% chance that the child will be a carrier, and a 25% chance that the child will be homozygous dominant and unaffected' — and derives it as 50% × 50% = 25%. Free full text. Retrieved 2026-07-29.
  3. [3]Lewis R. G. & Simpson B. Genetics, Autosomal Dominant. StatPearls, NCBI Bookshelf ID NBK557512, last update 1 May 2023. Source for the 50 % transmission probability from a heterozygous affected parent, and for the definition of penetrance as 'the percentage of individuals who inherit a disorder allele AND display the phenotype' — the assumption this calculator makes explicit. Free full text. Retrieved 2026-07-29.
  4. [4]MedlinePlus Genetics, US National Library of Medicine. Inheritance Patterns (formerly Genetics Home Reference), page last updated 19 April 2021. Source for the definitions of autosomal dominant, autosomal recessive and codominant inheritance used on this page, including 'Two different versions (alleles) of a gene are expressed, and each version makes a slightly different protein' for codominance. Free. Retrieved 2026-07-29.
  5. [5]OpenStax, Biology 2e, section 12.3 'Laws of Inheritance'. Rice University, 2018, CC BY 4.0. Independent derivation of the same numbers via the product and sum rules: 'the probability of a homozygous dominant at A is 1/4 and the probability of a heterozygote at A is 1/2. The probability of the homozygote or the heterozygote is 1/4 + 1/2 = 3/4 using the sum rule.' Free, openly licensed. Retrieved 2026-07-29.
  6. [6]Genetic Alliance & District of Columbia Department of Health. Understanding Genetics: A Guide for Patients and Health Professionals, appendix 'Inheritance Patterns' / 'Classic Mendelian Genetics'. NCBI Bookshelf IDs NBK115561 and NBK132145, 2009–2010. Plain-language statement of the five classical inheritance modes used for the scope statements on this page. Free full text. Retrieved 2026-07-29.
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