Punnett Square Calculator

Q: How do you use a Punnett square?

Write the alleles each parent can transmit along the top and side of a grid, fill each cell with the combination, then count cells. One gene gives four cells, two independent genes give sixteen. Divide a class by the number of cells for its probability. This calculator builds the same table and keeps the count out of the denominator, so 9/16 is printed as 56.25% and still shows the nine.

Q: What is the difference between genotype and phenotype ratio?

The genotype ratio counts genetic classes; the phenotype ratio counts what you can see. Aa × Aa is 1 : 2 : 1 by genotype but 3 : 1 by phenotype, because AA and Aa are indistinguishable under complete dominance. Choose incomplete or codominant here and the two ratios become identical, because the heterozygote gets its own phenotype class.

Q: If both parents are carriers, is the risk 25% each pregnancy or 25% overall?

25% each pregnancy, every time. The chance at least one child in a family of three is affected is 1 − 0.75³ = 57.8%, and the chance exactly one is affected is 42.2%. Both numbers are true; the second is the binomial over the family you are planning. The family mode gives you all three.

Q: Why is an unaffected sibling’s carrier risk 2/3 and not 1/2?

Because "unaffected" removes the aa cell from a four-cell grid, leaving AA : Aa : Aa. Two of the three survivors are carriers. Conditioning on what you already know changes the denominator, which is why the conditional mode renormalizes rather than reusing the original 1/2.

Q: Does a boy get color blindness from his mother or his father?

A son gets his only X from his mother, so an X-linked recessive condition always reaches a son through her — a father cannot pass an X-linked allele to a son at all, only his Y. An affected father’s daughters all inherit his disease X and are carriers unless the mother contributes one too. Set the mode to X-linked and the calculator splits the ratios by sex.

Q: What if my two genes are on the same chromosome?

Then the four offspring classes are no longer equal, and the ratio is set by the recombination fraction: parental gametes at (1 − r)/2 each and recombinants at r/2 each. Use the linked-genes mode with a published or self-measured r; it reports the recombinant percentage and the map distance in centiMorgans, and refuses r = 50% because that is indistinguishable from independent assortment.

Q: Can this tell me whether my child will have a genetic condition?

It tells you the probability for a pregnancy once the parental genotypes are known, which is not the same as knowing them. Carrier status, phase and penetrance usually come from testing and family history. Use these figures to understand a stated risk or to work a genetics course problem, and take a real reproductive decision to a genetic counselor who has the pedigree.

Q: Is there a Hardy-Weinberg calculator here?

Not on this page — the square starts from two parents whose genotypes you already know, while Hardy-Weinberg starts from frequencies across a population and predicts what a sample of strangers looks like. That question has its own page, the [Hardy-Weinberg calculator](/hardy-weinberg-calculator/), which counts allele frequencies from typed genotypes, tests the fit and inverts a disease rate into a carrier frequency. The two are commonly confused, so the [Genetics collection](/genetics/) keeps them apart, and the quantitation tools next door — such as the [DNA concentration calculator](/dna-concentration-calculator/) — cover the wet-lab side of the same alleles.

A Punnett square is just a multiplication table for gametes: list the alleles each parent can hand on, cross every combination, and count what comes out. This calculator does that for one gene up to four, and then answers the three questions the squares themselves cannot — how the risk moves once you know the family already has affected or unaffected children, which probability belongs to sons and which to daughters when the gene is on the X chromosome, and what the ratios become when two genes sit close enough on one chromosome that they no longer sort independently. Every answer is exact Mendelian arithmetic over whole zygote classes, printed as a percentage per pregnancy and as the ratio it came from.

The square works because a parent does not pass on a genotype, only one allele of it. A person who is Aa gives A to half their conceptions and a to the other half, and nothing about the rest of their body changes that split. Put the two parents’ possibilities against each other and every cell of the grid is one equally likely zygote — four cells for one gene, sixteen for two genes that assort independently, sixty-four for three. Counting cells is the entire method, and the Genetics collection keeps that counting visible instead of hiding it behind a phenotype label.

What the grid does not do is reason about a family you already have. Ask "what is the chance our third child is affected" and the answer is still the same 25%, because conceptions have no memory — but ask "what is the chance at least one of our three children is affected" and it becomes 57.8%, because there are now three independent draws to consider. Those two numbers are both correct and they answer different questions, which is exactly why genetic counseling quotes one and worried parents hear the other.

Conditioning changes the arithmetic a third time. If you already know a person does not have a recessive condition, the aa cell is no longer in the running: the denominator drops from four to three, and the carrier probability for an unaffected sibling becomes 2/3 rather than the intuitive 1/2. Push the same idea onto parents rather than children and you get a Bayesian update — a couple with one in a hundred prior chance of both being carriers who have two healthy children have moved to about 0.57%, because each healthy birth multiplies the odds by 3/4. The step-by-step guide walks both of those derivations slowly.

Two more situations break the square as textbooks draw it. Genes on the same chromosome do not sort independently, so the four offspring classes are no longer equal: their sizes are set by a single recombination fraction, and the deviation from 1:1:1:1 is how mapping distances in centiMorgans were measured long before sequencing. And a gene on the X chromosome makes sex part of the equation, because a son inherits his X only from his mother and his father’s X never reaches a son at all. Both are handled here as their own modes, with the ratios split by sex rather than averaged over children.

What to find

Number of genes

Genes are assumed to assort independently. Two genes that sit close together on one chromosome belong in the linked-genes mode.

Dominance

Only the phenotype labels change: the genotype arithmetic is identical under all three.

Parent 1 — gene A

Parent 2 — gene A

Parent 1 — gene B

Parent 2 — gene B

Parent 1 — gene C

Parent 2 — gene C

Parent 1 — gene D

Parent 2 — gene D

Class each child is tested against

Number of children (children)

Each birth is an independent draw of the same probability.

At least how many affected (children)

Which conditional question

Phenotype already observed

Knowing this discards the other zygote classes and renormalizes what is left.

Genotype to test

Prior carrier probability (%)

Before the children are counted: population carrier frequency, or the risk a pedigree gives you.

Healthy children so far (children)

Children who have not shown the recessive trait. Each one shifts the parents’ risk.

Mother’s X chromosomes

N is the normal allele, c the recessive disease allele on the X chromosome.

Father’s X chromosome

A father gives his X to daughters and his Y to sons, which is what splits the ratios by sex.

Arrangement in the heterozygous parent

Which alleles sit on the same chromosome decides which offspring classes are the common ones.

Second parent

Recombination frequency (%)

From your own cross, from a published map, or from 1% = 1 centiMorgan. Below 50%.

Most likely phenotype: dominant A75 %

Dominant at every gene75 %

Recessive at one or more25 %

Heterozygous at every gene50 %

Risk per child— %

At least one in the family— %

No child affected— %

Exactly that many— %

AA, among the survivors— %

Aa, among the survivors— %

aa, among the survivors— %

Prior carrier risk— %

Likelihood of healthy children— %

Updated carrier risk— %

Risk for the next child— %

Sons affected— %

Daughters affected— %

Daughters carriers— %

Affected, all pregnancies— %

Parental classes— %

Recombinant classes— %

Dominant at both loci— %

Recessive at both loci— %

Map distance— cM

The square itself

Rows are one parent’s gametes, columns the other’s. Every box is one equally likely zygote.

Every class this cross can produce

Genotype	Phenotype	Probability	Zygotes
Aa	dominant A	50%	2 of 4
AA	dominant A	25%	1 of 4
aa	recessive a	25%	1 of 4

The six single-gene matings, computed the same way

These are the crosses every textbook prints. Nothing here is typed in by hand — each line is the same engine this calculator runs on, so the table and your own result cannot disagree.

Mating	dominant A	recessive a
AA × AA	100%	—
AA × Aa	100%	—
AA × aa	100%	—
Aa × Aa	75%	25%
Aa × aa	50%	50%
aa × aa	—	100%

Read under complete dominance. Switching the dominance selector to incomplete or codominant splits the heterozygote out of the dominant class, which is why 1 : 2 : 1 becomes the phenotype ratio too.

What this calculator gives you that others don’t: The top results for this query are square generators, and the grid work itself is solid: the fullest-featured page in our sample draws up to five genes, offers complete, incomplete and codominant expression, and preloads testcross pairings. What none of the pages in that set does is arithmetic beyond the grid. Family size never appears — no tool answers "we are planning three children, what is the chance at least one is affected", even though that is the question a carrier couple arrives with, and its answer (57.8%, not the 25% on the square) is not obtainable from any grid on those pages. Conditional probability is equally absent: the 2/3 carrier risk for an unaffected sibling, the most mis-stated number in introductory genetics, is computed nowhere in the set, and neither is the Bayesian update from healthy children. X-linked crosses appear on some pages but only as a second square with no sex-stratified output, so the distinction between 50% of sons and 25% of pregnancies — the one that matters when a family is being counseled — is never made. Linkage is worse than missing: at least one established tool states outright that it does not cover linked genes, so the mode where the ratio is a measurement rather than a formula (parental (1−r)/2, recombinant r/2, map distance 100·r cM, refused at r = 50%) exists nowhere in the results. Length does not substitute for any of this: the longest page in our sample runs past three thousand words and spends them restating the same monohybrid square in prose. This page supplies what is missing — exact integer counts out of 4^L printed beside every percentage, six worked examples whose numbers the engine itself produces, four probability modes the generators do not compute, per-class citations with the inheritance model each rests on, and a dated method card that states the assumptions and limits of all six methods — inside a suite whose genetics pages keep distinct intents on distinct pages rather than absorbing population-frequency calculators onto the same one.

How to use the punnett square calculator

Pick what you want: offspring ratios from a cross, risk across several children, probability given a known phenotype, an X-linked cross, or a linked-gene cross.

In ratio mode, choose the number of genes and set each parent’s genotype at each gene from the AA / Aa / aa selectors.

Set dominance — complete, incomplete or codominant. Only the phenotype labels change; the genotype arithmetic is identical.

Read the result: the primary card is the most likely phenotype, and the table underneath lists every genotype class with its exact count out of 4, 16, 64 or 256.

For a family, enter the number of children and at least how many are affected; the cards give the per-child figure, the at-least-one figure and the probability nobody is affected.

For a conditional question, choose whether you are asking about a person whose phenotype you know, or about parents given healthy children — the second one wants a prior carrier probability.

For an X-linked cross, set the mother’s two X chromosomes and the father’s one; results are reported within sons, within daughters and across all pregnancies.

For linked genes, choose the phase (coupling or repulsion), the second parent and the recombination frequency — from your own counts or from a published map.

Press Calculate. Everything runs in your browser, and the method card states which assumption each number rests on.

Punnett Square formula

One gene: Aa × Aa → P(AA) = ½·½ = ¼, P(Aa) = ½·½ + ½·½ = ½, P(aa) = ¼

Independent assortment: L genes → 2^L gamete types per parent, 4^L zygotes, each equally likely

Dihybrid: AaBb × AaBb → A_B_ 9/16 = 56.25%, A_bb 3/16, aaB_ 3/16, aabb 1/16 = 6.25%

Family: P(at least j of n) = 1 − Σ (over k < j) C(n,k) · q^k · (1−q)^(n−k)

Condition: P(genotype | phenotype) = its zygote count ÷ the surviving zygote count

Bayes: P(carriers | k healthy) = prior·(3/4)^k ÷ (prior·(3/4)^k + 1 − prior)

Linkage: parental gametes (1−r)/2 each, recombinant gametes r/2 each; map distance = 100·r cM

X-linked: son = maternal X + paternal Y; daughter = maternal X + paternal X

Genes are labeled A/a, B/b, C/c, D/d. Uppercase is the dominant allele within that gene, and it carries no meaning across genes — gene B is not "more dominant" than gene a.

Variables and units

Symbol	Meaning	Unit
L	Number of genes assumed to assort independently	genes
q	Probability one child falls in the class you asked about	%
n	Children in the family	children
j	How many of those n you are asking about	children
C(n,k)	Number of birth orders giving k affected among n	—
k	Healthy children already observed (Bayesian question)	children
r	Recombination frequency between the two linked loci	% (0 to under 50)
prior	Carrier probability before the children are counted	%

How punnett square is calculated

Split each parent into the alleles they can transmit — one of two per gene, equally likely.
Form every combination: 4 zygotes for one gene, 16 for two, 64 for three, 256 for four.
Collapse the zygotes into genotype classes, then into phenotype classes using the dominance rule you chose.
If the question is about a family, take the per-child probability and expand it as a binomial over the number of children.
If a phenotype is already known, delete the incompatible zygotes and renormalize over what survives.
If the genes are linked, replace the equal gamete probabilities with (1−r)/2 for parental and r/2 for recombinant types.

Worked laboratory examples

Example 1 — Two carriers, one pregnancy

Given: Both parents Aa · complete dominance · the condition is the recessive phenotype

Each parent transmits the recessive allele to half their conceptions: ½ × ½ = ¼.
So 25% of pregnancies are affected, 50% carry one copy and 25% carry none.
The phenotype ratio is 3 unaffected : 1 affected — a statement about one pregnancy, not about a family.

Result: 25% affected per pregnancy

Example 2 — The same couple with three children

Given: Both parents Aa · q = 25% per child · three children

P(none affected) = 0.75³ = 42.19%.
P(at least one affected) = 1 − 42.19% = 57.81%.
The per-child risk never moved; the family risk is a different question, and the honest way to say it is both numbers together.

Result: 57.81% that at least one of three is affected

Example 3 — An unaffected sibling’s carrier risk (the 2/3 rule)

Given: Both parents Aa · the person is known unaffected

The four zygote classes are AA, Aa, Aa, aa; observing no disease deletes aa, leaving three.
Two of those three are heterozygous, so P(carrier | unaffected) = 2/3 = 66.67%.
Had you used the pre-birth 1/2 you would be understating a real cousin’s carrier risk by a third.

Result: 66.67% carrier probability

Example 4 — Healthy children as evidence about the parents

Given: Prior that both parents are carriers: 1% · two children, both unaffected

A carrier couple has an unaffected child with probability 3/4, so two give (3/4)² = 0.5625.
Posterior = 0.01 × 0.5625 ÷ (0.01 × 0.5625 + 0.99) = 0.565%.
Risk to the next pregnancy = 0.565% × ¼ = 0.141% — the couple who were "unlikely" are now merely "very unlikely".

Result: 0.565% that both are carriers; 0.141% risk to the next child

Example 5 — A carrier mother and an unaffected father (X-linked)

Given: Mother XᴺXᶜ · Father XᴺY · recessive X-linked condition

Sons receive the maternal X and the paternal Y: half of them get the disease copy, so 50% of sons are affected.
Daughters receive the father’s normal X on top of a maternal X: none are affected, half are carriers.
Across all pregnancies, 25% of children are affected — the same fact as "50% of sons", counted differently.

Result: 50% of sons affected; 0% of daughters affected; 25% of all children

Example 6 — Two linked genes in coupling, testcrossed

Given: Heterozygote in coupling (AB / ab) · testcross partner ab / ab · recombination frequency r = 20%

Parental gametes AB and ab are (1 − 0.20)/2 = 40% each; recombinant Ab and aB are 0.20/2 = 10% each.
A testcross shows those gametes directly as offspring phenotypes: 40 : 40 : 10 : 10.
Recombinant offspring are 20% of the progeny, which is a map distance of 20 centiMorgans.

Result: 20% recombinants, map distance 20 cM

Want the reasoning behind the numbers? Read How to Read a Punnett Square.

How to interpret the result

The primary card is the single most likely phenotype class, and the table under it is the whole distribution — every genotype, its zygote count out of the grid, and its percentage. Read the two together: a 56.25% top class in a dihybrid cross is nine of sixteen zygotes, and if you expected 75% you were probably thinking of a single gene. Percentages are per pregnancy; they say nothing about what a particular family of three will look like.

Where the number comes from changes how much weight it can carry. A ratio out of four is exact Mendelian bookkeeping, so its only uncertainty is whether your genotypes are right. A family figure inherits the per-child q plus the assumption that births are independent. A carrier probability given healthy children inherits the prior you typed in — that input is the soft part of the calculation, and a population frequency and a pedigree-derived number can differ by ten-fold for the same couple.

The X-linked mode deliberately quotes risks within each sex. "Half the sons" and "a quarter of children" are the same outcome counted over different denominators, and mixing them up is how a family ends up reassuring itself with the wrong number. The card labeled "any child affected" is the pregnancy-level figure; the son and daughter cards answer the question a person of that sex is actually asking. An affected son of an unaffected couple is evidence about his mother’s chromosomes, which is why the notes name which parent each risk came from.

In linkage mode the ratio itself is the measurement. Deviation from 1:1:1:1 in a testcross is what a recombination fraction means in practice, so the map distance printed here is 100·r by definition — and it is only honest while r is small enough that double crossovers stay rare. At r near 50% the classes become indistinguishable from independent assortment and the calculator says so instead of reporting a linkage nobody can see. If you need the physical order of features on a molecule rather than the genetic distance between them, that is a restriction map, and the restriction site finder works from the sequence itself.

Assumptions

Genes in ratio, family and conditional modes assort independently — one gene per chromosome, or far enough apart on one to behave as if.
Every zygote class survives and is observed: no prenatal lethality, no differential viability, no scoring error.
One dominance rule applies per gene and is applied the same way to every gene in the cross.
Allele transmission is 50/50; no meiotic drive, and no sex-ratio distortion in the X-linked mode.
In the Bayesian question, the alternative to "both carriers" is assumed to produce no affected child.

Limitations

Single-gene inheritance only: polygenic traits, mitochondrial inheritance, imprinting and repeat expansions need a different model.
Recessive X-linked only. X-linked dominant conditions and skewed X-inactivation change the daughter risks.
Map distance from recombination underestimates physical distance once double crossovers matter, and r = 50% is refused outright.
No population genetics. Allele and genotype frequencies across a population are a different question from a cross between two known parents.
Probabilities per pregnancy, not predictions for a family: three unaffected children from a carrier couple is a 42% event, not a refutation.

Common mistakes

Reading a 25% risk as "one in four of my children will be affected" — it is one in four of each pregnancy.
Quoting P(carrier) = 1/2 for an unaffected sibling of an affected person, instead of the conditioned 2/3.
Averaging sons and daughters together in an X-linked cross, which hides both the 50% son risk and the zero daughter risk.
Applying 9:3:3:1 to two genes on the same chromosome, then treating the shortfall as experimental error.
Turning a recombination frequency into a physical distance in base pairs without saying so.
Switching dominance and genotype: "dominant" describes the phenotype of a heterozygote, not how common the allele is.
Reporting the phenotype ratio as if it were the genotype ratio whenever the heterozygote is not identifiable.

FAQ

How do you use a Punnett square?

Write the alleles each parent can transmit along the top and side of a grid, fill each cell with the combination, then count cells. One gene gives four cells, two independent genes give sixteen. Divide a class by the number of cells for its probability. This calculator builds the same table and keeps the count out of the denominator, so 9/16 is printed as 56.25% and still shows the nine.

What is the difference between genotype and phenotype ratio?

The genotype ratio counts genetic classes; the phenotype ratio counts what you can see. Aa × Aa is 1 : 2 : 1 by genotype but 3 : 1 by phenotype, because AA and Aa are indistinguishable under complete dominance. Choose incomplete or codominant here and the two ratios become identical, because the heterozygote gets its own phenotype class.

If both parents are carriers, is the risk 25% each pregnancy or 25% overall?

25% each pregnancy, every time. The chance at least one child in a family of three is affected is 1 − 0.75³ = 57.8%, and the chance exactly one is affected is 42.2%. Both numbers are true; the second is the binomial over the family you are planning. The family mode gives you all three.

Why is an unaffected sibling’s carrier risk 2/3 and not 1/2?

Because "unaffected" removes the aa cell from a four-cell grid, leaving AA : Aa : Aa. Two of the three survivors are carriers. Conditioning on what you already know changes the denominator, which is why the conditional mode renormalizes rather than reusing the original 1/2.

Does a boy get color blindness from his mother or his father?

A son gets his only X from his mother, so an X-linked recessive condition always reaches a son through her — a father cannot pass an X-linked allele to a son at all, only his Y. An affected father’s daughters all inherit his disease X and are carriers unless the mother contributes one too. Set the mode to X-linked and the calculator splits the ratios by sex.

What if my two genes are on the same chromosome?

Then the four offspring classes are no longer equal, and the ratio is set by the recombination fraction: parental gametes at (1 − r)/2 each and recombinants at r/2 each. Use the linked-genes mode with a published or self-measured r; it reports the recombinant percentage and the map distance in centiMorgans, and refuses r = 50% because that is indistinguishable from independent assortment.

Can this tell me whether my child will have a genetic condition?

It tells you the probability for a pregnancy once the parental genotypes are known, which is not the same as knowing them. Carrier status, phase and penetrance usually come from testing and family history. Use these figures to understand a stated risk or to work a genetics course problem, and take a real reproductive decision to a genetic counselor who has the pedigree.

Is there a Hardy-Weinberg calculator here?

Not on this page — the square starts from two parents whose genotypes you already know, while Hardy-Weinberg starts from frequencies across a population and predicts what a sample of strangers looks like. That question has its own page, the Hardy-Weinberg calculator, which counts allele frequencies from typed genotypes, tests the fit and inverts a disease rate into a carrier frequency. The two are commonly confused, so the Genetics collection keeps them apart, and the quantitation tools next door — such as the DNA concentration calculator — cover the wet-lab side of the same alleles.

Scientific Sources

StatPearls — Genetics: Inheritance Patterns (autosomal, X-linked and mitochondrial patterns and their risks to offspring) · Tier 1 source
Wikipedia — Punnett square (the square construction and its gamete assumptions) · Tier 3 source
Wikipedia — Test cross (why a homozygous recessive partner reads gametes straight off the offspring) · Tier 3 source
Wikipedia — Genetic linkage (recombination fraction, coupling and repulsion, centiMorgans) · Tier 3 source

External links open in a new tab and carry rel="nofollow". We cite primary references (NIST, NIH/NCBI, peer-reviewed papers) and established manufacturer technical documentation (NEB, Thermo Fisher, Promega, IDT). Calculated results are estimates; your protocol and manufacturer guidance take precedence.

Last reviewed: 2026-10 · Method version: 1.0

Punnett Square Calculator