A Punnett square is a way of being certain. You work out which gametes each parent can produce, line them up, and every box is one possible offspring. No guessing, no coin flips — just every combination the parents are capable of making.
Most calculators stop once the grid is drawn. This one goes two steps further, and the second one is the part that actually matters in a genetics course. If your two genes sit on the same chromosome, they do not assort independently, and the famous 9:3:3:1 quietly becomes 3:1. Set the parents to AaBb × AaBb, flip the switch, and watch the ratio change.
Enter two parent genotypes and this builds the square box by box, shows you the gametes each parent can pass on, and gives the genotypic and phenotypic ratios. The option most calculators leave out is at the bottom: if your two genes are on the same chromosome they do not assort independently, and the classic 9:3:3:1 collapses to 3:1.
Two letters for one gene: AA, Aa or aa.
With complete linkage there is no recombination, so a parent only ever passes on the two combinations it already carries. Real genes sit somewhere between fully linked and fully unlinked — recombination frequency does the rest.
What a Punnett square actually shows you
Each parent contributes one allele per gene, and it can only pass on what it carries. That single idea generates everything else.
Start with one gene. A parent that is AA has two copies of the same allele, so every gamete it makes is an A. There is no choice, which is why an AA parent produces a single column. A parent that is Aa can pass on either, so it makes two gametes — half A, half a. A parent that is aa makes only a.
Put the first parent’s gametes down the side and the second parent’s across the top. Every cell is one allele from each, and every cell is equally likely. The ratio is just how many times each genotype appears.
For Aa × Aa you get four boxes: AA, Aa, Aa, aa. That is 1:2:1 genotypically. But AA and Aa both look dominant, so the phenotype ratio is 3 dominant : 1 recessive. Those two ratios answer different questions and mixing them up is where most marks get lost.
Two genes, and why the square gets bigger
With two genes you need four gametes per parent, because each gamete carries an allele for gene one and gene two. From AaBb you get AB, Ab, aB and ab — every combination of what it carries at each position.
Four by four gives 16 boxes. The genotypic ratio is 1:2:1:2:4:2:1:2:1, which is genuinely ugly, and almost nobody asks you for it. The phenotypic ratio is the one that matters:
| Phenotype | Boxes | Fraction |
|---|---|---|
| Both dominant (A–B–) | 9 | 9/16 |
| First dominant only (A–bb) | 3 | 3/16 |
| Second dominant only (aaB–) | 3 | 3/16 |
| Both recessive (aabb) | 1 | 1/16 |
9:3:3:1. That is the ratio everyone memorises, and the reason it comes out is that the genes are assumed to assort independently.
Linked genes break the 9:3:3:1
Independent assortment is not free. It only works if a gamete’s allele for gene one has no influence on which allele it gets for gene two — which is true when the two genes are on different chromosomes, or far enough apart on the same one.
Put them close together on the same chromosome and they travel together. A parent that is AB/ab does not hand out AB, Ab, aB and ab evenly. It hands out AB and ab, because those are the two combinations it actually carries. No recombination, no extra gametes.
Cross AaBb × AaBb with complete linkage and you get four boxes instead of sixteen:
| Offspring | Boxes |
|---|---|
| AABB | 1 |
| ABab | 2 |
| aabb | 1 |
Phenotypically that is 3 dominant : 1 recessive. Same parents, completely different ratio. The 3:1 is the classic signature of a recessive trait showing up in only one quarter of offspring, and it is the whole reason recessive inheritance looks rare when it is not.
Which brings up the arrangement. If the parent is cis (AB on one chromosome, ab on the other) it passes on AB and ab. If it is trans (Ab and aB) it passes on Ab and aB. The square changes; the 3:1 does not. Real genes sit somewhere in between — the recombination frequency is the percentage of gametes that are recombinant, and it is the number geneticists actually measure.
Three things that catch people out
Write both parents in the same gene order. AaBb and BbAa look identical but read as different genotypes. Pick one order and use it in both slots and in your working.
A ratio is a prediction, not a promise. Aa × Aa gives 1:2:1 across a large number of offspring. Any single offspring can still be AA, Aa or aa. A ratio of 1:2:1 does not mean you will get exactly one, two and one in a litter of four.
Upper case means dominant by convention only. A is not inherently dominant. A capital letter is just a label, and dominance has to be established experimentally — which is what a test cross is for.
When you cannot tell two genotypes apart
A dominant phenotype is AA or Aa. You cannot see the difference by looking, so any cross where the phenotype is all you have leaves the genotype ambiguous.
A test cross settles it by crossing the unknown with a homozygous recessive:
- Unknown AA × aa → every offspring Aa, so all dominant
- Unknown Aa × aa → half Aa (dominant) and half aa (recessive), a 1:1 split
One of those two results and you know. Enter each into the calculator above and compare. The population genetics calculator picks up the other half of this topic — testing a whole population against Hardy-Weinberg rather than a single cross.
Frequently asked questions
How do I work out the gametes?
For each gene, the parent passes on whichever allele it carries. Heterozygous means two different alleles, so two gamete types; homozygous means one allele, so one type. With two genes, take every combination.
What is the difference between the genotype and phenotype ratio?
The genotypic ratio counts the actual letter combinations. The phenotypic ratio groups them by what you would see. Aa × Aa is 1:2:1 genotypically but 3:1 phenotypically, because AA and Aa look identical.
Why is the dihybrid ratio 9:3:3:1?
Because the genes assort independently. Each dominant phenotype has three-quarters chance of appearing in each gene separately, so 3/4 × 3/4 = 9/16. The two mixed classes are 3/16 each and the double recessive is 1/16.
What does complete linkage mean?
The two genes are so close together on the same chromosome that crossing over effectively never separates them. A parent only passes on the two allele combinations it already carries, so a dihybrid cross gives 1:2:1 genotypically and 3:1 phenotypically.
What is the difference between cis and trans?
Cis means the two dominant alleles sit on the same chromosome (AB/ab), trans means they are split (Ab/aB). It changes which gametes the parent produces and therefore the genotypic ratio, but the 3:1 phenotypic ratio holds either way under complete linkage.
What is a Punnett square?
A grid that shows every possible combination of alleles a child could inherit, one box for each. It turns two parents genotypes into the ratio you expect in the offspring, which is why it is the fastest way to answer almost any basic genetics question. Reginald Punnett drew it as a checkerboard in 1910, and it has been the same four-box square ever since.
What is a 2×2 Punnett square and how do I fill one in?
A 2×2 is the smallest useful square and the right answer for a single gene. Write the two gametes from the first parent down the side and the two from the second across the top, then fill each box by combining the allele on its row with the allele on its column. Four boxes, four possible children. A worked example: for Bb x Bb you get BB, Bb, Bb and bb, so three brown to one blue, a 3 to 1 ratio. Two genes need a 4×4 with sixteen boxes instead, because each parent then passes on four gametes.
Related tools
- Population Genetics Calculator — Hardy-Weinberg ratios and a chi-square test on real counts
- GPA Calculator — the multi-scale tool for your grades
- All student GPA tools