Pick the phenotype you want for each trait. Because the genes assort independently, the probabilities multiply. The grid count is shown as a check.
How to type genotypes: Aa, AA, aa · blood types IAi, IAIB, ii · sex-linked XBXb, XbY. The order of the two alleles does not matter.
Example: two pea plants that are both heterozygous for seed shape, Rr × Rr (R = round, dominant; r = wrinkled, recessive).
For RrYy × RrYy, each parent makes four gametes: RY, Ry, rY, ry. Pick one allele from each gene, in every combination (the FOIL trick: first, outer, inner, last). The grid is 4×4 = 16 boxes, with 9 genotypes and the phenotype ratio 9 : 3 : 3 : 1. Try it with the Dihybrid example above.
Each extra heterozygous gene doubles the number of gametes. With $n$ heterozygous genes each parent makes $2^n$ gametes, so the square has $2^n \times 2^n = 4^n$ boxes: 64 boxes for 3 traits and 256 for 4 traits. The same result comes much faster from the product rule: work out each gene on its own, then multiply. For AaBbCc × AaBbCc, the chance of an offspring showing all three recessive traits is $\tfrac14 \times \tfrac14 \times \tfrac14 = \tfrac{1}{64}$. The calculator shows both methods side by side.
ABO blood type has three alleles: $I^A$ and $I^B$ are codominant, and $i$ is recessive to both. A parent still carries only two of them, so the square is built the same way. IAi × IBi gives types AB, A, B and O in a 1:1:1:1 ratio. For an X-linked trait, write the alleles on the X chromosome (XB, Xb). The father's other gamete is Y, which carries no copy. Read the results separately for daughters and sons.
| Cross | Grid | Genotype ratio | Phenotype ratio |
|---|---|---|---|
| Monohybrid Aa × Aa | 2×2 | 1 AA : 2 Aa : 1 aa | 3 : 1 |
| Test cross Aa × aa | 2×1 | 1 Aa : 1 aa | 1 : 1 |
| Homozygous AA × aa | 1×1 | all Aa | all dominant |
| Dihybrid AaBb × AaBb | 4×4 | 9 genotypes (1:2:1:2:4:2:1:2:1) | 9 : 3 : 3 : 1 |
| Dihybrid test cross AaBb × aabb | 4×1 | 1 : 1 : 1 : 1 | 1 : 1 : 1 : 1 |
| Trihybrid AaBbCc × AaBbCc | 8×8 | 27 genotypes | 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1 |
| 4 traits AaBbCcDd × AaBbCcDd | 16×16 | 81 genotypes | 16 phenotypes, 81 : 27×4 : 9×6 : 3×4 : 1 |
| Incomplete dominance Rr × Rr | 2×2 | 1 : 2 : 1 | 1 red : 2 pink : 1 white |
| Codominance Cc × Cc (roan cattle) | 2×2 | 1 : 2 : 1 | 1 red : 2 roan : 1 white |
| Blood type IAi × IBi | 2×2 | 1 : 1 : 1 : 1 | 1 AB : 1 A : 1 B : 1 O |
| X-linked XBXb × XBY | 2×2 | 1 : 1 : 1 : 1 | daughters all unaffected (half carriers); sons 1 unaffected : 1 affected |
Toss two coins together. There are four equally likely outcomes: heads-heads, heads-tails, tails-heads, tails-tails. A Punnett square is the same idea. Each parent “tosses” one of their two alleles into each sperm or egg, and the grid lists every way two of those tosses can meet. Because every box is equally likely, counting boxes gives probabilities.
A gene comes in versions called alleles. Your two alleles are your genotype (AA, Aa or aa). What you can see or measure is the phenotype. If one copy of a dominant allele is enough to show its trait, AA and Aa look the same and only aa shows the recessive trait. That is why a 1:2:1 genotype ratio becomes a 3:1 phenotype ratio. Mendel reported 5,474 round and 1,850 wrinkled pea seeds in 1866, a ratio of 2.96 : 1.
The two alleles of a gene separate in meiosis (the law of segregation). Genes on different chromosomes are sorted into gametes independently of each other (the law of independent assortment). So a dihybrid square is two monohybrid squares multiplied: $\left(\tfrac34 + \tfrac14\right)^2$ expands to $\tfrac{9}{16}+\tfrac{3}{16}+\tfrac{3}{16}+\tfrac{1}{16}$, which is the 9:3:3:1 ratio. With $n$ genes you get $2^n$ gametes and a $4^n$-box square. Real genetics adds twists that still fit in the square: incomplete dominance and codominance give a third phenotype, multiple alleles (ABO) give four blood types, and X-linked genes make sons and daughters inherit differently because sons get their only X from their mother. Genes close together on the same chromosome are linked and break the independence assumption. This calculator assumes no linkage.
1) Load Dihybrid 9:3:3:1. Change one parent to rr yy and watch it become a 1:1:1:1 test cross. 2) Load Sex-linked. Set the father to XbY and see that every daughter is affected or a carrier, while the sons' outcome depends only on the mother. 3) Load 4 traits and use the probability finder to get the chance of all four recessive traits (1/256). Then find those boxes in the 16×16 grid.
A Punnett square is a grid used to predict the possible genotypes and phenotypes of offspring from a cross. One parent's gametes go along the top, the other's down the side, and each box is one equally likely combination. It is named after the British geneticist Reginald C. Punnett, who devised it in the early 1900s.
Key takeaway: each box is one equally likely offspring, so counting boxes gives probabilities.List each parent's four possible gametes by taking one allele from each gene in every combination (for AaBb: AB, Ab, aB, ab). Put them on a 4×4 grid, fill in the 16 boxes, then count. Two parents heterozygous for both genes give 9 genotypes and a 9:3:3:1 phenotype ratio.
Key takeaway: 2 heterozygous traits → 4 gametes per parent → 16 boxes → 9:3:3:1.With n heterozygous genes each parent makes 2n gametes, so the grid is 2n × 2n. Three traits need an 8×8 grid (64 boxes) and four traits need a 16×16 grid (256 boxes). A homozygous gene adds no extra rows. For large crosses the product rule is faster: multiply the single-gene probabilities.
Key takeaway: 3 traits = 64 boxes, 4 traits = 256 boxes, or multiply the single-gene probabilities.A gamete is a sperm or egg cell. It carries only one allele of each gene because the two alleles separate during meiosis. In a Punnett square the gametes are the labels along the top and side of the grid, and each box joins one gamete from each parent.
Key takeaway: gametes have one allele per gene; they are the row and column labels.The genotype ratio counts the allele combinations (for Aa × Aa: 1 AA : 2 Aa : 1 aa). The phenotype ratio counts the visible traits. With complete dominance AA and Aa look the same, so the phenotype ratio is 3 : 1. With incomplete dominance or codominance the heterozygote looks different, so both ratios are 1 : 2 : 1.
Key takeaway: genotype = allele pairs, phenotype = appearance; dominance decides how they map.ABO blood type is controlled by three alleles: IA, IB and i. IA and IB are codominant and both are dominant to i. Each person carries two of them, so each parent still gives one allele per gamete and the square stays 2×2. For example, IAi × IBi gives 1/4 each of types AB, A, B and O.
Key takeaway: many alleles in the population, but only two per person, so the grid is still 2×2.Write the alleles as superscripts on the X chromosome, such as XB and Xb. The father's gametes are one X and one Y, and the Y carries no copy of the gene. Read daughters (XX) and sons (XY) separately. A carrier mother XBXb and an unaffected father XBY have unaffected daughters (half of them carriers), and half of their sons are affected. This is the pattern of red-green colour blindness and haemophilia.
Key takeaway: sons get their X from their mother, so X-linked recessive traits show up mostly in males.Yes. People sometimes call it a Mendel square, a Mendel box or an allele chart, but the standard name is Punnett square. Gregor Mendel found the ratios in pea-plant experiments that he published in 1866. The grid itself was introduced later by Reginald Punnett as a way to show Mendel's rules.
Key takeaway: same tool; Mendel found the ratios, Punnett drew the square.A Punnett square gives probabilities, not guaranteed counts. Each child is an independent event, like a new coin toss, so a family of four can easily have zero or three children with a 1/4-chance trait. Ratios only come close to the prediction in large numbers of offspring, as in Mendel's thousands of peas. Linkage, many genes acting together, and the environment can also change the outcome.
Key takeaway: the square predicts chances for each child, not exact family counts.