Dihybrid Punnett Square Calculator and Guide

A dihybrid Punnett square calculator predicts the possible offspring genotypes and phenotypes for two traits by combining the alleles in each parent’s gametes. Enter each parent’s genotype at both genes, and the calculator returns the expected combinations and their probabilities under the assumptions of a basic Mendelian cross.

Formula

This calculator gives the probability of each particular four-allele offspring genotype combination, assuming independent assortment and equal probability for each allele a parent can pass on. The expression is:

Probability of one listed combination (%) = 100 ÷ (2^{2 − p1a} × 2^{2 − p1b} × 2^{2 − p2a} × 2^{2 − p2b})

• p1a and p1b are Parent 1’s genotypes at genes A and B.
• p2a and p2b are Parent 2’s genotypes at genes A and B.
• For every gene, enter 0 for a homozygous dominant genotype (AA or BB), 1 for a heterozygous genotype (Aa or Bb), or 2 for a homozygous recessive genotype (aa or bb).
• The output is the probability, in percent, of any one specified offspring genotype combination. It is not the probability of a broad phenotype category unless that category contains just one genotype.

A homozygous parent can pass only one allele type at that gene, so it contributes one possible allele choice. A heterozygous parent has two equally likely choices. The denominator therefore counts all equally likely allele combinations across both genes and both parents. For a complete result, list the distinct offspring combinations in the Punnett square and add the probabilities of combinations that belong to the category you want.

Worked Example

The defaults represent a cross in which both parents are heterozygous at both genes: AaBb × AaBb. Each parent can produce four gamete types—AB, Ab, aB, and ab—each with a probability of 1/4 if the genes assort independently.

1. Substitute p1a = 1, p1b = 1, p2a = 1, and p2b = 1.
2. Calculate the number of equally likely combinations: 2¹ × 2¹ × 2¹ × 2¹ = 16.
3. Calculate the probability of any one specified four-allele genotype combination: 100 ÷ 16 = 6.25%.

For example, AABB can result only when both parents pass AB, so its probability is 6.25%. This does not mean every possible genotype has that probability: some genotypes can be formed in several different ways. For instance, the gene-A genotype AA can arise from two gamete combinations, while Aa can arise from two as well; across two genes, the number of routes to a combined genotype can differ. Add the probabilities of all routes that produce the same genotype before reporting its total probability.

How a Dihybrid Cross Works

A dihybrid cross follows two genes at once. In the classic example, A and B are dominant alleles and a and b are recessive alleles. A parent with genotype AaBb can pass one allele from each gene, making four possible gametes: AB, Ab, aB, and ab. A 4-by-4 Punnett square pairs each of one parent’s gametes with each of the other parent’s gametes, creating 16 equally likely boxes for an AaBb × AaBb cross.

For a straightforward case with complete dominance and independent assortment, those 16 boxes produce the familiar phenotype ratio 9:3:3:1: nine show both dominant traits, three show the dominant A trait and recessive b trait, three show recessive a and dominant B, and one shows both recessive traits. This ratio describes phenotype categories, not 16 different offspring genotypes. Several boxes can have the same genotype or phenotype.

How to Use the Calculator

• Write each parent’s genotype separately for gene A and gene B. For example, an AaBb parent has genotype Aa at A and Bb at B.
• Convert each genotype to the calculator’s code: 0 for two dominant alleles, 1 for one dominant and one recessive allele, and 2 for two recessive alleles.
• Use the output as the probability of one specific allele combination in the complete offspring genotype. Work out the relevant combinations in a Punnett square if you need a particular genotype or phenotype probability.
• To find a phenotype probability under complete dominance, group all genotypes that show that phenotype and add their probabilities.

For example, if both parents are AaBb, the probability of an offspring with genotype AABB is 1/16, or 6.25%. The probability of showing both dominant phenotypes is 9/16, or 56.25%, because nine Punnett-square boxes meet that description. These answers differ because phenotype categories can include multiple genotypes.

Assumptions and Limits

The standard dihybrid square assumes that each parent’s allele transmission follows the stated genotype and that the two genes assort independently. Independent assortment is a useful model when genes are on different chromosomes or sufficiently far apart on the same chromosome. Genes close together on one chromosome may be linked and inherited together more often than this model predicts.

The simple dominant/recessive phenotype ratio also assumes complete dominance at each gene. It does not automatically describe incomplete dominance, codominance, multiple alleles, gene interactions (epistasis), or traits influenced by many genes and the environment. In those situations, a genotype square may still help organize possible allele combinations, but translating combinations into observed traits requires a different inheritance model.

Finally, Punnett squares give probabilities, not guaranteed outcomes. A predicted 25% chance does not mean exactly one-quarter of a small group of offspring must have that result. Actual outcomes vary by chance, especially in small samples.

Common Mistakes

• Confusing genotype and phenotype: Aa and AA are different genotypes, even if both show the same dominant phenotype under complete dominance.
• Counting boxes instead of distinct genotypes: Multiple boxes can produce the same genotype. Combine those routes when calculating a genotype’s total probability.
• Assuming every cross has a 9:3:3:1 ratio: That ratio applies to a specific heterozygous-by-heterozygous cross at two independently assorting genes, with complete dominance.
• Mixing allele order: Use a consistent convention, such as writing the A/a pair first and the B/b pair second, so AaBb is not confused with a different pairing.
• Reading percentages as predictions for one individual: A probability describes the expected proportion over many comparable inheritance events, not a certainty about a particular offspring.

Frequently Asked Questions

What does a dihybrid Punnett square calculator calculate?
It helps determine possible offspring combinations for two genes and the probability of each outcome, based on the parental genotypes and the inheritance assumptions used.

What is the genotype ratio for AaBb × AaBb?
The cross has 16 equally likely gamete pairings, but the offspring genotype ratio is not simply 16 unique outcomes. Combine repeated genotypes from the square. With complete dominance and independent assortment, the phenotype ratio is 9:3:3:1.

How do I find the chance of two recessive traits?
For an AaBb × AaBb cross, an offspring must be aabb to show both recessive traits under complete dominance. Only one of the 16 equally likely boxes produces aabb, giving a probability of 1/16, or 6.25%.

Does a Punnett square predict exactly how many offspring will have a trait?
No. It gives probabilities. The observed number in a real group can be higher or lower, particularly when there are few offspring.

Can a dihybrid square be used for linked genes?
A basic square can list possible combinations, but its equal-probability assumption for gametes may be wrong when genes are linked. A model that includes linkage and recombination information is needed for more accurate probabilities.

Related

• Hardy-Weinberg Equilibrium Calculator
• Hardy-Weinberg Formula Calculator
• Hardy Weinberg Equilibrium Calculator

in p1a | Parent 1 gene A genotype (0=AA, 1=Aa, 2=aa) | - | 1 | 0
in p1b | Parent 1 gene B genotype (0=BB, 1=Bb, 2=bb) | - | 1 | 0
in p2a | Parent 2 gene A genotype (0=AA, 1=Aa, 2=aa) | - | 1 | 0
in p2b | Parent 2 gene B genotype (0=BB, 1=Bb, 2=bb) | - | 1 | 0
out r | Each listed genotype combination probability | % | 100 / ((2 ^ (2 - p1a)) * (2 ^ (2 - p1b)) * (2 ^ (2 - p2a)) * (2 ^ (2 - p2b))) | 2