Punnett square calculator
Cross two parents for one to four genes: see the square, the genotype and phenotype ratios and the probability of each offspring class.
Two letters per gene, a different letter for each gene: Aa, BB, bb. Uppercase is the dominant allele. Example for two genes: AaBb.
What does a Punnett square show?
A Punnett square lists every combination of gametes from two parents and so gives the probability of each offspring genotype. Each parent is heterozygous Aa in the classic cross; each makes A and a gametes with equal probability, because the two alleles of a gene separate at meiosis. The four cells of the Aa × Aa square give 1 : 2 : 1 for AA : Aa : aa, which is 3/4 dominant phenotype and 1/4 recessive when one allele is completely dominant. These are probabilities for each child, not guarantees for a family of four: for two Aa parents, every child has the same 1-in-4 chance of being aa, whatever their earlier children turned out to be, because each fertilization is independent of the others. A homozygous parent (AA or aa) makes only one kind of gamete, so crossing AA with aa gives a square in which every cell is Aa.
How do I enter genotypes?
Type each gene as two letters, and use a different letter for each gene: Aa, BB, bb. An uppercase letter is the dominant allele. For a dihybrid cross write AaBb in both boxes; for a test cross write Aa and aa. Both parents must carry the same genes in the same order. The calculator accepts up to four genes (eight letters) and treats them as independent. For one or two genes it draws the full square; for three or four it gives the probabilities directly, because a tetrahybrid square has 256 cells.
Worked example: the dihybrid cross
Cross two parents that are heterozygous for two genes, AaBb × AaBb. Each parent makes four gamete types, AB, Ab, aB and ab, each with probability 1/4, so the square has 16 cells. With complete dominance the phenotypes come out 9:3:3:1: 9/16 show both dominant traits, 3/16 show only A, 3/16 show only B and 1/16 show neither. This is the 9:3:3:1 ratio that OpenStax Biology 2e (section 12.3) reports for round and yellow, round and green, wrinkled and yellow, and wrinkled and green seeds. There are nine different genotypes, with ratio 1:2:1:2:4:2:1:2:1.
What is the product rule, and why does it replace the square for many genes?
If two genes are inherited independently, the probability that a child has a given outcome for both is the product of the single-gene probabilities: for an Aa × Aa cross, the chance of a dominant phenotype is 3/4, so two dominant phenotypes at independent genes is 3/4 × 3/4 = 9/16. For all recessive, it is 1/4 × 1/4 = 1/16. The same logic extends to more genes. For AaBbCc × AaBbCc the all-dominant class has probability 27/64, and in the tetrahybrid cross AaBbCcDd × AaBbCcDd it is 81/256 while all-recessive is 1/256, the numbers OpenStax gives for four genes. The sum rule adds the probabilities of alternative ways to the same outcome: AA (1/4) or Aa (1/2) gives 3/4.
What changes with incomplete dominance or codominance?
With incomplete dominance the heterozygote looks different from both homozygotes (an intermediate blend), and with codominance it shows both traits at once. In both cases each genotype has its own phenotype, so the phenotype ratio equals the genotype ratio. An Aa × Aa cross then gives 1:2:1 (AA : Aa : aa) instead of 3:1. Select “Incomplete dominance or codominance” to see that. The probabilities of genotypes do not depend on dominance at all; only the way genotypes are grouped into phenotypes does.
What is a test cross?
A test cross mates an individual of unknown genotype that shows the dominant phenotype with a homozygous recessive aa partner. If the unknown is AA, every child shows the dominant phenotype; if it is Aa, half do (1:1 with complete dominance). Because the recessive parent contributes only a, the children’s phenotypes reveal which gametes the unknown parent made. Try Aa × aa to see the 1:1 result.
Limits of this method
The calculator assumes that the genes assort independently, which holds for genes on different chromosomes or far apart on the same chromosome. Genes that sit close together on one chromosome are linked and are inherited together more often than the 9:3:3:1 pattern predicts, so a dihybrid cross of linked genes will not follow these numbers. It also does not model sex-linked genes, multiple alleles (such as the ABO blood groups), lethal genotypes, epistasis or environmental effects. Real counts of offspring also scatter around the predicted ratio by chance, so a chi-square test is needed to judge whether observed counts fit a predicted ratio.
Sources: OpenStax, Biology 2e, section 12.3 “Laws of Inheritance” (independent assortment, the 9:3:3:1 dihybrid ratio, product and sum rules, the tetrahybrid cross with 1/256 and 81/256). Related: Hardy-Weinberg calculator, chi-square calculator, probability calculator, binomial probability calculator and permutation and combination calculator.