The formula
Gametes of one parent × gametes of the other
What it means
Each parent passes one allele of each gene to every gamete, so an "Aa" produces "A" and "a" gametes in equal numbers while an "AA" produces only "A". The square puts one parent's gametes across the top and the other's down the side, and every box is a possible child. You do not have to remember the famous ratios: they fall out of counting boxes. A monohybrid "Aa × Aa" gives 3 to 1 in phenotype and 1:2:1 in genotype; a dihybrid "AaBb × AaBb" gives 9:3:3:1 across sixteen boxes.
How to work it out by hand
- Write out each parent's gametes: one for every allele of every gene
- Put one parent's gametes across the top and the other's down the first column
- Fill each box by joining the alleles from its row and its column
- Count how many boxes repeat each genotype and each phenotype
What is worth knowing
A 3 to 1 ratio does not promise that three out of four children will show the dominant trait: it is the probability of each pregnancy on its own, and each one starts from scratch. The square also assumes the genes assort independently, which happens when they sit on different chromosomes; two genes close together on the same chromosome are inherited together and the ratios fall apart. It does not cover cases where one allele does not fully win either: with incomplete dominance the heterozygote is intermediate (the pink flower from a red and a white parent), and with codominance both show, as in blood type AB.