A Punnett Square is a really useful tool for determining the outcome of genetic crosses in which some genes are dominant and some are recessive. By using a Punnett Square it is possible to work out the likelihood of certain particular genotypes occurring as a result of the combination of different alleles.

The method is named after Professor Reginald Crundall Punnett FRS (20 June 1875 - 3 January 1967) - Further Information.

If working with just one gene in a cross of diploid parents then the outcome is fairly easy to determine:

As can be seen in the above figure, two diploid parent cells containing one gene of interest with two alleles (alleles of the gene shown as dark green or light green) can each produce 2 haploid gametes (in the case of the parent cell on the left one dark green and one light green; and the parent on the right, two dark green). These gametes can fuse in 4 possible ways to produce 4 diploid offspring, two containing 2 dark green genes, and 2 containing one dark green and one light green, and these different combination of genes may lead to different phenotypes.

If you have heterozygous parents with 2 different genes then there are 16 possible outcomes, 3 genes gives 64 possible outcomes. (You can calculate the possible number of outcomes using 2^(2x), where x = number of genes.) Therefore, trying to work out crosses with more than 2 genes using the type of diagram above would be very complicated, hence the use of Punnett Squares.

It should be noted that the number of outcomes is NOT the same as the number of genotypes or phenotypes from a cross. In the above figure there are 4 possible outcomes, but only two genotypes (dark green/dark green, and dark green/light green), and depending on the function of the gene it could be 1 or 2 phenotypes.