Although no prediction is 100 percent accurate, you can get a rough approximation of your child's prospective eye color by using a Punnett square. If you know your parents' and your mate's parents' eye colors it's possible to use probability to determine what eye color your child will have. Two genes have thus far been linked to eye color; one contains alleles for brown or blue, where the other contains alleles for green and blue. Blue is always recessive.
First, you need your genotypes--or the genetic makeup. When diagramming a Punnett square, a capital B represents the allele for brown eyes, a lower-case b represents the one for blue eyes, and capital G represents green eyes. Assume, as an example, that one of your parents has a history of brown eyes in the family, so they likely have homozygous gene for brown eyes. This is represented by BB. Now, assume your other parent has blue eyes. This is represented by bb, because blue is a recessive color. Finally, assume you have brown eyes. Because one of your parents has blue eyes, you have a heterozygous brown eye gene. Do the same for your mate.
Write each gene pattern along the top and side of the Punnett square. Assume, for example, that your genotype is Bbbb, and your partner's is BbGG. Take the letter from each row and combine it with the one from each column and look at the results. Because a brown-eye gene is in the mix, your child will likely have brown eyes. Brown is dominant over green, which is dominant over blue.