Read this before using the result. Eye colour is not a one-gene trait. The brown-dominant, blue-recessive model below is a teaching simplification, and it makes predictions that fail in real families. Two blue-eyed parents genuinely can have a brown-eyed child. If you are here to settle a question about a real family, the square cannot do that.
The classic square
What the simple model gets right
Brown really is dominant over blue in a broad statistical sense, so the model is not pure fiction. Across a large population, brown-eyed parents do have more brown-eyed children, and two blue-eyed parents usually do have blue-eyed children. As a first illustration of dominance it works.
What it cannot do is make a reliable prediction about one specific family, and that is what most people arrive here wanting.
What it gets wrong
Most of the variation in human eye colour traces to a regulatory region near HERC2, which controls how much the neighbouring OCA2 gene is expressed. OCA2 governs melanin production in the iris. But at least a dozen other genes contribute, including ASIP, SLC24A4 and TYR.
That is why hazel, green and grey exist at all. A one-gene model has no room for them, and no room for a spectrum. Real eye colour is closer to a dial than a switch, which is exactly what you would expect from many genes each nudging pigment up or down.
Why blue eyes are not blue
There is no blue pigment in a human iris. Blue eyes have very little melanin in the front layer, so longer wavelengths pass through and get absorbed at the back, while shorter wavelengths scatter back out. The colour you see is a structural effect, the same physics that makes the sky blue. Brown eyes have enough melanin to absorb almost everything, so you see the pigment itself.
Common questions
Can two blue-eyed parents have a brown-eyed child?
Yes, and it is documented. The simple model taught in schools says no, but eye colour depends on many genes, not one. Two blue-eyed parents can each carry brown-associated variants at other loci, and the combination in a child can produce brown. It is uncommon, but it is not evidence of anything except that the school model is wrong.
Is eye colour really controlled by one gene?
No. The single-gene model is a teaching simplification. Most of the variation traces to a regulatory region near HERC2 that controls how much OCA2 is expressed, and OCA2 governs melanin in the iris. But at least a dozen other genes contribute, which is why hazel, green and grey exist at all.
Why is eye colour still taught as a simple dominant trait?
Because it is a convenient illustration of dominance, and brown really is dominant to blue in a rough statistical sense. The problem is that students then use it to make predictions about real families, where it fails often enough to matter.
What actually determines eye colour?
Melanin in the front layer of the iris. A lot of melanin scatters little light and looks brown. Very little melanin means short wavelengths scatter back out, which looks blue. Blue eyes have no blue pigment at all, the colour is a structural effect, the same reason the sky is blue.
Can a Punnett square predict my child's eye colour?
It can give a rough sense of likelihood if you treat brown as broadly dominant, but it cannot give a reliable probability. Anyone offering a precise percentage for eye colour is applying a one-gene model to a polygenic trait.
Why do some babies' eyes change colour?
Melanin production in the iris continues after birth. Many babies of European ancestry are born with little iris melanin and darken over the first year or so. The genotype has not changed, only how much pigment has been laid down.
Related tools
Punnett square calculator, for any single-gene cross.
Dihybrid cross calculator, for two genes at once.
Blood type Punnett square, which unlike eye colour really is a clean single-locus trait.
Sources
The HERC2 regulatory variant controlling OCA2 expression is described in Eiberg et al., "Blue eye color in humans may be caused by a perfectly associated founder mutation in a regulatory element located within the HERC2 gene," Human Genetics 123:177-187, 2008. The polygenic picture and the additional contributing loci are reviewed in White and Rabago-Smith, "Genotype-phenotype associations and human eye color," Journal of Human Genetics 56:5-7, 2011. The square on this page is the teaching model, presented as such.