Punnett Square Calculator

What is a Punnett square?

Every living thing carries two copies of most of its genes, one from each parent. A gene can come in different versions, called alleles. For a pea plant a flower-colour gene might have a purple version and a white version. You carry two of them, and which two you have is your genotype.

Some alleles are dominant and some are recessive. A dominant one, written with a capital letter like B, shows up whenever it is present. A recessive one, written with a small letter like b, only shows if both your copies are recessive. So BB and Bb both look the same on the outside, while only bb shows the recessive trait. What you actually look like is your phenotype.

A Punnett square is a little grid that works out what children two parents can have. Each parent hands down just one of their two alleles, picked at random. The grid lines up the choices from one parent along the top and the other down the side, and each inner box is one possible child. Because every box is equally likely, counting them tells you the odds.

Cross two Bb parents and the grid fills with one BB, two Bb and one bb. Three of the four show the dominant trait and one shows the recessive, the classic three-to-one ratio. The calculator at the top of the page draws that grid for any parents you type in.

How do you do a Punnett square?

The Punnett square is a picture of two of Gregor Mendel's rules. The law of segregation says the two alleles of a gene separate when eggs and sperm are made, so each gamete carries exactly one. The grid's row and column headers are those gametes.

For a monohybrid cross, one gene with two alleles, each parent makes at most two kinds of gamete, so the square is 2 by 2. Cross \(Bb \times Bb\) and the four boxes are BB, Bb, Bb, bb: a genotype ratio of \(1 : 2 : 1\) and, with B dominant, a phenotype ratio of \(3 : 1\). A test cross against a recessive parent, \(Bb \times bb\), gives a clean \(1 : 1\), which is how you find out whether a dominant-looking individual is BB or Bb.

Track two genes at once and you need the law of independent assortment: the allele you pass on for one gene does not depend on the one you pass on for the other. A \(BbEe\) parent therefore makes four gamete types, BE, Be, bE and be, in equal numbers, so a dihybrid cross is a 4 by 4 square with sixteen boxes.

Cross \(BbEe \times BbEe\) and those sixteen boxes sort into the famous \(9 : 3 : 3 : 1\) phenotype ratio: nine show both dominant traits, three show the first dominant and second recessive, three the reverse, and one shows both recessive traits. That ratio is just the monohybrid \(3 : 1\) applied to each gene and multiplied together, \((3:1) \times (3:1)\), because the genes assort independently.

Punnett squares assume the simplest case: two alleles per gene, full dominance, one gene per trait, and genes on different chromosomes. Real inheritance often bends those rules, and the square is where you start before adding the complications.

The probability behind Mendelian crosses

The square is a probability table

A Punnett square is really a way of multiplying probabilities. Each gamete a parent can make has a probability, and an offspring genotype is the product of the two independent gamete probabilities, summed over the ways to reach it. For \(Bb \times Bb\), P(B from each parent) \(= \tfrac12\), so P(BB) \(= \tfrac14\), P(bb) \(= \tfrac14\), and P(Bb) \(= 2 \times \tfrac12 \times \tfrac12 = \tfrac12\). The grid just lays that arithmetic out as equal-area boxes so you can count instead of multiply.

Independent assortment and the product rule

For unlinked genes the joint probability factorises: P(genotype at gene 1 and gene 2) = P(gene 1) × P(gene 2). This is why the dihybrid ratio is the monohybrid ratio squared, and why a forked-line or branching diagram gives the same answer as a 16-box grid with far less drawing. It generalises: an \(n\)-gene cross of heterozygotes has a \(3^n : \dots : 1\) phenotype spread and \(2^n\) gamete types, which is why nobody draws a trihybrid square by hand.

Where the simple ratios break down

Mendel's clean numbers assume complete dominance and independence. Incomplete dominance and codominance change the phenotype ratio to match the genotype ratio, \(1 : 2 : 1\). Epistasis, where one gene masks another, collapses the \(9 : 3 : 3 : 1\) into ratios like \(9 : 7\) or \(12 : 3 : 1\). And genes close together on the same chromosome are linked, so their alleles do not assort independently; the gamete frequencies shift toward the parental combinations, and the deviation measures the recombination distance between them.

From a grid to a population

A Punnett square predicts one family. Scale up to a whole breeding population and the same allele-and-gamete logic becomes the Hardy-Weinberg principle, which tracks genotype frequencies across generations rather than within a single cross. The square is the atom of Mendelian genetics; population genetics is what you get when you let it run on millions of matings at once.