TL;DR:
A Punnett square lists each parent's possible gametes on the sides and the offspring combinations inside the boxes.
A Bb × Bb cross gives genotypes BB : Bb : bb in a 1:2:1 ratio and a 3:1 ratio of dominant to recessive phenotypes.
A test cross with a homozygous recessive partner reveals whether a dominant-looking parent is BB or Bb.
In pea plants, purple flowers beat white ones. Two purple plants are crossed and some of the seeds grow into white-flowered plants. How is that possible, and how often should it happen? A Punnett square answers both.
The idea in plain words
Each parent carries two copies of a gene, called alleles. Each gamete (sperm, egg or pollen) gets just one of them. Which one it gets is a coin toss.
An allele is dominant if its trait shows when it is paired with a different allele, and recessive if the trait only shows when both copies are the recessive one. Capital letters mean dominant (B for purple), lowercase mean recessive (b for white). Two matching alleles are homozygous (BB or bb). Two different ones are heterozygous (Bb).
The genotype is the allele pair. The phenotype is the visible trait. BB and Bb have different genotypes but the same phenotype: purple.
Why the square works
The square is a tidy way to list every equally likely pairing of one gamete from each parent. Each parent's gametes go along one edge. Each box is one egg meeting one sperm, and all boxes are equally likely when the parents' alleles separate evenly.
So the chance of any box is 1/2 × 1/2 = 1/4 for a cross where each parent makes two kinds of gametes in equal numbers. Boxes with the same genotype are added together.
Worked example: a Bb × Bb cross
Find each parent's gametes: A Bb parent makes two kinds of gametes: half carry B and half carry b.
Draw the grid: Put B and b across the top (parent 1) and B and b down the side (parent 2).
Fill the boxes: Copy the top letter and the side letter into each box. Write the capital letter first.
Count genotypes: BB appears once, Bb twice, bb once.
Convert to phenotypes: BB and Bb are both purple, so 3 boxes are purple and 1 box is white.
Gametes | B | b |
|---|---|---|
B | BB | Bb |
b | Bb | bb |
The genotype ratio is 1 BB : 2 Bb : 1 bb. The phenotype ratio is 3 purple : 1 white. The probability of each box is 1/4, so the chance of a white offspring is 1/4, and the chance of a purple one is 1/4 + 1/4 + 1/4 = 3/4.
Suppose the cross produces 80 seeds (a made-up number for practice). The expected counts are 80 × 3/4 = 60 purple and 80 × 1/4 = 20 white. Real counts rarely match exactly, just as 80 coin flips rarely give exactly 40 heads. Probabilities describe what to expect, not what is guaranteed.
Test crosses: what is the hidden genotype?
A purple plant could be BB or Bb. To find out, cross it with a white plant, which must be bb. That is a test cross.
If the purple plant is BB: every offspring is Bb, so all are purple.
If the purple plant is Bb: half the offspring are Bb (purple) and half are bb (white), so
1/2are white.Even one white offspring proves the purple parent was Bb, because a white plant needs a b from each parent.
Notice the logic. A few purple offspring never prove BB, because chance could hide the b. Only a white offspring settles it, so a test cross needs a decent number of offspring.
Reading a square for other crosses
The same grid works for any single-gene cross. A BB × bb cross has only one kind of gamete on each side, so all four boxes read Bb and every offspring is purple. A Bb × bb cross gives two boxes Bb and two boxes bb, a 1:1 ratio, which is exactly the test cross above.
A useful habit is to predict first. Ask what gametes each parent can make, then guess the ratio, then draw the square to confirm. If the square disagrees with your guess, one of them has a slip, and finding which one is where the learning happens.
How to check your answer
The probabilities in your boxes should add to 1:
1/4 + 1/4 + 1/4 + 1/4 = 1.Each box should have one allele from each parent.
Your phenotype ratio should come from adding genotype boxes, never from a different cross.
Common mistakes
Writing bB. It is the same genotype as Bb. Put the capital letter first so you can count cleanly.
Mixing up genotype and phenotype. The 1:2:1 is a genotype ratio. The 3:1 is a phenotype ratio.
Thinking dominant means common. Dominance is about which trait shows in a heterozygote, not how many individuals have it.
Expecting exact numbers. The ratio is a probability, so small families can look quite different.
Where you will use it next
Two traits at once uses a 4 × 4 square, and sex-linked traits use X and Y. The method does not change: list gametes, fill boxes, count. To see what an allele actually is at the molecular level, read from DNA to protein.
Frequently asked questions
Why does the 3:1 ratio sometimes not appear?
Small samples vary by chance. Other causes include incomplete dominance, linked genes, or a trait controlled by more than one gene.
Can a recessive trait skip a generation?
Yes. Two Bb parents show the dominant trait but can pass on b to a child who then gets b from both.
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