Punnett Square Calculator

What a Punnett Square Shows

A Punnett square is a small grid that lists every way two parents can pass on their alleles. The British geneticist Reginald Punnett came up with it in the early 1900s, and it is still the first tool most biology students learn for predicting the offspring of a cross.

Each gene comes in versions called alleles, and every individual carries two of them, one from each parent. When a parent makes eggs or sperm (gametes), each gamete gets only one of the two. The square puts one parent's gametes along the side and the other parent's along the top, so each square is one possible child. Because every square is equally likely, counting squares gives you probabilities: two squares out of four is a 50% chance.

How to Do a Punnett Square

Take two pea plants that are both heterozygous for flower color, Pp × Pp, where purple (P) is dominant over white (p).

1. Write the genotypes with a capital letter for the dominant allele and the same letter in lower case for the recessive one.
2. Find the gametes. Each Pp parent makes two kinds, P and p, in equal numbers.
3. Draw a grid with one parent's gametes down the side and the other's across the top. Two gametes on each side give a 2 × 2 grid with four squares.
4. Fill each square with the allele at the start of its row and the allele at the top of its column: PP, Pp, Pp and pp.
5. Count the squares. One PP, two Pp and one pp is a 1 : 2 : 1 genotype ratio. PP and Pp both look purple, so three squares are purple and one is white: a 3 : 1 phenotype ratio.

So each seedling has a 3 in 4 (75%) chance of purple flowers and a 1 in 4 (25%) chance of white ones.

Show the pea plant cross

Genotype Ratio and Phenotype Ratio

The genotype is the pair of alleles a child carries, such as AA, Aa or aa. The phenotype is what you can see or measure, such as flower color or blood type. Two children can have different genotypes and the same phenotype, which is why a Punnett square usually gives you two ratios.

The genotype ratio counts each genotype separately. AA and aa are homozygous (two copies of the same allele) and Aa is heterozygous (one of each). The phenotype ratio groups the genotypes that look the same. With complete dominance, AA and Aa look alike, so the 1 : 2 : 1 genotype ratio becomes a 3 : 1 phenotype ratio. A heterozygous child that looks dominant still carries the recessive allele and can pass it on, which is what people mean by a carrier.

These are the crosses that come up again and again in class and in homework:

Monohybrid, Dihybrid and Trihybrid Crosses

A monohybrid cross follows one gene, a dihybrid cross follows two and a trihybrid cross follows three. The calculator works out which one you mean from the genotypes you type, so Aa gives a 2 × 2 square, AaBb a 4 × 4 square and AaBbCc an 8 × 8 square.

The size grows fast because of Mendel's law of independent assortment: genes on different chromosomes are sorted into gametes separately. A parent that is AaBb can pass on A or a and, on its own, B or b, so it makes four kinds of gametes: AB, Ab, aB and ab. In general, a parent heterozygous for n genes makes 2ⁿ kinds of gametes, and two such parents fill a square of 4ⁿ cells.

Crossing two AaBb parents gives the famous 9 : 3 : 3 : 1 ratio. You can reach it without drawing all 16 squares: each gene alone gives a 3/4 chance of the dominant trait, and chances for independent genes multiply, so both dominant traits come up 3/4 × 3/4 = 9/16 of the time, and both recessive ones 1/4 × 1/4 = 1/16. That shortcut is how geneticists handle crosses with many genes, where the grid would be far too big to draw.

Show the 9 : 3 : 3 : 1 cross

Incomplete Dominance and Codominance

Some genes have no allele that fully hides the other. In incomplete dominance, the heterozygote sits between the two parents. The textbook case is the snapdragon: red (RR) crossed with white (rr) gives pink (Rr) flowers. Cross two pink plants and you get red, pink and white in a 1 : 2 : 1 ratio, the same as the genotype ratio, because each genotype now looks different.

Show the pink snapdragon cross

In codominance, both alleles show up in full, side by side. Roan cattle are the usual example: a calf with one allele for red hair and one for white has a coat with both red and white hairs mixed together. The ratios work out the same as for incomplete dominance; only the description of the middle phenotype changes.

Show the roan cattle cross

In the calculator, set each gene to complete, incomplete or codominant. You can mix them in a dihybrid cross, for example one gene with complete dominance and one with incomplete dominance, which turns the 9 : 3 : 3 : 1 pattern into 3 : 6 : 3 : 1 : 2 : 1.

Blood Type Punnett Square

ABO blood types are controlled by one gene with three alleles. I^A and I^B are codominant, and both are dominant over i. That gives four blood types from six genotypes: type A is I^AI^A or I^Ai, type B is I^BI^B or I^Bi, type AB is I^AI^B, and type O is ii.

Since type A and type B can each hide an O allele, a blood type alone does not tell you the genotype. A type A parent who is I^Ai and a type B parent who is I^Bi can have a child of any of the four types, each with a 25% chance.

Show the A × B cross

The table lists which blood types are possible for a child, assuming the parents carry any hidden O allele:

Two type A parents can have a type O child only when both are I^Ai, and then the chance is 1 in 4 for each child. The Rh factor (the plus or minus in A+ or O−) comes from a different gene, so it needs a cross of its own.

Show two type A parents

X-Linked (Sex-Linked) Punnett Squares

Some genes sit on the X chromosome. Females have two X chromosomes (XX) and males have one X and one Y (XY), and the Y does not carry a copy of these genes. That is why X-linked recessive traits, such as red-green color blindness and hemophilia, are much more common in males: a single recessive allele on their only X is enough for the trait to show.

Write the allele as a letter after the X. A carrier mother is X^BX^b and a father with normal color vision is X^BY. Their square gives four equally likely children: a daughter X^BX^B, a carrier daughter X^BX^b, a son X^BY with normal vision and a color-blind son X^bY. Each son has a 50% chance of being color blind, and no daughter is, although half of them carry the allele.

Show the color blindness cross

With the roles reversed, the result changes: a color-blind father (X^bY) and a mother with two normal alleles (X^BX^B) have no color-blind children at all, but every daughter is a carrier, because she gets her father's only X. The calculator shows the chance for sons and for daughters separately, since that is usually the question being asked.

The Test Cross

A plant or animal with the dominant phenotype can be AA or Aa, and you cannot tell by looking. A test cross pairs it with a homozygous recessive partner (aa). If the unknown parent is AA, every offspring shows the dominant trait. If it is Aa, about half the offspring show the recessive trait, a 1 : 1 ratio. A single recessive offspring is enough to prove that the parent is heterozygous. Breeders still use this simple idea to check animals and plants before breeding from them.

Show the test cross

What a Punnett Square Cannot Tell You

A Punnett square gives the chance for each child. A 3 : 1 ratio means each child has a 75% chance of the dominant trait, and every child is a fresh draw, like a coin toss. Real families and small litters often land far from the ratio; it only shows up reliably across large numbers of offspring, as in Mendel's thousands of pea plants.

The simple square also rests on a few assumptions that real genes do not always meet:

• Genes on the same chromosome tend to be inherited together (linkage), so they do not sort independently and the 9 : 3 : 3 : 1 ratio breaks down.
• Height, skin color and eye color are shaped by many genes and by the environment, so a one-gene square cannot predict them. Brown versus blue eyes is a common classroom example, but real eye color is more complicated.
• Genes can interact. In epistasis one gene masks another, which changes the ratios (for example 9 : 3 : 4 or 9 : 7).
• Some genes have more than two alleles. ABO is one, and the calculator handles it as its own mode.

For genetic conditions in a real family, a genetic counselor looks at the whole family history and, where needed, at genetic test results.

Sources

• MedlinePlus Genetics, What are the different ways a genetic condition can be inherited?, on dominant, recessive, X-linked and codominant inheritance.
• MedlinePlus Genetics, Color vision deficiency, on the X-linked inheritance of red-green color blindness.
• Dean L., Blood Groups and Red Cell Antigens, chapter 5: The ABO blood group, NCBI Bookshelf, 2005.