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Formula
Boxes = (gametes from parent 1) × (gametes from parent 2); P(outcome) = boxes with that outcome ÷ total boxes
- gametes
- 2ⁿ allele combinations a parent heterozygous for n genes can pass on (fewer if homozygous for some)
- genotype
- the pair of alleles for each gene, e.g. Aa
- phenotype
- the trait shown: A_ means at least one dominant allele, aa means the recessive trait
What a Punnett square shows
A Punnett square is a grid that lists every way two parents’ alleles can combine in their offspring. It was devised by the British geneticist Reginald Punnett in the early 1900s to make Gregor Mendel’s results easy to see. Each parent’s possible gametes go along one edge, and each box in the grid is one equally likely offspring. Counting the boxes gives the expected ratios of genotypes and traits.
This Punnett square calculator builds the grid for you, for one gene (monohybrid, 2 × 2), two genes (dihybrid, 4 × 4) or three genes (trihybrid, 8 × 8). It then reports the genotype ratio, the phenotype ratio and the probability of each outcome.
How to use the Punnett square calculator
- Choose the cross type: one, two or three genes.
- Pick a letter for each gene. A capital letter is the dominant allele, lowercase the recessive one. Use a different letter for each gene.
- Choose each parent’s genotype. The menus show A, B and C as placeholders, and the results use your letters.
- Read the phenotype ratio at the top, then the genotype ratio, the probability of each outcome and the full square.
How to calculate a Punnett square by hand
One gene
Take a homozygous dominant parent (AA) and a heterozygous one (Aa). The first parent can only pass on A; the second passes on A or a.
| A | a | |
|---|---|---|
| A | AA | Aa |
| A | AA | Aa |
Two boxes are AA and two are Aa, so the genotype ratio is 1 AA : 1 Aa. Every box has at least one A, so all offspring show the dominant trait.
Two genes
List each parent’s gametes first. A parent that’s AaBb makes four: AB, Ab, aB and ab. A parent that’s aabb makes only ab. Crossing AaBb × aabb therefore gives four boxes, AaBb, Aabb, aaBb and aabb, one of each. The phenotype ratio is 1 : 1 : 1 : 1, or 25% for each combination of traits.
Turning counts into probabilities
Divide the count for an outcome by the number of boxes. To find a Punnett square ratio, divide every count by their greatest common factor, as you would with any ratio. For independent genes, you can also multiply the single-gene probabilities: in AaBb × AaBb, the chance of aa is ¼ and of bb is ¼, so the chance of aabb is ¼ × ¼ = 1⁄16. That product rule is the same one used in the probability calculator.
Common crosses and their ratios
Computed with the calculator under complete dominance.
| Cross | Genotype ratio | Phenotype ratio |
|---|---|---|
| AA × aa | All Aa | All dominant |
| AA × Aa | 1 AA : 1 Aa | All dominant |
| Aa × Aa | 1 AA : 2 Aa : 1 aa | 3 : 1 |
| Aa × aa | 1 Aa : 1 aa | 1 : 1 |
| AaBb × AaBb | 1 : 2 : 1 : 2 : 4 : 2 : 1 : 2 : 1 | 9 : 3 : 3 : 1 |
| AaBb × aabb | 1 : 1 : 1 : 1 | 1 : 1 : 1 : 1 |
| AaBb × AAbb | 1 : 1 : 1 : 1 | 1 : 1 |
| AaBbCc × aabbcc | 1 each of 8 genotypes | 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 |
The 3 : 1 and 9 : 3 : 3 : 1 ratios are the ones Mendel saw in his pea plants. Crosses with a homozygous recessive parent, such as Aa × aa or AaBb × aabb, are test crosses: every gamete type of the other parent shows up as its own phenotype.
Mendel’s laws behind the square
The square works because of two rules Mendel inferred from his experiments.
- Segregation – each parent carries two alleles for a gene and passes on just one, each with a 50% chance.
- Independent assortment – alleles of different genes are sorted into gametes independently, so every combination is equally likely. This holds for genes on different chromosomes or far apart on the same one.
Where these rules break, the square needs changes. Genes close together on one chromosome are linked and tend to be inherited together. Blood types follow codominance, in which the A and B alleles both show. Some flowers show incomplete dominance, in which Rr is pink rather than red. Traits like height and eye color depend on many genes at once.
Common mistakes
- Writing genotypes, not gametes, on the edges. For a dihybrid cross, each edge needs the four gametes, not the parent’s genotype AaBb.
- Reading ratios as exact counts. A 3 : 1 ratio doesn’t mean a litter of four will have exactly one recessive puppy. Each birth is an independent draw.
- Forgetting that A_ covers AA and Aa. Phenotype ratios merge every genotype with at least one dominant allele.
- Using the same letter for two genes. Each gene needs its own letter, or the alleles get mixed up.
Glossary
- Allele – one version of a gene.
- Genotype – the alleles an individual carries, such as Aa.
- Phenotype – the trait that shows.
- Homozygous / heterozygous – two identical alleles (AA or aa) versus two different ones (Aa).
- Monohybrid, dihybrid, trihybrid – crosses that follow one, two or three genes.
When you need to count arrangements rather than draw them, the combination calculator handles the counting.
Worked examples
Two heterozygous pea plants (Rr × Rr)
Mendel’s classic cross for round (R) versus wrinkled (r) seeds: genotypes 1 RR : 2 Rr : 1 rr.
Inputs (Monohybrid (1 gene)): Gene letter = R / r; Parent 1 genotype = Aa (heterozygous); Parent 2 genotype = Aa (heterozygous)
Parent 1 (Rr) gametes: R, r Parent 2 (Rr) gametes: R, r 2 × 2 = 4 boxes; count each genotype, then group genotypes that share a phenotype (any capital letter shows the dominant trait).
Answer: Rr × Rr: genotype ratio 1 RR : 2 Rr : 1 rr; phenotype ratio 3 R_ : 1 rr.
A test cross (Tt × tt)
Crossing a heterozygote with a homozygous recessive gives half dominant, half recessive offspring.
Inputs (Monohybrid (1 gene)): Gene letter = T / t; Parent 1 genotype = Aa (heterozygous); Parent 2 genotype = aa (homozygous recessive)
Parent 1 (Tt) gametes: T, t Parent 2 (tt) gametes: t, t 2 × 2 = 4 boxes; count each genotype, then group genotypes that share a phenotype (any capital letter shows the dominant trait).
Answer: Tt × tt: genotype ratio 1 Tt : 1 tt; phenotype ratio 1 T_ : 1 tt.
A dihybrid cross (YyRr × YyRr)
Yellow/green (Y/y) and round/wrinkled (R/r) peas, both parents heterozygous for both genes: the 16-box square gives the 9 : 3 : 3 : 1 ratio.
Inputs (Dihybrid (2 genes)): First gene letter = Y / y; Second gene letter = R / r; Parent 1 genotype = AaBb (dihybrid, heterozygous for both); Parent 2 genotype = AaBb (dihybrid, heterozygous for both)
Parent 1 (YyRr) gametes: YR, Yr, yR, yr Parent 2 (YyRr) gametes: YR, Yr, yR, yr 4 × 4 = 16 boxes; count each genotype, then group genotypes that share a phenotype (any capital letter shows the dominant trait).
Answer: YyRr × YyRr: genotype ratio 1 YYRR : 2 YYRr : 1 YYrr : 2 YyRR : 4 YyRr : 2 Yyrr : 1 yyRR : 2 yyRr : 1 yyrr; phenotype ratio 9 Y_R_ : 3 Y_rr : 3 yyR_ : 1 yyrr.
A trihybrid cross (AaBbCc × AaBbCc)
Three heterozygous genes in each parent: 8 gamete types each, 64 boxes, and the 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1 phenotype ratio.
Inputs (Trihybrid (3 genes)): First gene letter = A / a; Second gene letter = B / b; Third gene letter = C / c; Parent 1 genotype = AaBbCc (heterozygous for all three); Parent 2 genotype = AaBbCc (heterozygous for all three)
Parent 1 (AaBbCc) gametes: ABC, ABc, AbC, Abc, aBC, aBc, abC, abc Parent 2 (AaBbCc) gametes: ABC, ABc, AbC, Abc, aBC, aBc, abC, abc 8 × 8 = 64 boxes; count each genotype, then group genotypes that share a phenotype (any capital letter shows the dominant trait).
Answer: AaBbCc × AaBbCc: genotype ratio 1 AABBCC : 2 AABBCc : 1 AABBcc : 2 AABbCC : 4 AABbCc : 2 AABbcc : 1 AAbbCC : 2 AAbbCc : 1 AAbbcc : 2 AaBBCC : 4 AaBBCc : 2 AaBBcc : 4 AaBbCC : 8 AaBbCc : 4 AaBbcc : 2 AabbCC : 4 AabbCc : 2 Aabbcc : 1 aaBBCC : 2 aaBBCc : 1 aaBBcc : 2 aaBbCC : 4 aaBbCc : 2 aaBbcc : 1 aabbCC : 2 aabbCc : 1 aabbcc; phenotype ratio 27 A_B_C_ : 9 A_B_cc : 9 A_bbC_ : 3 A_bbcc : 9 aaB_C_ : 3 aaB_cc : 3 aabbC_ : 1 aabbcc.
Homozygous parents (edge case: GGHH × gghh)
Every offspring is GgHh, so all 16 boxes show both dominant traits.
Inputs (Dihybrid (2 genes)): First gene letter = G / g; Second gene letter = H / h; Parent 1 genotype = AABB; Parent 2 genotype = aabb
Parent 1 (GGHH) gametes: GH, GH, GH, GH Parent 2 (gghh) gametes: gh, gh, gh, gh 4 × 4 = 16 boxes; count each genotype, then group genotypes that share a phenotype (any capital letter shows the dominant trait).
Answer: GGHH × gghh: genotype ratio All GgHh; phenotype ratio All G_H_.
Assumptions and limitations
- Each parent passes on one allele per gene, and each allele is equally likely to be passed on (Mendel's law of segregation).
- In dihybrid and trihybrid crosses, the genes assort independently, as genes on different chromosomes do. Linked genes are not modeled.
- Dominance is complete. A capital letter is the dominant allele, a lowercase letter the recessive one, and one dominant allele is enough to show the dominant trait. Incomplete dominance, codominance (such as ABO blood types) and sex-linked genes are not covered.
- Ratios are reduced to the smallest whole numbers, and percentages are rounded to 2 decimal places.
- Ratios are probabilities for each offspring, not guarantees for a litter or family of any given size.
Frequently asked questions
How do you calculate a Punnett square?
Write each parent's possible gametes along the top and the side, then fill each box with the alleles from its row and column. Count how many boxes show each genotype, and group them by phenotype. Each box is equally likely, so the counts give the ratios.
How do you calculate Punnett square percentages?
Divide the number of boxes with an outcome by the total number of boxes and multiply by 100. In a 4-box square where 3 boxes show the dominant trait, the chance is 3 ÷ 4 = 75%. In a 16-box dihybrid square, each box is worth 6.25%.
What is the 9:3:3:1 ratio?
It's the phenotype ratio of a dihybrid cross between two parents heterozygous for both genes, such as AaBb × AaBb. Of the 16 boxes, 9 show both dominant traits, 3 show only the first dominant trait, 3 only the second, and 1 shows both recessive traits.
What is the difference between genotype and phenotype ratios?
The genotype ratio counts the actual allele combinations, such as 1 AA : 2 Aa : 1 aa. The phenotype ratio counts the visible traits. With complete dominance AA and Aa look the same, so the same cross gives 3 dominant : 1 recessive.
How big is a trihybrid Punnett square?
A parent heterozygous for three genes makes 2³ = 8 kinds of gametes, so crossing two such parents gives an 8 × 8 square with 64 boxes. The phenotype ratio is 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1.
Can a Punnett square predict a baby's eye color?
Only roughly. Eye color depends on several genes, not one with simple dominance, so two blue-eyed parents can occasionally have a brown-eyed child. A one-gene Punnett square is a teaching model for traits like this, not a prediction.
What is a test cross?
A test cross pairs an individual showing the dominant trait with a homozygous recessive one. If any offspring show the recessive trait, the dominant parent must be heterozygous. A 1 : 1 phenotype ratio is the classic result for a heterozygous parent.
Sources
- Biology 2e, 12.3 Laws of Inheritance — OpenStax, Rice University. Checked October 10, 2026.
- Biology 2e, 12.2 Characteristics and Traits — OpenStax, Rice University. Checked October 10, 2026.
- Talking Glossary of Genomic and Genetic Terms: Dominant — National Human Genome Research Institute. Checked October 10, 2026.