Punnett squares and Mendelian probability
A Punnett square enumerates combinations of parental gametes to show expected genotype probabilities under a specified inheritance model. Uppercase and lowercase letters conventionally represent dominant and recessive alleles.
The displayed percentages are theoretical probabilities for each offspring, not a guarantee that a small family or experiment will match the ratio exactly.
How to create a Punnett square
- Choose cross type: Use monohybrid for one gene or dihybrid for two independently assorting genes.
- Enter parent genotypes: Use matching gene letters and case, such as Aa × Aa or AaBb × AaBb.
- Generate the square: Review gametes, cell genotypes, and summarized ratios.
- Check the biological model: Confirm complete dominance and independent assortment are appropriate.
Formula and variables
The grid counts equally likely gamete pairings. A dihybrid cross assumes the two genes assort independently.
P(offspring genotype) = P(gamete from parent 1) × P(gamete from parent 2)- A, a — Alleles at gene one
- Uppercase is treated as completely dominant (allele)
- B, b — Alleles at gene two
- Second gene used in dihybrid mode (allele)
- P — Probability
- Expected fraction of grid outcomes (%)
Heterozygous monohybrid cross
Cross Aa with Aa under complete dominance.
- Parents
- Aa × Aa
- Gametes from each parent: A and a
- Grid: AA, Aa, Aa, aa
Result: Genotypes are 25% AA, 50% Aa, and 25% aa; phenotypes are 75% dominant and 25% recessive.
Each offspring independently has these model probabilities.
Understanding your results
Probability is not a pedigree diagnosis
Punnett ratios describe a simplified model and do not establish an individual genotype or clinical risk.
- Observed counts fluctuate around theoretical probabilities.
- Linked genes may not assort independently.
- Dominance concerns phenotype expression, not which allele is more common or more likely to be inherited.
Assumptions
- Each parent contributes one allele per gene.
- Alleles segregate equally and genes in dihybrid mode assort independently.
- Uppercase alleles are completely dominant over matching lowercase alleles.
Limitations
- Does not model linkage, recombination frequency, codominance, incomplete dominance, penetrance, sex linkage, mutation, or polygenic traits.
- Does not infer parental genotypes or provide medical genetic counseling.
- Dihybrid mode supports two genes and four-character genotype notation only.
Common mistakes
- Using different gene letters for the same locus between parents.
- Interpreting 25% as exactly one affected child in every four births.
- Applying independent assortment to tightly linked genes.
- Assuming a dominant allele is always beneficial or common.
Practical use cases
Genetics education
Visualize allele segregation in idealized Mendelian crosses.
Probability practice
Compare grid counts with multiplication and addition rules.
Frequently asked questions
What does Aa mean?
It represents a heterozygous genotype with two different alleles at one gene.
Does 75% dominant mean three of every four children?
It is the probability for each independent offspring under the model, not a guaranteed result for four births.
Can this predict complex human traits?
No. Most traits involve additional genes, environment, penetrance, and inheritance mechanisms not represented here.
Sources and review
- Mendelian Inheritance — National Human Genome Research Institute. Accessed 2026-07-13.
- Dominant Traits and Alleles — National Human Genome Research Institute. Accessed 2026-07-13.
Reviewed 2026-07-13.