Monohybrid Cross Calculator
Calculate the expected offspring ratios for a single-trait Mendelian genetic cross.
Enter parent genotypes to see phenotype and genotype probabilities.
Mendel’s discovery — the foundation of genetics
Gregor Mendel, an Augustinian monk working in the gardens of an Austrian monastery, published in 1866 the experimental results that founded modern genetics. By tracking 7 traits across 28,000 pea plants, he established two principles that would not be properly understood for 50 more years:
- Law of segregation: each parent passes one of two alleles for each trait to offspring, chosen randomly
- Law of independent assortment: different traits sort independently into gametes
His work was ignored for decades — Charles Darwin himself never read it — until rediscovered in 1900 by three independent researchers. The “monohybrid cross” is the simplest demonstration of his first law.
Genotype notation
Mendel-era notation, still used universally:
- A (capital): dominant allele — expressed when present
- a (lowercase): recessive allele — expressed only in homozygous form
- AA: homozygous dominant
- Aa or aA: heterozygous (also called “carrier”)
- aa: homozygous recessive
The convention pairs alleles together: AA, Aa, aa are the three possible genotypes for a single locus.
The Punnett square method
Reginald Punnett developed this visualization in 1905. List one parent’s two alleles across the top, the other’s down the side. Fill each cell with the combination. The resulting 2×2 grid shows all possible offspring genotypes and their relative probabilities.
For Aa × Aa (both heterozygous carriers):
| A | a | |
|---|---|---|
| A | AA | Aa |
| a | Aa | aa |
Resulting genotype ratio: 1 AA : 2 Aa : 1 aa Resulting phenotype ratio: 3 dominant : 1 recessive (the famous 3:1 ratio)
The six possible monohybrid crosses
For a single trait with two alleles, only six unique crosses are possible:
| Cross | Genotypes | Phenotypes |
|---|---|---|
| AA × AA | All AA | All dominant |
| AA × Aa | 1 AA : 1 Aa | All dominant |
| AA × aa | All Aa | All dominant (all carriers) |
| Aa × Aa | 1 AA : 2 Aa : 1 aa | 3 dominant : 1 recessive |
| Aa × aa | 1 Aa : 1 aa | 1 dominant : 1 recessive |
| aa × aa | All aa | All recessive |
The 3:1 ratio (Aa × Aa) is what Mendel saw most often — both parents are heterozygous carriers. The 1:1 ratio (Aa × aa) is a “test cross,” used to determine if an organism is homozygous or heterozygous for the dominant phenotype.
Real-world human single-gene traits
Most traits people think of as Mendelian are actually polygenic (eye color, height, hair texture). But some genuine single-gene traits exist:
| Trait | Inheritance | Notes |
|---|---|---|
| Sickle cell anemia | Recessive | aa = disease; Aa = carrier with malaria resistance |
| Cystic fibrosis | Recessive | aa = disease; ~1 in 25 European-descent are carriers |
| Tay-Sachs disease | Recessive | aa = disease; carrier frequency varies by population |
| Huntington’s disease | Dominant | Aa or AA = disease; aa = healthy |
| Marfan syndrome | Dominant | Aa or AA = disease |
| Albinism | Recessive | aa = albinism |
| ABO blood type | Co-dominant + multiple alleles | Beyond simple monohybrid |
| Rh factor | Dominant | Rh+ dominant over Rh− |
| PTC tasting (bitter) | Dominant | “Tasters” have at least one T allele |
| Widow’s peak | Dominant | Aa or AA = widow’s peak |
| Tongue rolling | Considered dominant (oversimplified) | Actually polygenic |
Carrier frequency in autosomal recessive diseases
For a recessive disease that’s rare, most carriers don’t know they carry. Using Hardy-Weinberg:
- If disease frequency is q² = 1/2,500 (cystic fibrosis in European-descent populations)
- Then q = 0.02
- Carrier frequency = 2pq ≈ 0.04 = 1 in 25
This is why genetic carrier screening for couples planning children targets diseases where carrier frequency × carrier frequency × 1/4 (for aa offspring) gives a non-trivial risk. A 1-in-25 carrier rate gives a 1-in-2,500 chance of an affected child between unrelated parents.
Beyond the simple monohybrid — exceptions to Mendelian inheritance
Many traits don’t follow simple A/a dominant/recessive logic:
| Pattern | Example |
|---|---|
| Incomplete dominance | Snapdragon flower color: red × white = pink (Aa is intermediate) |
| Codominance | ABO blood types: AB shows both A and B antigens |
| Multiple alleles | ABO has 3 alleles (A, B, O), not just 2 |
| Polygenic inheritance | Height, skin color, eye color — many genes contribute |
| Pleiotropy | One gene affects multiple traits (e.g., PKU affects mental development AND skin pigment) |
| Epistasis | One gene’s expression depends on another gene |
| Sex-linked | X-linked traits like color blindness, hemophilia |
| Mitochondrial | Inherited only from mother |
| Variable expressivity | Same genotype, different severity (Marfan ranges from mild to lethal) |
| Penetrance | Some carriers of “dominant” alleles don’t express the trait |
Probability vs reality
The 3:1 ratio is expected, not guaranteed. Each offspring is an independent event, like a coin flip. From Aa × Aa, the probability of any single offspring being aa is exactly 0.25. But out of 4 children:
- Probability of exactly 1 being aa: about 42%
- Probability of 0 being aa: about 32%
- Probability of 2 being aa: about 21%
- Probability of all 4 being aa: about 0.4%
A family of 4 children from carrier parents won’t always have 1 affected child. Genetic counseling stresses this — “1 in 4 chance” applies to each pregnancy independently.
Worked example — cystic fibrosis carrier risk
Both parents are confirmed CF carriers (Aa).
- 25% chance child is AA (homozygous normal) — won’t develop CF, won’t be carrier
- 50% chance child is Aa (carrier) — won’t develop CF, but can pass it on
- 25% chance child is aa (affected) — will have cystic fibrosis
For each individual pregnancy, these are independent. Prenatal genetic testing can confirm specific genotype around 10-14 weeks.
Bottom line
Monohybrid crosses are the foundation of genetics but represent the simplest case. The 3:1 phenotype ratio for heterozygous × heterozygous crosses has held up for 150+ years across countless species. Real human inheritance is often more complicated due to incomplete dominance, polygenic traits, and sex-linkage. The Punnett square is a teaching tool — real genetic counseling uses full pedigree analysis and DNA testing.