What this calculator does
A dihybrid cross between two AaBb parents produces the 9:3:3:1 phenotype ratio, one of the most recognisable results in genetics. Nine sixteenths show both dominant traits, three show the first dominant and second recessive, three the reverse, and one sixteenth shows both recessive.
The ratio comes from independent assortment. Each parent makes four gamete types in equal numbers, AB, Ab, aB and ab, and combining four with four gives sixteen equally likely outcomes. Mendel derived the law of independent assortment from exactly this pattern, and a cross that departs from it is evidence the two genes are linked.
The formula
Both parents produce four gamete types in equal proportion. The sixteen possible pairings are enumerated, each combination resolved to a phenotype on the basis that one dominant allele is enough to show the dominant trait, and the results counted. This cross has no variables: the ratio is fixed at 9:3:3:1 whenever both parents are AaBb and both traits show full dominance.
| Term | Meaning |
|---|---|
| Dihybrid cross | A cross tracking two genes at once, here both heterozygous in both parents. |
| Independent assortment | Mendel's second law: genes on different chromosomes segregate independently of each other. |
| 9:3:3:1 | The phenotype ratio of a dihybrid cross with full dominance at both loci. |
| Linkage | Genes close together on the same chromosome, which breaks independent assortment and distorts the ratio. |
The inputs explained
| Field | What to enter |
|---|---|
| Parents (both AaBb, standard dominant/recessive) | A label for the cross rather than a variable. Both parents are taken as AaBb with full dominance at both loci, so the ratio does not change whatever is entered here. |
When to use it
Checking a genetics answer
The 9:3:3:1 ratio is the expected result, and having it to hand is a quick confirmation when working a problem by hand.
Testing whether genes are linked
Observed offspring counts departing significantly from 9:3:3:1 suggest the two genes are not assorting independently, which is how linkage is detected.
Teaching independent assortment
The ratio is the classic demonstration, and seeing that it follows from four gametes crossed with four is what makes the law concrete rather than asserted.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What are the dihybrid cross ratios?
The four phenotype classes from a standard dihybrid cross. This cross has no variable inputs, so there is a single row.
| Cross | Dominant/Dominant (AB) | Dominant/Recessive (Ab) | Recessive/Dominant (aB) | Recessive/Recessive (ab) |
|---|---|---|---|---|
| AaBb x AaBb | 9 / 16 | 3 / 16 | 3 / 16 | 1 / 16 |
Questions
Why is the ratio 9:3:3:1?
Because each single gene gives a 3:1 ratio, and two independent genes multiply: 3/4 times 3/4 is 9/16 for both dominant, 3/4 times 1/4 is 3/16 for each mixed class, and 1/4 times 1/4 is 1/16 for both recessive. The grid of sixteen squares is the same calculation laid out visually.
What is the genotype ratio?
1:2:1:2:4:2:1:2:1 across the nine possible genotypes, which is considerably less memorable than the phenotype ratio and is why the 9:3:3:1 is the one quoted. The phenotype ratio is shorter only because dominance collapses several genotypes into one visible class.
What if the genes are linked?
The ratio breaks down. Linked genes are inherited together more often than independent assortment predicts, so parental combinations are over-represented and recombinant ones under-represented. The size of the departure indicates how close the two loci sit on the chromosome.
Does this work without full dominance?
No. Incomplete dominance or codominance makes heterozygotes visibly distinct, so the phenotype classes no longer collapse and the ratio becomes 1:2:1:2:4:2:1:2:1, matching the genotype ratio instead.
For probabilities across more than two genes, see the multi-gene cross calculator. For allele frequencies in a whole population, see the Hardy-Weinberg calculator.