Dihybrid Cross Punnett Square Calculator

Construct a Mendelian dihybrid cross.

Nature 4×4 Punnett 9:3:3:1 check
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AaBb × AaBb → 9:3:3:1

Mendelian dihybrid cross · 4×4 Punnett square

Instructions — Dihybrid Cross Punnett Square Calculator

1

Type both parent genotypes

Use 4-letter format: AaBb. First two letters are trait 1 alleles; last two are trait 2. Capital = dominant, lower-case = recessive.

2

Read the Punnett square

The 4×4 grid shows all possible offspring genotypes. Identical genotypes appear in multiple cells when both parents contribute the same gamete combination.

3

Check the ratio

Phenotype ratio appears as both fractions and simple form. The classic dihybrid cross (AaBb × AaBb) gives 9:3:3:1 — the calculator flags this automatically.

Formulas

Law of Independent Assortment
$$ P(A\_B\_) = P(A\_) \times P(B\_) $$
Each trait segregates independently. Probability of both dominant phenotypes equals the product of single-trait probabilities.
9:3:3:1 Ratio
$$ \frac{9}{16}A\_B\_: \frac{3}{16}A\_bb: \frac{3}{16}aaB\_: \frac{1}{16}aabb $$
Classic outcome of AaBb × AaBb. From 16 equally probable offspring, 9 show both dominant traits, 1 shows both recessive, 3 + 3 show mixed.
Single Genotype Probability
$$ P(\text{AaBb}) = 0.5 \times 0.5 \times 0.5 \times 0.5 = \frac{1}{16} $$
From two Aa parents, P(Aa offspring) = 0.5. Multiply across independent traits.
Gamete Count
$$ n_{gametes} = 2^h $$
h = number of heterozygous traits in the parent. AaBb has 2 heterozygous traits → 4 gametes (AB, Ab, aB, ab). AABb has 1 → 2 gametes (AB, Ab).
Test Cross
$$ \text{Unknown} \times \text{aabb} \to \text{phenotype reveals genotype} $$
Crossing an unknown with a fully recessive partner exposes the recessive alleles hiding behind dominant phenotype.
Chi-Square Test
$$ \chi^2 = \sum \frac{(O - E)^2}{E} $$
Test observed offspring ratios against expected 9:3:3:1. Critical value at p = 0.05 and df = 3: χ² = 7.815.

Reference

Common Dihybrid Crosses
CrossPhenotype ratioNotes
AaBb × AaBb9: 3: 3: 1Classic Mendelian dihybrid
AaBb × aabb1: 1: 1: 1Test cross
AABB × aabbAll AaBbPure dominant × pure recessive
AABb × aaBb1: 1 → 3: 1 (for B trait)Mixed dominance
AaBB × aaBb1: 1 → 1: 1 (for B trait)Half heterozygous
AaBb × AaBB3: 1 → uniform B_One trait fixed dominant

Article — Dihybrid Cross Punnett Square Calculator

Dihybrid Cross Punnett Square Calculator

A dihybrid cross is a genetic cross involving two traits at the same time. The classical AaBb × AaBb cross gives a 9:3:3:1 phenotype ratio in the offspring — 9 with both dominant traits, 3 with first dominant only, 3 with second dominant only, and 1 with both recessive. The 4×4 Punnett square shows every possible combination.

What a dihybrid cross is

Mendelian genetics studies how traits move from parents to offspring. A monohybrid cross looks at one trait — say, pea seed color. A dihybrid cross looks at two traits at the same time — pea seed color and seed shape. The math gets richer because each parent now contributes a combination of alleles from both genes.

Gregor Mendel performed dihybrid crosses on pea plants in the 1860s and used them to establish his second law: independent assortment. Each trait segregates separately during gamete formation, so the offspring distribution comes from multiplying single-trait probabilities. That insight is the foundation of modern genetics, breeding, and biotechnology.

Did you know

Mendel ran his dihybrid experiments on 556 pea plants. The phenotype counts came out 315 round-yellow, 108 round-green, 101 wrinkled-yellow, 32 wrinkled-green. Expected from 9:3:3:1: 312.75, 104.25, 104.25, 34.75. Modern statistics suggest his numbers may have been "too good" — but the underlying biology was right.

The dihybrid Punnett square method

The 4×4 Punnett square is the workhorse tool. Each parent (AaBb) makes 4 possible gametes: AB, Ab, aB, ab. List parent 1 gametes down the left side, parent 2 gametes across the top. Each cell shows the offspring genotype from combining one gamete from each parent. Total: 16 cells, 16 equally likely outcomes.

Once the square is filled, count genotypes. Most will appear in multiple cells because different gamete combinations produce the same offspring. Identify each unique phenotype (based on dominant/recessive rules) and tally how many of the 16 cells produce it. That's your phenotype ratio.

AaBb × AaBb gametes
Parent gametes AB, Ab, aB, ab
Each gamete prob 1/4
Cells in grid 16
P(A_B_) 9/16
P(A_bb) or P(aaB_) 3/16 each
P(aabb) 1/16

Why dihybrid crosses give 9:3:3:1

The ratio comes from the product rule applied to two independent monohybrid crosses. For one trait, Aa × Aa gives 3:1 phenotype ratio (3 dominant: 1 recessive). For the second trait, Bb × Bb similarly gives 3:1. Independent assortment means the probabilities multiply across traits.

Both dominant
9/16
56.25%
Both recessive
1/16
6.25%

So P(dominant for both) = 3/4 × 3/4 = 9/16. P(dominant for A, recessive for B) = 3/4 × 1/4 = 3/16. Same for the symmetric case. P(recessive for both) = 1/4 × 1/4 = 1/16. Sum: 9 + 3 + 3 + 1 = 16 — the total — and the ratio 9:3:3:1 is the phenotype distribution.

Mendel's original dihybrid experiments

Mendel chose seven traits in garden peas for his work, all with clear dominant/recessive distinction. His dihybrid crosses paired traits two at a time and counted offspring rigorously. The 556-plant cross of round-yellow vs wrinkled-green seeds gave the now-famous 9:3:3:1 ratio that established independent assortment as a law of inheritance.

The 1866 publication of these results sat almost unread for 34 years. When Hugo de Vries, Carl Correns, and Erich von Tschermak independently rediscovered Mendel's work in 1900, it became the foundation of the new science of genetics. The 9:3:3:1 ratio is taught in every introductory biology class today because it captures, in four numbers, the entire mathematical structure of Mendelian inheritance.

Tip

To estimate offspring counts from real-world crosses, multiply the expected ratio by total offspring divided by 16. For 80 offspring: 80 × 9/16 = 45 both-dominant, 80 × 3/16 = 15 each mixed, 80 × 1/16 = 5 both-recessive. Real data scatter around these expected values; the chi-square test quantifies how much scatter is reasonable.

Test cross with dihybrid traits

A test cross uses a fully recessive partner (aabb) to expose hidden recessive alleles. If you have an organism with both dominant phenotypes (A_B_) and want to know whether it's homozygous dominant (AABB) or heterozygous (AaBb), cross it with aabb and look at the offspring.

Outcomes: AABB × aabb gives all AaBb offspring — uniform dominant. AaBb × aabb gives 1:1:1:1 ratio across all four phenotype classes. AABb × aabb gives 1:1 (A_B_: A_bb). Each parent genotype produces a distinctive offspring distribution, so the phenotype ratio of the test-cross progeny reveals the unknown.

When dihybrid 9:3:3:1 breaks down

Three situations break the classical 9:3:3:1 ratio. Incomplete dominance: heterozygotes show intermediate phenotype, so the cross gives a 1:2:1:2:4:2:1:2:1 nine-class ratio instead. Snapdragon flower color is the textbook example. Codominance: both alleles express simultaneously, producing distinct phenotypes for each combination. Blood groups (AB type) work this way.

Linkage: when the two genes sit close together on the same chromosome, they don't assort independently. Gametes carrying parental allele combinations (AB and ab) outnumber recombinant gametes (Ab and aB), shifting the ratio toward more parent-like offspring. The deviation from 9:3:3:1 lets geneticists estimate how close the two genes are on the chromosome — Morgan's principle of genetic mapping.

Common dihybrid cross mistakes

Four pitfalls trip up students and instructors alike.

Gamete from a heterozygote

An Aa parent makes A gametes 50% of the time and a gametes 50% — not 100% Aa gametes. The gamete carries only one allele per trait, not the full genotype. This is the single most common confusion in monohybrid and dihybrid Punnett squares.

Second: assuming 9:3:3:1 always applies. The ratio holds only for AaBb × AaBb with complete dominance and independent assortment. Any deviation from these conditions changes the ratio. Third: counting genotypes when the question asks about phenotypes. The 16 cells contain 9 distinct genotypes (AABB, AABb, AaBB, AaBb, AAbb, Aabb, aaBB, aaBb, aabb) but only 4 phenotype classes (with complete dominance). Fourth: confusing the genotype ratio with the phenotype ratio. They are different — genotype ratios are more diverse because they distinguish AABB from AaBB even though both look dominant for A.

FAQ

A dihybrid cross is a genetic cross involving two different traits. Each trait has its own pair of alleles. Mendel's classic example crossed pea plants for seed shape (round vs wrinkled) and seed color (yellow vs green) at the same time. The expected outcome from two heterozygotes is the 9:3:3:1 phenotype ratio.
Each trait independently gives 3:1 (dominant:recessive) in monohybrid form. Combined: P(A_) × P(B_) = 3/4 × 3/4 = 9/16; P(A_) × P(bb) = 3/4 × 1/4 = 3/16; P(aa) × P(B_) = 1/4 × 3/4 = 3/16; P(aa) × P(bb) = 1/4 × 1/4 = 1/16. Total = 16, ratio = 9:3:3:1.
Mendel's second law: alleles for different traits separate independently during gamete formation. A parent's contribution of an A or a allele does not influence whether it passes B or b. This is what makes the 9:3:3:1 ratio possible. It holds when the genes are on different chromosomes (or far apart on the same chromosome).
A test cross uses a fully recessive partner (aabb) to determine an unknown's genotype. If the unknown is AABB, all offspring show dominant phenotype. If AaBb, the cross produces 1:1:1:1 ratio of all four phenotype classes. Breeders use this when they have a desirable dominant phenotype but need to confirm whether the genotype is pure-bred (homozygous) or carries hidden recessive alleles.
Rows = parent 1 gametes; columns = parent 2 gametes. Each cell shows one possible offspring genotype. Count the cells with the same genotype to get its frequency out of 16. For AaBb × AaBb the AABB genotype appears 1 time; AaBb appears 4 times; aabb appears 1 time. Sum to 16.
Only with complete dominance and independent assortment. The 9:3:3:1 ratio breaks down if (1) heterozygotes show intermediate phenotype (incomplete dominance), (2) both alleles express (codominance), or (3) the genes are linked on the same chromosome and don't segregate independently. In linked genes, the ratio shifts toward parental combinations.
Four: AB, Ab, aB, ab. Each represents an independent combination of one allele from each trait. A homozygote like AABb produces only 2 gamete types (AB, Ab) because the A trait is fixed. A double homozygote like AABB produces 1 gamete type. General rule: 2 raised to the power of heterozygous traits.
Chi-square tests whether observed offspring counts match the expected 9:3:3:1 ratio. χ² = Σ (Observed − Expected)² / Expected. With 3 degrees of freedom and p = 0.05, the critical value is 7.815. If your calculated χ² is less, the data are consistent with Mendelian inheritance; if more, something else is going on (linkage, selection, sampling error).
Monohybrid involves one trait, dihybrid involves two. A monohybrid Aa × Aa gives 3:1 phenotype ratio; the dihybrid AaBb × AaBb gives 9:3:3:1. The Punnett square grows from 2×2 (4 cells) to 4×4 (16 cells). Trihybrid (three traits) jumps to 8×8 = 64 cells with a 27:9:9:9:3:3:3:1 ratio.