Dihybrid Cross Punnett Square

The question this two-locus model answers

The calculator answers a narrow probability question: if two parents have the selected genotypes at two loci, what proportions of offspring genotypes follow from the basic segregation model? Each parent contributes one allele at the A locus and one allele at the B locus to a modeled gamete. The offspring receives one contribution from each parent at each locus. Because the page starts with specified genotypes, it does not infer those genotypes from a visible trait, a family story, or an unknown laboratory result.

The output has two layers. The first keeps the allele pairs separate and lists all nine canonical genotype states from AABB through aabb. The second groups those states into four phenotype categories under complete dominance. Separating the layers is important because two different genotypes can belong to the same phenotype class. The output describes expected proportions across repeated comparable outcomes. It does not say that one particular offspring must match the most frequent percentage or that an observed individual can be classified from the percentage alone.

• Input: one exact two-locus genotype for each parent.
• Output: nine genotype and four phenotype percentages.
• Model: sixteen equally weighted gamete pairings.
• Interpretation: expected proportions, not an individual guarantee.

Alleles, loci, genotypes, and phenotypes

The letters in this page are symbols for a teaching model. A and a represent two allele forms at the first locus, and B and b represent two forms at the second locus. A locus is the position being modeled, while an allele is one possible form at that position. A genotype records the pair of allele copies at both loci. Thus AaBb contains one A-locus pair, Aa, and one B-locus pair, Bb. The letter case is a convention that identifies the form treated as dominant in the simplified phenotype grouping.

A phenotype is a category produced by applying an expression rule to a genotype in a biological context. This calculator uses complete dominance independently at both loci. Any genotype with at least one A is placed in the A_ group, and any genotype with at least one B is placed in the B_ group. That shorthand does not mean the dominant allele is better, more common, or always expressed in nature. It simply defines how genotype counts are grouped for the four displayed categories.

• A/a and B/b are symbolic allele pairs.
• The four-character value contains two allele pairs.
• A_ and B_ mean at least one dominant-form allele.
• Dominant is a model label, not a value judgment or diagnosis.

Why there are exactly nine parent choices

At each locus, a diploid genotype can be homozygous for the first form, heterozygous, or homozygous for the second form. For A/a those states are AA, Aa, and aa. For B/b they are BB, Bb, and bb. Combining the three first-locus states with the three second-locus states gives 3 x 3 = 9 canonical two-locus genotypes. The interface lists those nine values rather than accepting arbitrary text, so the engine knows exactly which allele positions and probabilities it must process.

The choices use a stable order: the two A-locus characters come first and the two B-locus characters come second. Mixed pairs use the spelling Aa or Bb rather than also allowing aA or bB. Reversing the characters within a heterozygous pair would represent the same unordered genotype for this calculation, not a new state. Canonical spelling prevents duplicate choices and makes the output keys predictable for tests, downloads, and comparisons.

• There are three states at each of two loci.
• Three times three gives nine canonical genotypes.
• The A locus precedes the B locus in every value.
• Free-form genotype text is intentionally not accepted.

How each parent produces gamete slots

A modeled gamete receives one allele from the A pair and one allele from the B pair. If a parent is AABB, every slot contains AB. If the parent is AaBb, the four possible combinations are AB, Ab, aB, and ab. If one locus is homozygous, repeated slots remain in the four-slot representation. For example, AABb produces AB, Ab, AB, and Ab. The repeated values are not four different biological allele types; they preserve the equal weighting of the two segregation positions at each locus.

The handler forms these slots by taking the first and second A-locus characters and pairing each with the first and second B-locus characters. It does not draw random samples and it does not depend on a network, a table, or the DOM. The four slots are a deterministic representation of the assumptions. When two identical slots occur, counting them separately is useful because each occupies one quarter of the parent contribution under the simple model.

• A gamete carries one allele from each modeled locus.
• AaBb produces AB, Ab, aB, and ab slots.
• Homozygous loci create repeated slots.
• The engine enumerates slots deterministically rather than sampling.

Building the four-by-four cross

Once each parent has four slots, the cross contains sixteen pairings. Pair the first Parent A slot with each Parent B slot, then continue for the other three Parent A slots. Each pairing supplies one A-locus allele from each parent and one B-locus allele from each parent. The two alleles at each locus are normalized to a canonical order before the complete offspring genotype is counted. This is the two-locus equivalent of filling a four-box one-locus square, but the grid has sixteen interior outcomes.

Every slot pairing has weight 1/16 because the contract assigns each parent slot probability 1/4 and treats the parental contributions as independent. A homozygous parent may make several identical-looking boxes, but those boxes still represent the same total probability when counted. The grid is therefore a counting device, not a claim that every real cell division produces a perfectly balanced sample. It is a compact expression of the assumptions selected for this educational calculation.

• Four slots from one parent cross four from the other.
• The total number of modeled outcomes is sixteen.
• Each outcome contributes 1/16 before aggregation.
• Allele pairs are normalized before genotype counting.

Counting the nine genotype percentages

The nine output states are AABB, AABb, AAbb, AaBB, AaBb, Aabb, aaBB, aaBb, and aabb. For each of the sixteen pairings, the engine increments exactly one of those counters. The percentage for a state is its count divided by sixteen and multiplied by 100. For example, a count of four gives 25 percent. The genotype percentages should sum to 100 percent because every modeled pairing is assigned to one and only one canonical state.

Keeping genotype counts separate until the end prevents a common error: grouping by visible category too early can hide whether an offspring is homozygous or heterozygous. Genotype information affects the gametes that the offspring could later contribute, even when two genotypes share a complete-dominance phenotype. The nine-state output therefore contains more information than the four phenotype categories. A displayed percentage may have a decimal form because sixteen outcomes are converted to a percentage, but each underlying count is an integer number of slots.

• Each pairing increments one genotype counter.
• Percentage = count / 16 x 100.
• The nine genotype percentages sum to 100 percent.
• Genotype states remain separate from phenotype groups.

Grouping genotypes into four phenotype classes

The phenotype grouping is based on whether a genotype contains at least one uppercase A and at least one uppercase B. A genotype with both is placed in A_B_. A genotype with A and bb is A_bb. A genotype with aa and at least one B is aaB_. The genotype aabb is the only member of the double-recessive class. The underscore means that either homozygous or heterozygous dominant-form status at that locus qualifies under complete dominance.

The phenotype percentages are sums of genotype percentages, not independent extra probabilities. For example, A_B_ includes AABB, AABb, AaBB, and AaBb. A_bb includes AAbb and Aabb. aaB_ includes aaBB and aaBb. aabb remains alone. The four class percentages should sum to 100 percent for the same reason as the nine genotype percentages. If a different expression rule applies, the genotype distribution may still be a useful starting point, but this particular phenotype mapping should not be reused automatically.

• A_B_ includes at least one A and at least one B.
• A_bb includes A_ with bb.
• aaB_ includes aa with at least one B.
• aabb is the double-recessive class.

The AaBb by AaBb worked example

With AaBb selected for both parents, each produces AB, Ab, aB, and ab. The sixteen pairings produce one AABB, two AABb, one AAbb, two AaBB, four AaBb, two Aabb, one aaBB, two aaBb, and one aabb. Dividing these counts by sixteen gives 6.25%, 12.5%, 6.25%, 12.5%, 25%, 12.5%, 6.25%, 12.5%, and 6.25% in the catalog order. The central AaBb class has the largest single genotype count, but it is not the same as the whole dominant phenotype group.

For the phenotype grouping, A_B_ contains nine of the sixteen slots, so it is 56.25%. A_bb contains three slots, so it is 18.75%. aaB_ also contains three slots, giving 18.75%. The remaining one slot is aabb, giving 6.25%. Adding the first two genotype classes within A_B_ and the appropriate double-recessive combinations provides an independent check on the grouping. Both genotype and phenotype totals return to 100%.

• AaBb produces four distinct gamete types in this model.
• The nine genotype counts are 1, 2, 1, 2, 4, 2, 1, 2, 1.
• The four phenotype counts are 9, 3, 3, and 1.
• The result is an expected distribution, not a required family pattern.

Homozygous crosses and mirrored inputs

Boundary crosses make the mechanics easy to inspect. AABB crossed with aabb produces AaBb in every modeled slot because one parent can supply only AB and the other can supply only ab. The genotype result is therefore 100% AaBb and the phenotype result is 100% A_B_. At the other extreme, aabb crossed with aabb produces 100% aabb and 0% for every other genotype. Crosses with one heterozygous locus show how one part of the distribution can vary while the other remains fixed.

Switching Parent A and Parent B should not change the final genotype or phenotype percentages. The labels identify the sides of the conceptual grid, but the offspring genotype is an unordered allele pair at each locus in this model. For example, AABb crossed with AaBB and the reversed cross are mirrors. This symmetry is a useful independent test because a handler that accidentally gives the parents different biological roles would violate the stated two-parent contract.

• AABB x aabb gives 100% AaBb.
• aabb x aabb gives 100% aabb.
• Homozygous loci remove variation at that locus.
• Reversing the parent selections preserves the distribution.

Validation, normalization, and finite percentages

Both parent fields are closed selections. The handler checks membership in the exact nine-value list before reading allele positions. A blank string, a number, a value with trailing whitespace, or a nearly correct spelling is rejected. This strict boundary prevents the engine from making up a gamete rule for an input it does not understand. It also ensures that the catalog options, browser form, direct handler call, and focused tests share one stable input contract.

The handler counts sixteen internal outcomes, converts each count to a percentage, and applies finite-result checks to every displayed value. Because all counts are bounded integers, the results are finite and normalized by construction. The focused tests still sum both output groups over every combination of the nine parent states. That exhaustive check catches errors that a single AaBb example could miss, including misplaced locus characters, incorrect heterozygote normalization, and phenotype groups that omit a genotype state.

• Only the nine canonical selection values are valid.
• Whitespace and arbitrary genotype strings are rejected.
• Sixteen outcomes are counted for every valid cross.
• Both genotype and phenotype totals are checked for 100 percent.

Independent assortment and real biological variation

Independent assortment means that the model treats the A-locus and B-locus segregation choices as independent when forming a gamete. It is the reason an AaBb parent receives four equally weighted combinations rather than only the parental combinations AB and ab. Random segregation supplies the one-half probabilities for a heterozygous pair, and the combination of two loci supplies the four-slot representation. These are explicit assumptions, not facts that the two select fields can verify for a particular organism or locus.

Real inheritance questions can depart from this simple model. Linked loci may produce non-independent gamete frequencies. Selection, reduced viability, segregation distortion, mutation, uncertain genotype assignments, and sampling variation can change observed counts. The calculator has no fields for recombination, viability, phase, population structure, or experimental error. Its output is therefore exact for the abstract contract and not a guarantee that a measured sample will match the ideal percentages.

• Independent assortment is assumed between the two loci.
• Heterozygous segregation is treated as random and balanced.
• Linkage and viability differences are not modeled.
• Observed counts can differ from ideal expected percentages.

What the phenotype output cannot establish

The four phenotype labels are abstract categories created by the complete-dominance rule. They do not name a real trait, disease, ability, ancestry group, or health state. A dominant-looking category can contain both homozygous and heterozygous genotypes, and an actual phenotype can depend on penetrance, environment, developmental stage, or a different expression relationship. The output cannot identify what a person has, predict a medical outcome, or diagnose a condition from a percentage.

The tool also does not infer an unknown parent genotype. If a parent is known only to show the dominant category, both AA and Aa may remain possible under this model. Choosing one of them would add a premise that the phenotype observation did not establish. Questions about an actual family, laboratory result, or population risk require a separate evidence and probability framework. Use this page when the two genotypes are already specified or intentionally supplied for an exercise.

• Phenotype classes are symbolic model categories.
• A dominant category does not reveal AA versus Aa.
• No health, ancestry, trait, or diagnosis claim is produced.
• Unknown genotypes require separate evidence and assumptions.

Reporting a cross and extending the result

A useful report names the two loci, the allele convention, both parent genotypes, the genotype order, the phenotype rule, and the output percentages. Include the fact that the grid contains sixteen equally weighted pairings under random segregation and independent assortment. This context prevents a reader from treating a four-locus-looking string as a universal genetic code or from mistaking A_B_ for a named phenotype. The calculator supplies the arithmetic; the report supplies the biological interpretation of the chosen abstraction.

Repeated-offspring questions can use the displayed probabilities as inputs to a separate binomial or sequence calculation, but that extension adds independence and sampling assumptions. A question about at least one outcome is not the same as a question about one outcome, and a conditional question after observing a phenotype is not the same as the whole-cross distribution. The current page deliberately stops at one cross so those extensions remain visible rather than being hidden inside a broad, ambiguous result.

• Record loci, allele notation, and both parent selections.
• State independent assortment and complete dominance.
• Keep genotype percentages separate from phenotype percentages.
• Treat repeated-offspring questions as a separate probability model.

A comparison with one fixed locus

Consider AABb crossed with AaBB. Parent A can supply AB or Ab because its A pair is fixed as AA and its B pair is mixed. Parent B can supply AB or aB because its B pair is fixed as BB and its A pair is mixed. The four-slot representation repeats each combination, and the sixteen pairings reduce to a small set of genotype states. The calculation still enumerates all slots rather than assuming that a visually simple cross needs no probability accounting.

Every offspring from this cross must receive a B allele from Parent B and can receive either B or b from Parent A. At the A locus, the first parent always supplies A while the second can supply A or a. This makes the genotype and phenotype boundaries easier to inspect: no offspring can be aa, and no offspring can be bb because at least one B is always supplied. The exact percentages come from the same count-and-normalize procedure used for the default cross.

This example shows why the two-locus page is more informative than reporting only a double-dominant percentage. A fixed locus can remove entire genotype and phenotype classes, while a heterozygous locus preserves variation. In a classroom, compare this cross with its reversed input and with AaBb crossed with AaBb. In an applied discussion, do not turn the abstract A and B labels into a real trait or health statement without a separate biological model and evidence.

• AABb supplies AB and Ab slots.
• AaBB supplies AB and aB slots.
• A homozygous locus can make some classes impossible.
• The same sixteen-slot method handles simple and varied crosses.

Checking the distribution one locus at a time

A useful hand check separates the two loci before recombining them. First inspect the A-locus cross and ask whether AA, Aa, or aa is possible. Then inspect the B-locus cross and ask whether BB, Bb, or bb is possible. Under independent assortment, a two-locus genotype probability can be reconstructed by multiplying the corresponding one-locus probabilities. The handler reaches the same result by enumerating the sixteen gamete pairings, which keeps repeated slots and canonical spelling explicit.

For AaBb crossed with AaBb, the A-locus proportions are one quarter AA, one half Aa, and one quarter aa. The B-locus proportions have the same pattern. Multiplying one value from each list gives the nine familiar genotype proportions, while grouping the one-locus dominant categories gives the four phenotype proportions. This check is not a second biological assumption beyond independent assortment; it is another way to inspect the same arithmetic. If the two methods disagree, examine the gamete list or the locus ordering.

This factorized view also shows why the output can contain zero classes for homozygous inputs. If a parent makes only A at one locus, any offspring aa class is impossible. If a parent makes only b at the other, any BB class is impossible. The sixteen-slot enumeration records those zeros rather than dropping the categories. Keeping all nine keys in a stable order makes comparisons, tests, and reports clearer even when some values are absent.

• Inspect the A-locus and B-locus crosses separately.
• Independent assortment permits multiplication of one-locus probabilities.
• Impossible classes remain visible as zero percentages.
• Stable nine-key output makes cross comparisons auditable.