Pedigree Probability Calculator

Background.

Most genetics calculators run forwards: you give them genotypes and they give you offspring odds. This one runs backwards. It answers the question that actually comes up in a family — given where someone sits in the pedigree, and given that their children so far are unaffected, what should we now believe about whether they carry the variant?

That is Bayes' theorem, and it is how genetic counsellors do this arithmetic: a prior from the pedigree, a conditional likelihood from what has been observed, and a posterior that combines them. This page shows all three, so the answer is auditable rather than a black box.

Start with the prior. If someone is the unaffected sibling of a person with an autosomal recessive condition, both of their parents must be carriers, so at conception they had a 25% chance of being affected, a 50% chance of being a carrier and a 25% chance of inheriting neither variant. But we already know they are unaffected, which removes the 25% affected class. Renormalising what is left gives 0.50 ÷ (0.50 + 0.25) = 2/3. That two-thirds figure is one of the most useful numbers in clinical genetics and one of the most commonly missed — the intuitive but wrong answer is one half.

Then add the evidence. Each unaffected child is weak evidence against carrier status, because a carrier with a carrier partner has a one-in-four chance of an affected child each time, so a run of unaffected children is slightly surprising if they really do carry. The strength of that evidence is the likelihood ratio, and for the autosomal case it is three-quarters raised to the number of children — 0.75 for one child, 0.42 for three, 0.24 for five. Being below 1 is what makes it evidence against.

The default example works it through. An unaffected sibling of an affected person, prior 2/3, with a partner who is a confirmed carrier and three unaffected children already born: the likelihood ratio is 0.421875, and the posterior comes out at 27/59, or 45.76%. Three unaffected children moved the belief from 66.67% down to 45.76% — real movement, but far less than most people expect. The risk to the next child falls from 16.67% to 11.44%.

The X-linked scenario behaves quite differently, and comparing them is the most instructive thing on the page. A woman whose brother has an X-linked recessive condition starts at a 1/2 prior. Each unaffected son carries a likelihood of one half rather than three quarters, because if she carries, every son is a straight coin flip. Two unaffected sons take her from 50% to 20% — a much bigger shift than three unaffected children manage in the autosomal case. Her unaffected daughters, meanwhile, tell you nothing at all, because a carrier's daughters are not affected when the father is unaffected. The calculator ignores them, which is correct rather than an oversight.

What this is not: a clinical risk assessment. The model assumes full penetrance, no new mutation, no germline mosaicism, a single causative gene and a correctly reported family history, and every one of those assumptions pushes the true risk upward when it fails. It also ignores genetic testing entirely, and testing dominates real risk revision — a negative carrier test moves the answer far more than any number of unaffected children, with a residual risk that depends on the assay's mutation-detection rate for that condition and ancestry. This page supplies no carrier frequency for any condition: the partner's carrier probability is an input you bring from a laboratory report or a professional guideline. Real carrier risk assessment belongs with a clinical geneticist or a certified genetic counsellor.

What is pedigree probability calculator?

Pedigree probability, or genetic risk calculation, is the use of Bayes' theorem to combine what a family tree implies with what has since been observed. It is the standard method in genetic counselling, and it is written out as a four-row table: the prior probability of each hypothesis, the conditional probability of the observed evidence under each hypothesis, the joint probability (prior × conditional), and the posterior (each joint divided by their sum).

The two hypotheses here are simply that the person does or does not carry the variant. The prior comes from their position in the pedigree. The evidence is the set of unaffected children they already have. The posterior is the answer.

Three pedigree positions are modelled, each with a published prior. An unaffected sibling of someone with an autosomal recessive condition has a prior of 2/3 — the figure stated verbatim in the Genetics in Medicine practice guideline for cystic fibrosis, and independently derivable by conditioning the GeneReviews at-conception figures of 25% affected, 50% carrier and 25% neither on the observation that the sibling is unaffected. A child of one known carrier has a prior of 1/2, straight from segregation. And in an X-linked recessive pedigree, the sister of an affected male whose mother is an obligate carrier has a prior of 1/2, because a carrier mother passes the variant to half her daughters.

The conditional likelihoods differ between the autosomal and X-linked cases in a way worth understanding. For an autosomal recessive condition with a carrier partner, each child is unaffected with probability 3/4, so k unaffected children give a likelihood of (3/4)^k. For an X-linked recessive condition, each son of a carrier is unaffected with probability 1/2, so s unaffected sons give (1/2)^s — a much sharper update. Daughters in the X-linked case give a likelihood of exactly 1 under both hypotheses, which is another way of saying they carry no information, so they cancel out of the calculation entirely.

How to use this calculator.

1. 01Pick the pedigree position that matches the person whose risk you want. The three options differ in their prior — 2/3 for an unaffected sibling of an affected person, 1/2 for the child of a known carrier, 1/2 for the sister of an affected male in an X-linked family.
2. 02Enter how many unaffected children that person already has, split by sons and daughters. Use 0 for both if there are none yet; the posterior will then simply equal the prior, which is correct.
3. 03Set the partner's carrier probability. Enter 100 if the partner has tested positive as a carrier. Otherwise bring the carrier frequency for that specific condition and ancestry from a laboratory report or a professional-society guideline — this page deliberately does not supply one.
4. 04Read the prior, the likelihood ratio and the posterior together rather than the posterior alone. The likelihood ratio tells you how much work the evidence is actually doing: 0.42 means the unaffected children are mild evidence against carrying, not proof.
5. 05Use the next-child risks for the forward question. For an autosomal condition the son and daughter figures are identical; for the X-linked scenario only sons are at risk, and the daughter figure is 0% on the assumption that the partner is unaffected.
6. 06Check the Bayes chain output — it shows the prior, the evidence, the likelihood ratio and the posterior in one line, which is what you would write out by hand and what a marker or a colleague will want to see.
7. 07Do not stop here for a real decision. Carrier testing changes the answer far more than any number of unaffected children, and interpreting a negative test requires the assay's mutation-detection rate. Take the pedigree to a clinical geneticist or a certified genetic counsellor.

The formula.

Two hypotheses, four rows, one division.

Let H₁ be 'this person carries the variant' and H₂ be 'they do not'. Bayes' theorem in the form genetic counsellors write it:

posterior(H₁) = prior(H₁)·P(E|H₁) ⁄ [ prior(H₁)·P(E|H₁) + prior(H₂)·P(E|H₂) ]

P(E|H₂) is always 1 here, because in this model a non-carrier cannot have an affected child, so any number of unaffected children is certain under H₂. That is why the likelihood ratio reported on this page is just P(E|H₁), and why it can never exceed 1.

AUTOSOMAL RECESSIVE. With k unaffected children and a partner whose carrier probability is q, the likelihood has to allow for the partner's status being unknown:

P(E|H₁) = q·(3/4)^k + (1 − q)·1

If the partner carries (probability q), each child is unaffected with probability 3/4. If the partner does not (probability 1 − q), no child can be affected whatever this person's genotype, so the term is 1. Setting q = 1 for a confirmed carrier partner reduces this to the familiar (3/4)^k.

The next child's risk needs both parents, so all four joint terms are carried: (carrier, partner carrier) = p·q·(3/4)^k, (carrier, partner not) = p·(1−q), (not carrier, partner carrier) = (1−p)·q, and (neither) = (1−p)·(1−q). Dividing each by their sum gives the joint posteriors, and then next child affected = P(both carry | E) × 1/4, while next child a carrier = ½ × (1 − P(neither carries | E)).

X-LINKED RECESSIVE. Only unaffected sons are informative:

P(E|H₁) = (1/2)^s

because a carrier mother's son inherits the affected X with probability ½. Her daughters are not affected when the father is unaffected, so their likelihood is 1 under both hypotheses and they cancel out. The next-child figures follow: next son affected = posterior × ½; next daughter affected = 0 on the stated assumption of an unaffected partner; next child affected = posterior × ¼, because half of children are sons.

WORKED THROUGH. Prior 2/3, three unaffected children, partner a confirmed carrier. The conditional under H₁ is (3/4)³ = 27/64 = 0.421875 and under H₂ it is 1. The joints are (2/3)(27/64) = 27/96 and (1/3) = 32/96. The posterior is 27/59 = 45.7627%. The next child's risk is 27/59 × ¼ = 27/236 = 11.4407%.

DIRECTION CHECK. The posterior is always at or below the prior, never above it, because unaffected children can only be evidence against carrying. And the posterior falls monotonically as more unaffected children accumulate. Both are pinned by the test suite, because a sign or direction error here would be invisible in a single spot check.

ROUNDING STAGE. Rounding happens only at the final return, to ten decimal places. The priors are exact rationals (2/3, 1/2), the conditionals are exact powers of 3/4 or 1/2, and every Bayes-table term is carried at full arbitrary precision in between. The Bayes-chain summary line additionally displays four decimal places for readability, but that display rounding never feeds another calculation.

NO SINGULARITY. The denominator is a sum of non-negative terms with at least one strictly positive, because every prior on this page is strictly between 0 and 1. There is no input that can make it zero. A partner carrier probability of 0% is legal and correct: the evidence becomes uninformative, the posterior equals the prior, and the next child's affected risk is exactly 0 because two parents cannot produce a homozygote when one of them carries nothing.

WHAT IS DELIBERATELY NOT MODELLED. Genetic test results, which dominate real risk revision. Reduced penetrance, which would make an unaffected child weaker evidence than the model assumes. De novo mutation and germline mosaicism, which can produce an affected child from parents this model calls unaffected. Locus heterogeneity, where more than one gene causes the same clinical picture. Age-dependent penetrance, which needs a condition-specific onset curve. Each omission biases the answer in the same direction — the true risk is higher than the number shown, not lower.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Moskowitz S. M., Chmiel J. F., Sternen D. L., et al. (2008). Clinical practice and genetic counseling for cystic fibrosis and CFTR-related disorders. Genetics in Medicine 10(12):851–868. doi:10.1097/GIM.0b013e31818e55a2, PMID 19092437. Source of the 2/3 prior, verbatim: 'For an at-risk sibling who is known to be unaffected but has not yet undergone molecular genetic testing, the risk of being a carrier is 2/3.' Also the source for the point that residual risk after a negative carrier test depends on the carrier frequency and the mutation-detection rate. Open access via PMC. Retrieved 2026-07-29.
2. [2]Savant A., Lyman B., Bojanowski C. & Upadia J. Cystic Fibrosis. GeneReviews®, University of Washington, Seattle; NCBI Bookshelf ID NBK1250, last revision 8 August 2024. Independent source of the at-conception figures from which the 2/3 prior follows: 'each sib of an affected individual has at conception a 25% chance of being affected, a 50% chance of being heterozygous, and a 25% chance of inheriting neither of the familial pathogenic variants.' Conditioning on being unaffected gives 0.50/(0.50+0.25) = 2/3. Free full text. Retrieved 2026-07-29.
3. [3]Gulani A. & Weiler T. Genetics, Autosomal Recessive. StatPearls, NCBI Bookshelf ID NBK546620, last update 1 May 2023. Source for the segregation figures underlying the autosomal likelihoods — 'Each parent has a 50% chance of passing on the disease allele' and the 25% affected / 50% carrier / 25% homozygous dominant outcome of a carrier × carrier cross. Free full text. Retrieved 2026-07-29.
4. [4]Bin Shlhoob R., Tanaka J. & Pandya A. M. Genetics, X-Linked Inheritance. StatPearls, NCBI Bookshelf ID NBK557383, last update 22 March 2026. Source of the X-linked prior and likelihood: for a carrier mother, 'each male offspring has a 50% chance of being affected, and each female offspring has a 50% chance of being a carrier.' Free full text. Retrieved 2026-07-29.
5. [5]Ogino S. & Wilson R. B. (2004). Bayesian analysis and risk assessment in genetic counseling and testing. Journal of Molecular Diagnostics 6(1):1–9. PMID 14736820. The standard methods reference for the prior / conditional / joint / posterior table structure implemented here. PROVENANCE NOTE: bibliographic reference only — the publisher's full text was not retrievable during this build and no free copy was located, so no numeric figure on this page is attributed to it. Cited by PMID so the record is identifiable rather than presented as a working link.
6. [6]MedlinePlus Genetics, US National Library of Medicine. Inheritance Patterns, page last updated 19 April 2021. Source for the inheritance-mode definitions framing the three pedigree scenarios, including that the parents of an individual with an autosomal recessive condition 'each carry one copy of the altered gene, but they typically do not show signs and symptoms.' Free. Retrieved 2026-07-29.