Consanguinity & Inbreeding Coefficient Calculator
Consanguinity calculator. Pick a relationship — or describe any shared ancestry yourself — and see the coefficient of inbreeding F for a couple’s child, as an exact fraction, with every term of Wright’s formula written out. Educational, not medical advice.
Consanguinity & Inbreeding Coefficient Calculator
Coefficient of inbreeding F
Wright’s formula, term by term
Educational only. This calculator reports a published statistic and is not medical, genetic or legal advice. Marriage law differs by jurisdiction and is not addressed here. Anyone with a specific concern should consult a genetic counsellor.
How to use the consanguinity calculator
Pick how the parents are related
Seventeen standard relationships are listed, from first cousins through to a parent and child. The coefficient shown is for their child, not for the couple themselves.
Or describe the ancestry yourself
Switch to custom mode and set how many generations run from each parent up to the shared ancestor, and how many ancestors are shared there. A shared couple is two; a single shared ancestor makes it a “half” relationship.
Read F as a fraction
F is always a fraction with a power of two underneath, so it is printed as one — 1/16 rather than 0.0625. The percentage, the coefficient of relationship between the parents, and the risk band sit alongside it.
Check the working
The panel below writes out each term of Wright’s sum: the exponent, the (1 + FA) factor where the shared ancestor was themselves inbred, and what each path contributes to the total.
What the coefficient of inbreeding actually measures
Sewall Wright introduced F in 1922 to answer a specific question: given a pedigree, what is the chance that the two copies of a gene in an individual are identical by descent — the same ancestral copy, arriving twice, once down each parental line? It is a probability, not a verdict, and it has been the standard measure ever since, in livestock breeding, in conservation genetics and in the public-health literature on consanguineous marriage.
The formula sums over every chain connecting the two parents through a common ancestor. Each chain contributes one half raised to the number of generations up one side, plus the number up the other, plus one — and is multiplied by one plus that ancestor’s own inbreeding coefficient, for the case where the shared ancestor was themselves the child of relatives. This tool prints every term rather than only the total, because the total on its own is a number to be believed, while the terms are a calculation to be checked.
The numbers worth knowing
First cousins share a pair of grandparents. Two chains, four generations of separation each, gives an exponent of five: 1/32 per chain, doubled for the two grandparents, and F comes out at exactly 1/16. Halve the shared ancestry — half first cousins, one shared grandparent — and F halves to 1/32. Double it, as double first cousins do when two brothers marry two sisters, and F rises to 1/8, the same figure as an uncle and niece. Full siblings reach 1/4, as does a parent and child.
These are not approximations. F is always a dyadic fraction, and printing it as 0.0625 rather than 1/16 loses information about where it came from, which is why this tool prints the fraction.
F is the child’s coefficient; r is the parents’. For non-inbred parents one is exactly twice the other, which is why both “12.5%” and “6.25%” are correct about first cousins.
F, r, and the factor of two that confuses everyone
Two numbers circulate for every relationship and they differ by a factor of two, which produces an enormous amount of confusion. The coefficient of relationship r describes the two parents: first cousins have r of 1/8, so they share about 12.5% of their DNA. The inbreeding coefficient F describes their child: 1/16, or 6.25%. Both statements are true because they are about different people. F for a child equals the kinship coefficient of its parents, and r is twice that kinship coefficient — which is the whole of the relationship between the two figures, once parental inbreeding is accounted for.
A note on what this tool will not tell you
It reports a statistic. It does not assess risk for any particular couple, and it does not address the law. What the published literature says about first-cousin unions is that the increase in the risk of recessive conditions is real but more modest than commonly assumed — a few percentage points above the population baseline, and heavily dependent on family history that no calculator can see. The legal position varies enormously by jurisdiction: first-cousin marriage is lawful across most of the world, including the United Kingdom and much of Asia, and restricted in many US states. Anyone with a specific question should speak to a genetic counsellor and check their own jurisdiction.
Why it matters across South and Southeast Asia
Marriage within an extended family is common in a number of communities across South Asia, the Middle East and parts of Southeast Asia, often for reasons of property, trust and continuity that have nothing to do with genetics. That makes the coefficient a genuinely useful thing to be able to compute rather than a curiosity: it is also the figure that explains why DNA matches in such communities read as one step closer than the documented relationship, which is a recurring source of confusion for anyone using a consumer test there.
10 facts about consanguinity coefficients
Sewall Wright published the coefficient of inbreeding in 1922.
F for a first-cousin couple’s child is exactly 1/16.
Double first cousins reach 1/8 — the same as an uncle and niece.
The relationship coefficient r is twice the kinship coefficient.
F for the child equals the kinship coefficient of its parents.
The paths in Wright’s sum must not share any individual but the ancestor.
An inbred common ancestor raises F through the (1 + FA) term.
F ≥ 1/64 — second cousins — is a common definition of consanguinity.
Cousin marriage is legal in most of the world, including the UK and much of Asia.
Everything here is computed in your browser; nothing is uploaded.
Frequently asked questions
-
Written F, it is the probability that the two copies of a gene in an individual are identical by descent — that is, both inherited from the same ancestor through both parents. Sewall Wright defined it in 1922 and it remains the standard measure. F is zero for the child of unrelated parents, 1/16 for the child of first cousins, and 1/4 for the child of full siblings.
-
By summing over every chain that connects the two parents through a common ancestor. Each chain contributes (1/2) raised to the power of the number of generations from one parent up to the ancestor, plus the number from the other parent, plus one — multiplied by (1 + F of that ancestor). This tool writes out every term so you can see where the total comes from rather than taking it on trust.
-
Two first cousins share a pair of grandparents, so there are two chains. Each runs two generations up from one parent and two from the other, giving an exponent of 2 + 2 + 1 = 5, so each chain contributes 1/32. Two grandparents, two chains: 2/32 = 1/16. Change it to half first cousins, who share only one grandparent, and the answer halves to 1/32.
-
F is the inbreeding coefficient of a child; r is the coefficient of relationship between the two parents. For non-inbred parents r is exactly twice F, which is why first cousins are said to share 12.5% of their DNA while their child has an F of 6.25%. Both statements are true and they are not in conflict — they measure different people.
-
This is an educational tool and cannot answer that for any particular couple. What the published literature reports is that the increase in risk of recessive conditions for first-cousin couples is real but more modest than commonly assumed — a few percentage points above the population baseline. Anyone with a specific concern should speak to a genetic counsellor, who can take account of family history in a way no calculator can.
-
It depends entirely on where you are, and this tool does not attempt to say. First-cousin marriage is legal across most of the world, including the United Kingdom, much of Asia and much of Europe, and prohibited or restricted in many US states and some other jurisdictions. Uncle–niece and closer unions are prohibited essentially everywhere. Check your own jurisdiction.
-
It accounts for shared ancestors who were themselves the product of related parents. If a shared great-grandparent was the child of first cousins, that ancestor’s own F of 1/16 raises the contribution of every path running through them by a factor of 17/16. You can set it in the custom mode and watch the total move.
-
Yes — switch to custom mode and give the number of generations from each parent up to the shared ancestor, how many ancestors are shared at that position, and that ancestor’s own F. A shared couple is two ancestors; a single shared ancestor makes it a “half” relationship. This covers any single-link pedigree, which is most real cases.
-
The arithmetic is exact — F is always a fraction with a power of two underneath, and the tool prints it as one rather than as a rounded decimal. It is checked two ways: the path formula is verified against an independent implementation of the Malécot kinship recursion over explicit family graphs, and both are checked against the published values for seventeen standard relationships.
-
Completely free, with no account and no limit. Everything runs in your browser, so nothing you enter about your family is transmitted anywhere, and the page keeps working offline once loaded.
Pick up where you left off
Stored only in this browser — never sent to our servers.