How the degree of kinship between two parents sets their child's inbreeding coefficient

The coefficient of inbreeding, written F, is the probability that a child carries two copies of a gene inherited from one ancestor through both parents. Counted the civil way, by adding the generations on each side up to the shared ancestor, the degree of kinship is the length of the path that Sewall Wright's 1922 formula sums over. For relatives outside a direct line who share one ancestral couple, a child's F is one half raised to that degree. First cousins are four degrees apart and give 1/16, as do a great-uncle and great-niece. We worked out 27 whole-blood relationships, up to six generations on each side. At any one civil degree, F varied at most twofold. Under the longer-line count of the 1917 Code of Canon Law, the same relatives spread 32-fold by its sixth degree.

Civil and longer-line counts come out the same only in a direct line

The civil count adds both lines, so first cousins, two generations and two, are in the fourth degree. The longer-line count takes only the longer side and puts them in the second. Taiwan's Civil Code and the 1983 canon code use the first method; the 1917 code used the second. Our guide to cousin degrees sets out both counts. For a grandparent and grandchild, one side has zero generations to the common ancestor, so both counts give a degree of two. It is only off the direct line that the two methods part ways.

Relatedness between cousins comes to twice their child's F

Three figures travel together for first cousins. The 12.5% in our cousin guide is the coefficient of relationship, r, between the cousins: the expected share of DNA they inherit from shared grandparents. Their kinship coefficient is half that, 1/16, and equals the inbreeding coefficient of a child they might have; Magnus Vigeland's 2020 paper in the Journal of Mathematical Biology calls it "the kinship/inbreeding coefficient".

So for parents who are not themselves inbred, r is twice F: the 12.5% describes the cousins, the 1/16 (6.25%) their child. That link is textbook, not ours: Wright named both coefficients in the title of his 1922 paper, "Coefficients of Inbreeding and Relationship".

Half-blood relatives match whole-blood relatives a degree further out

Wright's path formula, printed as Eq. (1) in Vigeland's open-access paper, adds one term per shared ancestor: (1/2) to the power of the civil degree plus one, times (1 + F) of that ancestor. A couple gives two terms, cancelling the plus one. A single shared ancestor contributes only one term. This means a half-blood relative has the same F as a whole-blood relative one degree more distant. Direct-line relatives, who also have only one shared ancestor, follow the same pattern.

The first two rows show why the degree alone does not fix F: parent and child are one degree apart, full siblings two, and both come to 1/4.

Our consanguinity calculator takes these inputs, plus the ancestor's own F, in its custom mode; its kernel matched Wright's formula on all 63 relationships we swept, half and double included. Until 21 October 2026 the custom form accepted any count from one to four, and it computed 78 of its 324 slider combinations that describe no possible family. For example, a parent and child through four shared ancestors came out as F = 1/1. The revision made that day refuses more shared ancestors than the shorter side can have and prints the civil degree beside each term. Set 1 and 2 generations up, two shared ancestors and an ancestor F of zero, and it gives 1/8; one ancestor gives 1/16.