Cousin calculator: names, relatedness and shared DNA

The calculator asks two questions and gives six answers. Tell it how many generations each person sits below the ancestors they share, and whether those ancestors are a couple or one person. It returns the relationship name both ways, Wright's coefficient of relationship, expected shared DNA as a percentage and in centimorgans (cM), and two counts of the degree of kinship.

Counting down from the shared ancestor

Find the most recent ancestor the two people both descend from. For you and a first cousin that is a pair of grandparents; for you and a second cousin, a pair of great-grandparents. Then count down each line separately: a child of the shared ancestor is 1, a grandchild 2, a great-grandchild 3. One count goes in as person A, the other as person B.

Two slips are common: counting from a couple too far back (siblings share grandparents too, but their nearest shared ancestors are their parents), and numbering the ancestor 1 instead of 0. If one person is the shared ancestor, enter 0 for them and the tool reports a direct line: parent, grandparent, great-grandparent, great-great-grandparent, then 3rd great-grandparent.

How the name is built

English cousin names come from two numbers. The cousin degree is the smaller count minus 1, so two grandchildren of a couple (2 and 2) are first cousins and two great-grandchildren (3 and 3) are second cousins. "Removed" is the difference between the counts, one removal per generation of difference. When a count is 1, that person is a child of the shared ancestor and the pair are not cousins: two counts of 1 make siblings, and otherwise the result is an aunt or uncle, niece or nephew, with "grand" and "great" added as the gap grows.

Here is the tool's naming for counts 1 to 4. Pick the row for A's count and the column for B's; the cell says what B is to A.

Cousin cells mirror each other across the diagonal; aunt and niece cells swap. Kin-type notation names the same positions letter by letter (F father, M mother, B brother, Z sister, S son, D daughter, so FBS is a father's brother's son); our notation guide has the full set.

Wright's coefficient of relationship

Sewall Wright's coefficient of relationship, r, published in The American Naturalist in 1922, adds up the paths that join two people through a shared ancestor. Each path is worth one half for every parent and child link on it. The path from A up to the ancestor and down to B has a + b links, and a couple supplies two such paths, one through each partner:

full relationship: r = 2 × (1/2)^(a + b)

half relationship or direct line: r = (1/2)^(a + b)

The long version, with diagrams, double cousins and the inbreeding coefficient, is in the coefficient of relationship, worked out by hand.

Worked example: the default setting

The tool opens with person A two generations below a shared couple and person B three generations below them. Picture a hypothetical couple whose granddaughter is Ana and whose great-grandson is Ben.

1. Name. The smaller count is 2, so the cousin degree is 2 minus 1, which is 1: first cousins. The counts differ by 1: once removed. Ben is Ana's first cousin once removed, and Ana is his.
2. Relatedness. Two paths, each with 2 + 3 = 5 links: r = 2 × (1/2)^5 = 2/32 = 1/16, or 6.25%.
3. Shared DNA as a percentage. For relatives who are not inbred, the expected share equals r: about 6.25%.
4. Shared DNA in cM. In the relationships this tool covers, full siblings apart, two relatives share at most one of their two copies at any spot, so shared segments are expected to cover 2r of one genome copy: 2 × 1/16 = 1/8. The tool assumes 3,500 cM per copy, and 3,500 / 8 = 437.5, shown as about 438 cM. The two DNA figures agree once you see that the percentage counts both copies: 437.5 / 7,000 = 6.25%.
5. Degrees. Civil count 2 + 3 = 5; canon count, the longer line, 3.

Shared DNA is an average

r is an expectation, not a measurement. Chromosomes pass to children in long blocks, so which blocks two relatives share is a matter of chance, and real totals scatter widely. The Shared cM Project, run by the genetic genealogist Blaine Bettinger, collects totals from testers who know how they are related. In version 4.0 (March 2020), built from nearly 60,000 submissions, 3,700 pairs of first cousins once removed shared between 102 and 980 cM, averaging 433. The tool's 438 sits near the middle; any one pair may sit far from it. Bettinger notes that the data include entry errors, misreported relationships and cousin marriages, which raise sharing, so weigh a real match against the project's published ranges, not this single figure.

Civil and canon degrees

Laws on marriage and inheritance speak of degrees of kinship, counted two ways. The civil method, from Roman law, counts every link up to the shared ancestor and back down, so it equals a + b: first cousins are related in the fourth degree. The canon method counts only the longer of the two lines, which puts first cousins in the second degree; the 1908 Catholic Encyclopedia article "Consanguinity" describes it as the church's marriage rule, and the tool shows that traditional count. The Catholic Church has since switched: canon 108 of the 1983 Code of Canon Law counts the collateral line by the persons in both lines together, which gives the civil number. When a text cites a degree, check which count it means.

Half relationships

Choose "one person only" when the two people descend from one shared ancestor through different partners, as when their parents were half-siblings. There is one path instead of two, so r and both DNA figures halve while the degrees stay put. At the default counts the tool reports a half-first cousin once removed, r = 1/32 (3.125%), about 219 cM. Half does not apply to a direct line, so the option is switched off when either count is 0.

Questions

Is my second cousin's child my third cousin?

No. You and your second cousin are both 3 generations below your shared great-grandparents, so the child is 4. Enter 3 and 4: second cousin once removed. Third cousins are both 4 generations down.

Can the calculator handle double cousins?

Not directly. It follows one shared couple or one shared person, and double first cousins descend from two couples. Run it once per couple and add: 1/8 + 1/8 = 1/4. Families where cousins married work the same way, and the pedigree collapse calculator shows how such loops thin out a tree.

Does it matter whether our parents were brothers, sisters, or a brother and a sister?

Not to r or the expected DNA, which depend only on the counts. It matters a great deal to many kinship terminologies, which call cross and parallel cousins by different terms; see cross and parallel cousins.

Can two documented cousins share no DNA at all?

Yes, at third cousin and beyond. The Shared cM Project gives those relationships a minimum of zero, and its averages for them leave out the pairs who shared nothing detectable. A missing match does not disprove a well-documented tree.