Acousin chart, ortable ofconsanguinity, is helpful in identifying the degree of cousin relationship between two individuals using their most recent common ancestor as the reference point. Cousinship between two individuals can be specifically described in degrees and removes by determining how close, generationally, the common ancestor is to each individual.

Additional modifying words are used to clarify the exact degree of relatedness between the two people.Ordinal numbersare used to specify the number of generations between individuals and a common ancestor, and further clarification of exact cousinship is made by specifying the difference in generational level between the two cousins, if any, by usingdegrees of remove. For example, "first cousins once removed" describes two individuals with one cousin's grandparents as the common ancestor but who themselves are one generation different from each other.

Assuming a common ancestor, in principle any two individuals might share a cousin relationship (except as noted above) if the common ancestor and number of generations of descent to each individual from that common ancestor could be determined.

Reminder: the closest relationship prevails - note that cousinship is not calculated between individuals when one is descended from the other, for example, two individuals are not called cousins if they are any degree of grandparent, parent and child. Also cousinship is not calculated between individuals of any degree of aunt/uncle and nephew/niece relationship to each other.

• If we sharegrandparentsbut have differentparentswe arefirst cousins
• If we sharegreat grandparentsbut have differentgrandparentswe aresecond cousins
• If we sharegreat-great grandparentsbut have differentgreat grandparentswe arethird cousins

• Myfirst cousin's childand I arefirst cousins once removed(one generation difference between us)
• Myfirst cousin's grandchildand I arefirst cousins twice removed(two generations difference between us)

Similarly

• Myparent's first cousinand I arefirst cousins once removed(one generation difference between us)
• Mygrandparent's first cousinand I arefirst cousins twice removed(two generations difference between us)

• Mysecond cousin's childand I aresecond cousins once removed(one generation difference between us)
• Mysecond cousin's grandchildand I aresecond cousins twice removed(two generations difference between us)

Similarly

• Myparent's second cousinand I aresecond cousins once removed(one generation difference between us)
• Mygrandparent's second cousinand I aresecond cousins twice removed(two generations difference between us)

Following this pattern, it can be determined thatxth cousiny-times removed means either of the following:

• Thexth cousin of your direct ancestorygenerations previously (eg. your great-grandparent's fifth cousin isyourfifth cousin thrice removed); or
• Yourxth cousin's direct descendantygenerations away (eg. your fifth cousin's great-grandchild isalso yourfifth cousin thrice removed)

Determining cousin type

The name of the cousinship is not determined by oneself, but rather is always determined by the generational level of the individual most closely related to the ancestor in common. The following assumes there are nodouble cousins:

1. To work out if two people are first, second, or third cousins, count back the generations to their common ancestor. For example, if the common ancestor is one's grandmother, that is two generations. If it is one's great-grandmother, that is three generations.
2. Identify the one of the two descendants who is generationally closest to the common ancestor. For example, if one of the cousins is a great-great-grandchild (four generations) and the other is a grandchild, the grandchild is generationally closest to the common ancestor.
3. If the generationally closest descendant of the common ancestor is a grandchild (two generations), then the cousins are first cousins; if three generations separate the common ancestor and the generationally closest cousin, then the two are second cousins, and so on.
4. If the cousins are separated from the common ancestor by an equal number of generations, there is no "remove," for instance if both are grandchildren of the common ancestor. But if the number of generations between the common ancestor is different for each cousin, that difference is expressed by using a clarifier, "removed," with the number of removes. For example, if one person is a grandchild of (2 generations from) the common ancestor, and the other person is a great-great-grandchild of (4 generations from) that common ancestor, then the two are first-cousins-twice-removed.

Note that the above system issymmetric; if personAis personB's second cousin once removed, then personBis personA's second cousin once removed as well, even though the relationship between them is not symmetric (since the two are not from the same generation).

Also note that much of this terminology is variable; for example, many dictionaries give "a child of one's first cousin" as a secondary sense for the termsecond cousin(the primary sense being "a child of a first cousin of one's parent").

Double cousins and half cousins

Generally, one's cousinship to another is determined by a connection through only one parent's biological family. But an individual's cousinship to another individual may be determined by a connection through both one's parents. These cousins are biologically connected to both the maternal and paternal family trees and that cousinship is termed adouble cousin. Another term used to describe this iscousins on both sides.

If a pair of siblings from one family each form a couple with a pair of siblings from another family, then the children of these two couples will be double first cousins to one another. The children of the couples would already automatically be first cousins due to the fact that they are children of one of their parent's siblings, but in this case the children of their mother's sibling, are also the children of their father's sibling, and thus they are double first cousins. Such cousins have double theconsanguinityof ordinary cousins and are as related ashalf-siblings. Instead of the 12.5%consanguinitythat simple first cousins share with each other, double first cousins share a 25%consanguinitywith each other. Further, ifidentical twinsform a coupling with a corresponding set of identical twins, the children of these two couples, though legally (double) first cousins to one another, would genetically be as closely related to each other as ordinary fullsiblings.

Sometimes the children of these unions are called cousin-siblings, cousin-brothers, or cousin-sisters. Note that noincesthas occurred to create these close kinships.

Half-siblingsshare only one parent. Extrapolating from that, if one of John's parents and one of Mary's parents are half-siblings, then John and Mary are half-cousins. The half-sibling of each of their respective parents would be their half-aunt or half-uncle but these terms although technically specific are rarely used in practice. While it would not be unusual to hear of another's half-brother, or half-sister, so described, in common usage one would rarely hear of another's half-cousins or half-aunt, so described, and instead hear them described simply as the other's cousin or aunt.

Mathematical definitions

Thefamily relationshipbetween two individualsaandb, whereG_aandG_brespectively are the number ofgenerationsbetween each individual and their nearest commonancestor, can be calculated by the following:

• Ifx=0 andy=0 then they are the same person.
• Ifx=0 andy=1 then they are parent and child.
• Ifx=0 andy=2 then they are grandparent and grandchild.
• Ifx=0 andy>2 then they are great ... great-grandparent and great ... great-grandchild, withy-2 greats.

• Ifx=1 andy=0 then they are siblings (brothers or sisters).
• Ifx=1 andy=1 then they are uncle/aunt and nephew/niece.
• Ifx=1 andy>1 then they are great ... great-great-uncle/great-great-aunt and great ... great-greatnephew/great-great-niece, withy-1 greats.

• Ifx>1 andy=0 then they are (x-1)^thcousins.
• Ifx>1 andy>0 then they are (x-1)^thcousinsytimes removed.

So two people sharing a pair of grandparents havex=2 andy=0 and are described as beingfirst cousins.

Ifx>0 and they only share one nearest common ancestor rather than two, then the word "half" is sometimes added at the beginning of the relationship.

The mathematical definition is more elegant if you always express consanguinity as the ordered pair of natural numbers (x, y) as defined above. In that case, the relationship one has with oneself is (0, 0), the relationship between parent and child is (0, 1), and the relationship between grandparent and grandchild is (0, 2). The relationship between siblings is (1, 0); and between aunt/uncle and nephew/niece is (1, 1). First cousins are (2, 0). The first number expresses how many generations back the two people'smost recent common ancestoris, while the second number expresses the generation difference between the two people.