Cousin chart

Cousin chart is the common name for a Table of Consanguinity. It identifies the correct name for the relationship between any two specific people using their closest common ancestor as a reference point. This chart uses formal English relationship terms.

Overview

The term cousin commonly refers to the child of one's aunt or uncle (i.e. the child of one's parent's sibling), but the relationship between that person and oneself is more precisely termed "first cousin".

"Cousins", more specifically, are any relatives of oneself that are neither one's siblings, nor one's siblings' direct descendants, nor one's direct ancestors, nor one's direct descendants; neither are one's "cousins" any siblings of one's direct ancestors. In common and familiar terms then, never are one's brothers and sisters, nor one's parents nor grandparents; nor one's children or grandchildren; nor one's aunts nor uncles, grand-aunts nor grand-uncles, nephews nor nieces, nor grand-nephews nor grand-nieces of any degree, one's cousin by that relationship.

Generations

Ordinal numbers (first, second, third, etc) are used to quantify in which preceding generation the common direct ancestor of the two specific individuals is located. And because generations determine one's first, second, third, fourth, etc, cousinship, those cousins are always of the same generation as oneself. (Think of a symmetrical pyramid with one's own and one's cousin's generation forming the base, then the larger the ordinal number of the cousinship is, i.e. first, second, third, etc., the higher the pyramid will be, always culminating with the two cousins' ancestor in common at the peak of this pyramid. First cousins form a pyramid with their shared grandparent at the peak, second cousins form a pyramid with their shared great-grandparent at the peak, third cousins form a pyramid with their shared great-great-grandparent at the peak, and so forth.)

Generation often implies age contemporaries, but that is not the definition of a generation. A generation is defined in terms of parent, child, grandparent, grandchild, great-grandparent, great-grandchild and so forth. When there is a difference in generational level between the two individuals for whom the relationship is being defined, then the cousinship term is completed with a number removed, which indicates how many generations separate the two specific individuals in question, i.e. the two individuals for whom one is defining the relationship. First cousins once removed are very often also simply referred to (though incorrectly) as second cousins. Their children are sometimes referred to as third cousins. This vernacular is not technically correct, but very frequently used, and often a source of debate and confusion.

Examples

If Andrew's great-great-grandfather, Tom, is also Beatrice's great-great-great-great-grandfather, then Andrew and Beatrice are "third cousins twice removed". Tom is the ancestor in common of the two, and there are five generations between him and Beatrice, but only three generations between him and Andrew. Since Andrew holds the closer relationship status to the ancestor he has in common with Beatrice, his place determines that they are third cousins. But Beatrice and Andrew are themselves two generations removed from each other, thus Andrew and Beatrice, in this example, are "third cousins twice removed".

In the above example, Andrew himself, and Beatrice's unnamed grandparent are both of the same generation and so they form the base of the symmetrical pyramid with Tom at the peak, but Beatrice is still two generations descended below this base line. So the symmetrical pyramid formed by the ancestor in common and the individual closest generationally is in this example a third cousin pyramid, then each succeeding generation beneath this symmetrical pyramid's base is removed from that third cousin pyramid. To restate, the ordinal number of cousinship (first, second, third, etc) is determined by how many generations exist between the ancestor in common and the one of the two individuals who is closest to that common ancestor's generation, while the degree of remove of the same cousinship is determined by any generational difference which may exist between the two individuals for whom one is defining the relationship.

Stated yet another way, in order to correctly name the exact cousinship of two specific individuals, one must know the ancestor the two have in common, and that person's relationship to each of the two (which will be the number of generations down from that common ancestor to each of the two individuals) and also the difference in generational level which exists between the two specific individuals. If one knows the exact number of generations from the common ancestor to each of the specific individuals, then one will automatically know the difference in generations between the two as well. As the example above shows: Tom is both Andrew's great-great-grandfather, and Tom is also Beatrice's great-great-great-great-grandfather.

Double cousins and half cousins

Generally, one's cousinship to another individual is determined by a connection through only one parent to an individual in that parent's biological family. But an individual's cousinship to another individual may be determined by a connection through both parents. These cousins are biologically connected to both the maternal and paternal family trees and that cousinship is termed a double cousin.

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. They 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.

Whether the first family siblings are brother and sister forming a coupling with a sister and brother of the second family, or whether the first family sibling pair are brothers forming a coupling with a pair of sisters from the second family, whenever two siblings from one family each form a couple with two siblings from another family, the offspring of these two couples will be double first cousins to one another.

Sometimes the children of these unions would be called cousin-siblings, cousin-brothers, or cousin-sisters.

Note that no incest has occurred to create these close kinships.

Half-siblings share only one parent. Extrapolating, 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 though technically correct 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.

Chart

The chart below helps explain cousin relationships.

Note that in informal usage, a granduncle is often called a great uncle and a grandaunt is often called a great aunt. Note also that cousinship is not calculated between individuals when one is descended from the other.

If one person's →		Parent	Grandparent	Great Grandparent	Great Great Grandparent	Great Great Great Grandparent	Great Great Great Great Grandparent	Great Great Great Great Great Grandparent
is the other person's ↓	then they're ↘	Parent	Grandparent	Great Grandparent	Great Great Grandparent	Great Great Great Grandparent	Great Great Great Great Grandparent	Great Great Great Great Great Grandparent
Parent		Siblings	Niece/Nephew or Aunt/Uncle	Grand- Niece/Nephew or Aunt/Uncle	Great Grand- Niece/Nephew or Aunt/Uncle	Great Great Grand- Niece/Nephew or Aunt/Uncle	Great Great Great Grand- Niece/Nephew or Aunt/Uncle	Great Great Great Great Grand- Niece/Nephew or Aunt/Uncle
Grandparent		Niece/Nephew or Aunt/Uncle	First Cousins	First Cousins Once Removed	First Cousins Twice Removed	First Cousins Thrice Removed	First Cousins Four Times Removed	First Cousins Five Times Removed
Great Grandparent		Grand- Niece/Nephew or Aunt/Uncle	First Cousins Once Removed	Second Cousins	Second Cousins Once Removed	Second Cousins Twice Removed	Second Cousins Thrice Removed	Second Cousins Four Times Removed
Great Great Grandparent		Great Grand- Niece/Nephew or Aunt/Uncle	First Cousins Twice Removed	Second Cousins Once Removed	Third Cousins	Third Cousins Once Removed	Third Cousins Twice Removed	Third Cousins Thrice Removed
Great Great Great Grandparent		Great Great Grand- Niece/Nephew or Aunt/Uncle	First Cousins Thrice Removed	Second Cousins Twice Removed	Third Cousins Once Removed	Fourth Cousins	Fourth Cousins Once Removed	Fourth Cousins Twice Removed
Great Great Great Great Grandparent		Great Great Great Grand- Niece/Nephew or Aunt/Uncle	First Cousins Four Times Removed	Second Cousins Thrice Removed	Third Cousins Twice Removed	Fourth Cousins Once Removed	Fifth Cousins	Fifth Cousins Once Removed
Great Great Great Great Great Grandparent		Great Great Great Great Grand- Niece/Nephew or Aunt/Uncle	First Cousins Five Times Removed	Second Cousins Four Times Removed	Third Cousins Thrice Removed	Fourth Cousins Twice Removed	Fifth Cousins Once Removed	Sixth Cousins

Chart relationships as sentences

Note also that cousinship is not calculated between individuals when one is descended from the other.

My sibling has the same parents as I do (NOTE:--- half-siblings share only one parent --- step-siblings share no biological parent)

The child of my sibling is my nephew/niece and I am his/her uncle/aunt
The grandchild of my sibling is my grand nephew/niece and I am his/her grand uncle/aunt
The great grandchild of my sibling is my great grand nephew/niece and I am his/her great grand uncle/aunt

If our parents are siblings we are first cousins, and have the same grandparents
If our grandparents are siblings we are second cousins and have the same great grandparents
If our great grandparents are siblings we are third cousins and have the same great-great grandparents

My first cousin's child and I are first cousins once removed to each other (one generation difference between us)
My first cousin's grandchild and I are first cousins twice removed to each other (two generations difference between us)

Similarly

My parent's first cousin and I are first cousins once removed to each other (one generation difference between us)
My grandparent's first cousin and I are first cousins twice removed to each other (two generations difference between us)

My second cousin's child and I are second cousins once removed to each other (one generation difference between us)
My second cousin's grandchild and I are second cousins twice removed to each other (two generations difference between us)

Similarly

My parent's second cousin and I are second cousins once removed to each other (one generation difference between us)
My grandparent's second cousin and I are second cousins twice removed to each other (two generations difference between us)

Following this pattern, it can be determined that xth cousin y-times removed means either of the following:

The xth cousin of your direct ancestor y generations previously (eg. your great-grandparent's fifth cousin is your fifth cousin thrice removed); or
Your xth cousin's direct descendant y generations away (eg. your fifth cousin's great-grandchild is also your fifth cousin thrice removed)

Mathematical definitions

The family relationship between two individuals a and b, where G_a and G_b respectively are the number of generations between each individual and their nearest common ancestor, can be calculated by the following:

x = min (G_a,G_b)

y = |G_a-G_b|

If x=0 and y=0 then they are the same person.
If x=0 and y=1 then they are parent and child.
If x=0 and y=2 then they are grandparent and grandchild.
If x=0 and y>2 then they are great ... great-grandparent and great ... great-grandchild, with y−2 greats.

If x=1 and y=0 then they are siblings (brothers or sisters).
If x=1 and y=1 then they are uncle/aunt and nephew/niece.
If x=1 and y>1 then they are great ... great uncle/aunt and great ... great nephew/niece, with y−1 greats.

If x>1 and y=0 then they are (x−1)^th cousins.
If x>1 and y>0 then they are (x−1)^th cousins y times removed.

So two people sharing a pair of grandparents have x=2 and y=0 and are described as being first cousins.

If x>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's most recent common ancestor is, while the second number expresses the generation difference between the two people.

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