Reference [Wikipedia]

A cousin is a relative with whom one shares a common ancestor. In modern usage, the term is rarely used when referring to a relative in one's own line of descent, or where there is a more specific term to describe the relationship: e.g., brother, sister, aunt, uncle. The term blood relative can be used synonymously, and underlines the existence of a genetic link. A system of degrees and removes is used to describe the relationship between the two cousins and the ancestor they have in common.

The degree (first, second, third cousin, et cetera) indicates one less than the minimum number of generations between both cousins and the nearest common ancestor. For example, a person with whom one shares a grandparent (but not a parent) is a first cousin; someone with whom one shares a great-grandparent (but not a grandparent) is a second cousin; and someone with whom one shares a great-great-grandparent (but not a great-grandparent) is a third cousin; and so on.

The remove (once removed, twice removed, etc.) indicates the number of generations, if any, separating the two cousins from each other. The child of one's first cousin is one's first cousin once removed because the one generation separation represents one remove. Oneself and the child are still considered first cousins, as one's grandparent (this child's great-grandparent), as the most recent common ancestor, represents one degree. Equally the child of one's great(also known as "grand")-aunt or uncle (who is one's parent's cousin) is one's first cousin once removed because their grandparent (one's own great-grandparent) is the most recent common ancestor.

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Non-genealogical usage often eliminates the degrees and removes, and refers to people with common ancestors merely as cousins or distant cousins. Alternatively, the terms 'second cousin' and 'first cousin once removed' are often incorrectly used interchangeably^.

 

The system can handle kinships going back any number of generations (subject to the genealogical information being available).

 

Calculate Your Cousinal Relationship

 

A cousin chart, or table of consanguinity, 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 numbers are 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 using degrees of remove. For example, "first cousins once removed" describes two individuals with the common ancestor being the grandparent of one cousin (one degree) and the great-grandparent of the other cousin (two "degrees"). The degree of lowest number is considered the degree. The cousins themselves are one generation different from each other (one remove). So, the difference between the degrees is the "removed" part of the equation.

To make this easy to remember, think about it this way. Assign a 1 to each grand and 1 to each great. This example represents two people with a common ancestor. If person one's great-great-great grandfather is another person's grandfather, the total number is 4 (great + great + great + grand = 4) and if person two's number is 1 (grand = 1). Take the smaller number (1 in this case). So, you are first cousins. The smallest of the two persons' numbers is the degree. Now, what is the difference between the two numbers? 4 - 1 = 3 So, you are 3 times removed.

Example 2: If your great-great-great grandparent (great + great + great + grand = 4) is another person's great-great-great grandparent (great + great + great + grand = 4), then you are 4th cousins. There is no removed, because you are on the same generational level (4 - 4 = 0).

Example 3: If your great grandparent (great + grand = 2) is the second person's great-great-great-great-great grandparent (great + great + great + great + great + grand = 6), then you are second cousins, four times removed. Why? Because your number is the lowest, being 2 (so, the degree is second cousin), and the difference between your two numbers is 4 (6 - 2 = 4), which is the number of removes (generational difference).

 

If one person's →		Grandparent	Great-grandparent	Great-great-grandparent	Great3-grandparent	Great4-grandparent	Great5-grandparent
is the other person's ↓	then they are ↘
Grandparent		1st cousins	1st cousins once removed	1st cousins twice removed	1st cousins thrice removed	1st cousins four times removed	1st cousins five times removed
Great-grandparent		1st cousins once removed	2nd cousins	2nd cousins once removed	2nd cousins twice removed	2nd cousins thrice removed	2nd cousins four times removed
Great-great-grandparent		1st cousins twice removed	2nd cousins once removed	3rd cousins	3rd cousins once removed	3rd cousins twice removed	3rd cousins thrice removed
Great3-grandparent		1st cousins thrice removed	2nd cousins twice removed	3rd cousins once removed	4th cousins	4th cousins once removed	4th cousins twice removed
Great4-grandparent		1st cousins four times removed	2nd cousins thrice removed	3rd cousins twice removed	4th cousins once removed	5th cousins	5th cousins once removed
Great5-grandparent		1st cousins five times removed	2nd cousins four times removed	3rd cousins thrice removed	4th cousins twice removed	5th cousins once removed	6th cousins

Double cousins

Double first cousins arise when two siblings of one family reproduce with two siblings of another family. The resulting children are related to each other through both parents' families. Double first cousins share both sets of grandparents in common and have double the degree of consanguinity than ordinary first cousins. Genetically, they are as related as half-siblings, sharing 25% of their DNA (a coefficient of relationship of 1/4). Their coefficient of coancestry is 1/8th or 0.125. While double first cousins have the same coefficient of coancestry (1/8) as half-siblings, they do have higher chances of sharing both alleles (1/16 vs 0) and lower chances of sharing one allele (3/8 vs 1/2) with each other than half-siblings.

When identical twins reproduce with a pair of siblings, the resulting children are more related than half-siblings but less related than full siblings (they are genetically equivalent to 3/4 siblings) although they are legally double first cousins.

When identical twins reproduce with another set of identical twins (sometimes called quaternary marriage), the resulting children are likewise genetically indistinguishable from full siblings, although they are genealogically double first cousins.

Double cousin marriage is specifically prohibited in the US state of North Carolina (N.C. Gen. Stat. § 51-3). It is permitted in the other 25 states that permit marriage between first cousins.

Other types of cousins

When identical twins reproduce with the same person, the resulting children are likewise genetically indistinguishable from full siblings, although they are legally half-siblings and first cousins. When identical twins reproduce with siblings the resulting children are more related than half-siblings but less related than full siblings. When two siblings who are not identical twins reproduce with the same person, the resulting children are likewise more related than half-siblings but less related than full siblings. Both of these scenarios produce 3/4 siblings. Similar situations arise when two half-siblings marry the same person and when identical twins reproduce with two half-siblings. Children of double first cousins are double second cousins to each other.

Chart relationships as sentences:

• If two first cousin men have children with two first cousin women then these children are double second cousins because they share both sets of great-grandparents on both the maternal and the paternal family trees.

• If two female first cousins have children with two male second cousins, these children are maternal second cousins / paternal third cousins.

• If two siblings procreate with two second cousins then the resulting children would be paternal first cousins and maternal third cousins, or vice versa.

• Inbreeding: If a male and a female third cousins have children, then these children would be siblings / double fourth cousins. (See cousin marriage.) This could be construed as incest in some cultures, especially if the third cousins know that they are related. Technically, it is considered inbreeding as geneticists can easily detect a genetic relationship with third cousins.

• If a male and a female second cousins have children with siblings a brother and sister and then these children are first cousins / double third cousins.

Half-cousins

Half-siblings share 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-first 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. Also, children of half-first cousins are half-second cousins to each other and so on because they would share only one common great-grandparent out of eight instead of two, and so on.

One-and-a-half-cousins

One and a half cousins may be produced when two full siblings have children with two half-siblings. However, if a set of half-siblings has children with another set of half-siblings, the resulting children would be double-half first cousins, and would have the same consanguinity as full first cousins. Furthermore, if a person's half-sibling marries the person's half-sibling from the other parent, assuming they are not step-siblings, then the child of that couple and the child of the half-sibling who is related to both partners in the married couple will likewise be double-half first cousins.

Step-cousins

Step-cousins are either stepchildren of an individual's aunt/uncle, or children of a step-aunt/uncle. No blood relationship exists between step-cousins, although there does not need to be a "blood" relationship between cousins as in the case of one or both of the siblings being adopted, their children would still be first cousins. Step first cousins once removed would be the stepchildren of your first cousins. Step 2nd cousins are when someones first cousin once removed gets married to a individual and that individual's child is the step 2nd cousin.

Cousin-in-law

A cousin-in-law is the spouse of an individual's cousin, similarly the cousin of an individual's spouse.

Cousin from mother/father side

Everybody may have cousins from his/her mother's or father's side for example: Tina is Jim's cousin from his Mother's side and John is Jim's cousin from his Father's side. Tina and John are not related to each other but both of them are Jim's cousins.

In Chinese kinship, among other systems, the terms for cousins related through only paternal relationships are different.

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 = 1 and y = 0 then they are siblings (brothers, sisters or brother and sister).
• If x = 1 and y = 1 then they are either parent and child or uncle/aunt and nephew/niece.
• if x = 1 and y = 2 then they are either grandparent and grandchild or granduncle/grandaunt and grandnephew/grandniece (or great-uncle/great-aunt and great-nephew/great-niece).
• If x = 1 and y > 2 then they are either great ... great-grandparent and great ... great-grandchild, with y − 2 greats or great ... great-granduncle/great-grandaunt and great ... great-grandnephew/great-grandniece, with y − 2 greats (or great- ... great-uncle/great- ... great-aunt and great- ... great-nephew/great- ... great-niece, with y − 1 greats).

• If x > 1 and y = 0 then they are (x − 1)th cousins. First cousins are usually just called cousins when contrast with more distant relations is not called for.
• If x > 1 and y > 0 then they are (x − 1)th cousins y times removed.

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

Granduncle/grandaunt and grandnephew/grandniece are equivalent to great-uncle/great-aunt and great-nephew/great-niece. Both great-uncle and granduncle refer to an uncle of one's father or mother. Neither form is definitively more correct than the other.

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 between parent and child is (1, 1), and the relationship between grandparent and grandchild is (1, 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.

 

Alternative canon law charts

Another visual chart used in determining the legal relationship between two people who share a common ancestor is based upon a diamond shape, and is usually referred to as a canon law relationship chart.

The chart is used by placing the "common progenitor" (the person from whom both people are descended) in the top space in the diamond shaped chart, and then following each line down the outside edge of the chart. Upon reaching the final place along the opposing outside edge for each person, the relationship is then determined by following that line inward to the point where the lines intersect. The information contained in the common "intersection" defines the relationship.

For a simple example, in the illustration to the right, if two siblings use the chart to determine their relationship, their common parents are placed in the topmost position and each child is assigned the space below and along the outside of the chart. Then, following the spaces inward, the two would meet in the "brother (sister)" diamond. If their children want to determine their relationship, they would follow the path established by their parents, but descend an additional step below along the outside of the chart (showing that they are grandchildren of the common progenitor); following their respective lines inward, they would come to rest in the space marked "1st cousin." In cases where one side descends the outside of the diamond further than the other side because of additional generations removed from the common progenitor, following the lines inward shows both the cousin rank (1st cousin, 2nd cousin) plus the number of times (generations) "removed."

In the example provided at the right, generations one (child) through ten (8th great-grandchild) from the common progenitor are provided; however the format of the chart can easily be expanded to accommodate any number of generations needed to resolve the question of relationship.