Cousin
A cousin in English kinship terminology is a relative with whom one shares a common grandparent or more distant ancestor, and who is not in one's own line of descent. The term cousin is rarely used where there are other specific terms to describe relationships.
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, etc.) indicates the minimum number of generations between either cousin and the nearest common ancestor; the remove (once removed, twice removed, etc.) indicates the number of generations, if any, separating the two cousins from each other.
For example, the child of one's aunt or uncle is one's first cousin, because there is one generation (unshared parents) between the cousins and their shared grandparents. The child of one's first cousin is one's first cousin once removed because the child belongs to the next generation following one's own.
The system can handle kinships going back many generations. In 2004, genealogists discovered that U.S. Presidential candidates George W. Bush and John Kerry shared a common ancestral couple in the 1500s. It was reported that the two men are sixteenth cousins, three times removed. However, the two are in fact ninth cousins, two times removed. Also, in 2007, it was revealed that U.S. vice president Dick Cheney and senator Barack Obama are eighth cousins.
Non-genealogical usage often eliminates the degrees and removes, and refers to people with common ancestors merely as cousins or distant cousins.

# Family tree
This family tree diagram shows the relationship of each person to the orange person, with cousins colored in green.

# Cousin chart, or table of consanguinity
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 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.

### Chart
The closest relationship prevails (nearest common ancestor) - 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.

## Chart relationships as sentences
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 share grandparents but have different parents we are first cousins
- If we share great grandparents but have different grandparents we are second cousins
- If we share great-great grandparents but have different great grandparents we are third cousins
- My first cousin's child and I are first cousins once removed (one generation difference between us)
- My first cousin's grandchild and I are first cousins twice removed (two generations difference between us)
Similarly
- My parent's first cousin and I are first cousins once removed (one generation difference between us)
- My grandparent's first cousin and I are first cousins twice removed (two generations difference between us)
- My second cousin's child and I are second cousins once removed (one generation difference between us)
- My second cousin's grandchild and I are second cousins twice removed (two generations difference between us)
Similarly
- My parent's second cousin and I are second cousins once removed (one generation difference between us)
- My grandparent's second cousin and I are second cousins twice removed (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 (e.g. your fifth cousin's great-grandchild is also your fifth 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 no double cousins:
- 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.
- 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.
- 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.
- 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.
An alternative method is as follows.  You and your cousin count the generations between you and the common ancestor.  Do not count the common ancestor and do not count yourselves.  Thus, if it is a grand parent, this number is one.  Let this be X.  If X is different for the two of you, then let the difference between be Y.  Now, use the smaller X (if there is a difference).  You are X cousins, Y times removed.  If Y is zero, (because the number of generations between you and your ancestor is the same as for your cousin), then you are simply X cousins.  X is stated as an ordinarial, i.e. first, second, etc.
Note that the above system is symmetric; if person A is person B's second cousin once removed, then person B is person A'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 term second cousin (the primary sense being "a child of a first cousin of one's parent").
A different and partly conflicting system that is sometimes used is asymmetric (i.e. it mirrors the fact that aunt/uncle and niece/nephew are asymmetric names). With this system to work out what cousinage X is to Y, identify the descendant or ancestor of X that is the same generation as Y (i.e. the same number of generations from the common ancestor), then count how many generational removes there are up or down the tree from those same-generation cousins. In other words go across the family tree first, then up or down. For example take X and Y who have common ancestors who are X's great grandparents and Y's grandparents. From Y's point of view, X is Y's first cousin's child, and thus is Y's first cousin once removed (downwards), but from X's point of view Y's child is X's second cousin, and Y therefore is X's second cousin once removed (upwards).

# Kinship chart
Recently, a kinship chart has been proposed that takes into account which relative belongs to the older generation.  The terms in this chart are already in common usage.

### Chart
The closest relationship prevails (nearest common ancestor)

# 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 of one's parents. These cousins are biologically connected to both the maternal and paternal family trees and that cousinship is termed a double cousin. Another term used to describe this is cousins 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 the consanguinity of ordinary cousins and are as related as half-siblings. Instead of the 12.5% consanguinity that simple first cousins share with each other, double first cousins share a 25% consanguinity with each other. Further, if identical twins form 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 full siblings.
Sometimes the children of these unions are 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 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
The family relationship between two individuals a and b, where Ga and Gb respectively are the number of generations between each individual and their nearest common ancestor, can be calculated by the following:
- 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-granduncle/great-grandaunt and great ... great-grandnephew/great-grandniece, 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.

# Alternative canon law charts
Another visual chart used in determining the legal relationship between two people who share a common ancestor (blood) 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 which both people are descended) in the top space within 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 the 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 wanted to use the chart to determine their relationship using the chart to the right, their common parents would be placed in the top most position and each child 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 would 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 respect 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.