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How to Calculate the Coefficient of Relatedness

Updated on December 21, 2016
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TR Smith is a mathematician who enjoys puzzles and knows too many gamblers.


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Full sisters have a coefficient of relatedness equal to 1/2.
Full sisters have a coefficient of relatedness equal to 1/2.

The coefficient of relatedness or coefficient of relationship (CR) is how related you are to a particular family member. The closer the number is to 1, the closer the relative; the closer the number is to 0 the more distant the relative. A high CR between two people means their offspring will be more inbred.

This tutorial will show you how to calculate the coefficient of relationship by drawing a family tree. Also included is an extensive table of various family relations and their coefficients.


Basic Principles

Everyone gets half their autosomal DNA from each parent, making the coefficient of relationship between parent and child 1/2. As you go up the tree for ascendants or down the the tree for descendants, each generation removed reduces the CR by a factor of 1/2. Therfore, grandparents and grandchildren have CR = 1/4, great grandparents and great grandchildren have CR = 1/8, etc.

To calculate the coefficient of relatedness for someone who is not in your direct line, you go up the family tree to the nearest common ancestor and back down the tree to the relative in question, multiplying by 1/2 at every stage. Do this for every unrelated closest common progenitor and then add all the numbers. This is the CR.

For example, the CR between you and your full sibling is 1/2, which is obtained from 1/4 + 1/4 as in the diagram below.

You and your full sister are 1/4 similar via your mother, and 1/4 similar via your dad, making your total similarity equal to 1/2. In contrast, the similarity between you and your half sister is only 1/4. Using the fact that siblings have a coefficient of relationship equal to 1/2 , you can make shortcuts when calculating the CR from a family tree.

For example, your coefficient of relationship with your full aunt is (1/2)*(1/2) = 1/4. Your CR with your full first cousin is (1/2)*(1/2)*(1/2) = 1/8. This can be seen in the diagram below using the horizontal 1/2 relation between full siblings.

Calculating Coefficient of Relationship from Family Trees

Here are some more complicated examples applying the basic principles set forth in the previous section. As an example, let's calculate the CR between you and Dana, who is the daughter of your maternal grandmother's maternal half sister Ellen.

There are five copies of 1/2 that we need to multiply, so we get

(1/2)*(1/2)*(1/2)*(1/2)*(1/2)
= (1/2)^5
= 1/32
= 0.03125

This means that you and Dana are 3.125% related. The coefficient of relatedness between you and her is 1/32. The term for how you and Dana are related is half first cousin once removed. Dana is your mother's half first cousin. Ellen is your mother's half aunt. Ellen is also your great half aunt.

Now what if we discover that Dana is related to you through another connection? Suppose Dana's father is your paternal grandfather because he had an affair with Ellen. (Scandalous!) The coefficient of relation calculated through this branch is shown in the diagram below.

Dana is your father's paternal half sister and your paternal half aunt. Your relation to her through your paternal grandfather gives a relatedness coefficient of (1/2)^3 = 1/8.

Since you are related to Dana in two different ways, your total coefficient of relationship with Dana is 1/32 + 1/8 = 5/32 = 0.15625 = 15.625%. To you, Dana is both your half aunt and your half first cousin once removed. To Dana, you are the child of her paternal half brother with her maternal half first cousin.

The table below gives coefficients for many other family relations. Notice that different relationships can have the same coefficient of relationship. For example, first double cousins are as genetically similar as half-siblings and grandparents-grandchildren.

Coefficients of Relationship for Various Family Connections

Description of Relationship
Usual Family Member Term
Coefficient of Relation
Coefficient of Relation
Your identical twin.
Identical twin
1
1
Your identical twin's child.
Niece or Nephew
1/2
0.5
Your parent's identical twin.
Aunt or Uncle
1/2
0.5
Child of your mother's identical twin with your father's identical twin.
Double first cousin
1/2
0.5
Your parent.
Mother or Father
1/2
0.5
Child of both your parents.
Full sibling (Sister or Brother)
1/2
0.5
Your child.
Daughter or Son
1/2
0.5
You and this person have the same mother but your fathers are full brothers. Or you and this person have the same father but your mothers are full sisters.
Sibling cousin, also 3/4 sibling
3/8
0.375
You and this person have the same mother but your fathers are father-and-son. Or you and this person have the same father but your mothers are mother-and-daughter.
3/4 Sibling
3/8
0.375
You and this person have the same mother but your fathers are half brothers. Or you and this person have the same father but your mothers are half sisters.
Sibling cousin
5/16
0.3125
You and this person have the same mother but your fathers are first cousins. Or you and this person have the same father but your mothers are first cousins.
Sibling cousin
9/32
0.28125
Your parent's parent.
Grandparent
1/4
0.25
Your child's child.
Grandchild
1/4
0.25
Your parent's full sibling.
Aunt or Uncle
1/4
0.25
Your full sibling's child.
Niece or Nephew
1/4
0.25
You and this person have the same mother but have unrelated fathers. Or you and this person have the same father but unrelated mothers.
Half sibling
1/4
0.25
Child of your mother's identical twin. Or child of your father's identical twin.
(Full) First cousin
1/4
0.25
Child of your mother's sister with your father's brother. Or child of your mother's brother with your father's sister.
Double first cousin
1/4
0.25
Child of your maternal half sibling with your paternal half sibling.
Double half niece/nephew
1/4
0.25
This person is simultaneously your mother's half sibling and your father's half sibling.
Double half aunt/uncle
1/4
0.25
Child of your mother's half sibling with your father's half sibling where both of these half siblings are common to your mother and father. (Your parents born from a wife-swap.)
Quadruple half first cousin
1/4
0.25
Child of one parent's full sibling with the other parent's parent.(E.g., your maternal aunt with your paternal grandfather.)
-
1/4
0.25
Child of your mother's half sibling with your father's half sibling, where one of these half siblings is common to your mother and father.
Triple half first cousin
3/16
0.1875
Child of one parent's full sibling with your other parent's half sibling.
-
3/16
0.1875
Child of your maternal half sibling with your paternal first cousin. Or child of your paternal half sibling with your maternal first cousin.
-
3/16
0.1875
Your grandparent's parent.
Great grandparent
1/8
0.125
Your grandchild's child.
Great grandchild
1/8
0.125
Your grandparent's full sibling.
Great aunt or Great uncle
1/8
0.125
Your full sibling's grandchild.
Great niece or Great nephew
1/8
0.125
Child of your parent's full sibling.
Full first cousin
1/8
0.125
Your parent's half sibling.
Half aunt or Half uncle
1/8
0.125
Your half sibling's child.
Half niece or Half nephew
1/8
0.125
Your double first cousin's child. Or your parent's double first cousin.
Double first cousin once removed
1/8
0.125
Child of your mother's half sibling with your father's half sibling.
Double half first cousin
1/8
0.125
Child of your mother's maternal half sibling and her paternal half sibling. Or child of your father's maternal half sibling and his paternal half sibling.
Double half first cousin
1/8
0.125
Child of your mother's and father's common half sibling. Aka child of your double half aunt/uncle.
Double half first cousin
1/8
0.125
Child of one parent's double first cousin with the other parent's double first cousin.
Quadruple second cousin
1/8
0.125
Child of your maternal first cousin with your paternal first cousin.
Double first cousin once removed
1/8
0.125
This person is simultaneously your mother's first cousin and your father's first cousin.
Double first cousin once removed
1/8
 
Child of one parent's double first cousin with the other parent's first cousin.
Triple second cousin
3/32
0.09375
Your first cousin's child. Or your parent's first cousin.
Full first cousin once removed
1/16
0.0625
Child of your parent's half sibling.
Half first cousin
1/16
0.0625
Child of your mother's full first cousin with your father's full first cousin.
Double second cousin
1/16
0.0625
Your parent and this person's parent are double first cousins.
Double second cousin
1/16
0.0625
Your grandparent's half sibling.
Half great aunt/uncle
1/16
0.0625
Your half sibling's grandchild.
Half great niece/nephew
1/16
0.0625
Your great grandparent's parent.
Great great grandparent
1/16
0.0625
Your great grandchild's child.
Great great grandchild
1/16
0.0625
Grandchild of your grandparent's full sibling. Equivalently, your parent and this person's parent are first cousins.
Full Second Cousin
1/32
0.03125
Your first cousin's grandchild. Or your grandparent's first cousin.
First cousin twice removed
1/32
0.03125
Your half first cousin's child. Or your parent's half cousin.
Half first cousin once removed
1/32
0.03125
Your first cousin's great grandchild. Or your great grandparent's first cousin.
First cousin three times removed
1/64
0.015625
Your second cousin's child. Or your parent's second cousin.
Second cousin once removed
1/64
0.015625
Your parent and this person's parent are half first cousins.
Half second cousin
1/64
0.015625
Your parent and this person's parent are secound cousins.
Third cousin
1/128
0.0078125

In the table above, all pairs of parents are assumed to be unrelated. Inbreeding will increase the coefficient of relationship.

The coefficient of relatedness (CR) between you and your Nth cousin M times removed is given by the formula

CR = (1/2)^[2N + M + 1]

assuming there is no multiple relationship or half relationship in the tree that connects you.


Cousin Relationships FAQ

Here are several frequently asked questions regarding the relatedness of cousins, legality of cousin marriage, distinctions among full cousins, whether "half cousin" is a real term, and what the heck Nth cousin M times removed means.

What are parallel cousins and cross cousins? Maternal and paternal cousins? Are these distinctions genetically important?
Parallel cousins are the children of your parents' same sex siblings -- your mother's sisters and your father's brothers. Cross cousins are the children of your parents' opposite sex siblings -- your mother's brothers and your father's sisters. Maternal cousins are the children of your mother's siblings. Paternal cousins are the children of your father's siblings. Genetically, the coefficient of relationship between you and any type of full first cousin is 1/8. Some cultures make distinctions between these for the purposes of marriage. For example, some Muslims consider cousin marriage between brothers' children to be preferable, while the Iroquois only permitted cousin marriage between cross cousins.

What types of cousin marriages are legal?
The legality of first cousin marriage depends on where you live. Since full first cousins are 1/8 similar, one would think that countries/states where cousin marriage is permitted would permit other CR = 1/8 relations and ban all relationships where the coefficient is greater than 1/8. Unfortunately, laws are not written by scientists or logical thinkers and there are many inconsistencies in the application of the law. For example, places that permit cousin marriage don't have exceptions for double first cousins, who are as related as half siblings, yet they do explicitly ban half sibling marriages. These same places will often explicitly ban marriage between direct ascendants and descendants, even though these relationships might have a coefficient of 1/8 or less. Second cousin marriages (CR = 1/32 or 3.125%) are generally permitted most places.

Someone on a genealogy forum said there's no such thing as a half cousin, that you cannot be half of someone's cousin.
If you accept the existence of half siblings, then you must accept all the relationships that arise from half siblings -- half aunts/uncles, half nieces/nephews, and half cousins. Half siblings are not half of a sibling, they are simply 1/2 as related to you as your full siblings are. Likewise, "half cousin" does not mean half of a cousin. People who insist that half cousins aren't real often cite legal codes where no distinctions among different types of first cousins are made (double, half, etc.). However, legal codes do not (and should not!) govern how we study biology and genetics.

At what point are distant cousins essentially the same as unrelated strangers?
All humans are 99.9% genetically similar, which means the coefficient of relationship is actually a refinement of that remaining 0.1%. According to the formula, fifth cousins are 1/1024 = 0.09765625% similar to each other, so cousins this distant are basically equivalent to strangers.

What is a 3rd cousin twice removed?
An Nth cousin is a cousin in the same generation as you. You can think of your full sibling as your zeroth cousin. The children of a pair of full siblings are first cousins. The children of a pair of first cousins are second cousins. The children of a pair of second cousins are third cousins, etc.

M times removed means the Mth generation descendant of one of the Nth cousins, and the reciprocal relationship as well. For example, an uncle-nephew relationship is a zeroth cousin once removed. The child of your first cousin is your first cousin once removed. Likewise, your parent's first cousin is also your first cousin once removed. The grandchild of your third cousin is your third cousin twice removed. Likewise your grandparent's third cousin is your third cousin twice removed. You can use the chart below to figure the cousin relationship between two people with a common ancestor.

Images from public domain stock and created by author.


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    • Nina 19 months ago

      My grandfather has a much younger half-sister who is around my dad's age. (My great-grandfather remarried late in life to a much younger woman.) She has a daughter Anne who is around my age and we went to college together. What is Anne's relation to me--the correct term and coefficient of relatedness? Is she closer than a second cousin?

    • Janine 16 months ago

      Nina: she's your half first cousin once removed. Coefficient is the same as for a full second cousin.

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