I recently read a discussion online regarding the terminology for describing the various relations for those beyond the usual first cousins. There are generally accepted terms for these relationships among genealogists, but there was a lot of confusion about how these terms are used.
There’s actually a fairly simple, and mathematical way to describe these relationships, which I’ll explain. The names for these relationships, such as first cousins, second cousins, fifth cousins twice removed are determined by the individuals common ancestors, and how closely each individual is related to those ancestors. Let me start off, though, with a few examples, and then I’ll explain the basic formula for figuring this out.
All of our examples will be given from the perspective of you, the reader. But it’s also important to note that each of these terms are reversible. That is to say, that if someone is your second cousin twice removed, you are also their second cousin twice removed.
So, first cousins are the most common and easiest to understand. When someone says cousin, there’s a good chance they are talking about a first cousin. Your first cousins are the people who have a same set of grandparents as you. So, your closest relationship is your grandparents, but also their grandparents.
Second cousins are a simple extension of this. They have the same great-grandparents as you. If your great-grandparents are also their great-grandparents (but you have different grandparents), they are your second cousins.
This can be extended ad infinitum. Your grandparents are two generations from you. Your great-grandparents are three generations from you. So, you and your Nth cousin have common ancestors who are N+1 generations from you. Your sixth cousin would have a common ancestor who is seven generations from you: your great-great-great-great-great-grandparents, or fifth great-grandparents.
So, what about a cousin once removed? What are they removed from? Your first cousin once removed is your first cousin’s children, or your parent’s first cousin. You can see that they are a first cousin relationship, in that the closest ancestor is a grandparent, but they are a generation apart.
So, let’s put this another way. Let’s look at your cousin’s children. You have a common ancestor with them. That common ancestor is your grandparents (two generations from you). Those same people are their great-grandparents (three generations from them). Since the difference between the relationship between your common ancestor and you, and the relationship between your common ancestor and them is one, they are once removed.
So, if your first cousin has grandchildren, they are your first cousin twice removed. This is because your common ancestor, your grandparents (two generations away), are their great-great-grandparents (four generations away). Since the difference between the two relationships is two, they are twice removed.
So, now we can come to the formula for describing any cousin relationship. So, let’s look at you and a cousin of some sort. You have a common ancestor who is N generations away from you, and M generations away from them. The difference between M and N is X (M - N = X). If M is less than N, just swap them, so that X is positive. So, with such a relationship, you and this other person are (N - 1)th cousins X times removed.
Or, lets look at it the other way. You have an Nth cousin X times removed. That means that closest common ancestor is N+1 generations away from one of you, and N+X generations from the other.
You’ve probably heard of a half-sibling. That half relationship can also apply to cousins. Generally, when we talk about cousins, we assume we’re talking about two people who have a set of common ancestors, for example, the same grandmother and grandfather. However, since a person can have children with multiple people, that’s not always the case. If your closest ancestor is a single ancestor, rather than a couple, you would be half cousins. So, if your grandfather has a child with one woman, who is your cousin’s grandmother, and then has a child with a different woman, who is your grandmother, you would be half cousins.
This term is not often used. Additionally, adoption can change this relationship, as can family customs.
What about double cousins? That’s what happens when you and a first cousin share both sets of grandparents. So, if your mother and father get married and have kids, and then your father’s brother (your uncle) marries your mother’s sister (your aunt) and they have kids, you would be double cousins with those kids.
We use the term cousin when the common ancestor is at least two generations away. But what if we used the same logic for closer relationships? You and your siblings share common ancestors (your parents) who are just a single generation away. So if N is one, then N - 1 is zero, which would make them zeroth cousins.
Also, your aunts and uncles share a common ancestor with you who are your grandparents. That’s two generations from you, but only one generation from them. That makes your aunts, uncles, nieces, and nephews your zeroth cousins once removed.
Finally, you and yourself share a common ancestor of yourself, who is zero generations from you, making you your own negative first cousin. It also makes your parents and children your negative first cousins once removed.
That’s just a bit of silliness, since nobody would ever use those terms, but I suppose they are valid mathematically.
These are the terms that are generally used by genealogists. However, individual families may use slightly different terms for their own personal reasons, or for cultural reasons. So, keep that in mind before you start to “correct” someone on their usage.