This is a very good question. Sometime ago I found a chart as well as the explanation. But I'm not sure that it qualifies as an easy to remember and use explanation. Even the explanation confuses me sometimes, but it might be worth a check: https://en.wikipedia.org/wiki/Cousin

If you think of your ancestral relationships as a series of "levels" or "steps" then the "cousin" and "cousin-removed" relationship is easier is to understand.

If our common ancestors are on the same level, ie, your great-grandparents are my great-grandparents also, then we are "cousins" or "numbered-cousins". If our common ancestors are not on the same level, ie, your great-grandparents are my great-great-grandparents, then we are "cousins-removed".

A very basic example would be Ada & Bob being the common ancestors among a group of people. Ada & Bob had two sons Colin & David. Colin had a son Ethan and David had a son Francis. Ethan had a son George and Francis had a son Harold. George had a son Ian and Harold had a son Joshua. Finally Ian had a son Kyle and Joshua had a son Laurie.

Therefore the line from Colin is : Colin, Ethan, George, Ian and Kyle. The line from David is: David, Francis, Harold, Joshua and Laurie.

Ethan and Francis are first cousins since Ada & Bob are grandparents to both boys.
George and Harold are second cousins since Ada & Bob are great-grandparents to both boys.
Ian and Joshua are third cousins since Ada & Bob are great-great-grandparents to both boys.
Kyle and Michael are fourth cousins since Ada & Bob are great-great-great-grandparents to both boys.

If we use Colin's line to illustrate the "cousins-removed" concept it would go like this:
Ethan and Harold are first cousins-once removed because Harold's father Francis is Ethan's first cousin.
Ethan and Joshua are first cousins-twice removed because Joshua's grand-father Harold is Ethan's first cousin.
Ethan and Laurie are first cousins-thrice removed because Lauries's great-grandfather Harold is Ethan's first cousin.

George and Joshua are second cousins-once removed because Joshua's father Harold is George's second cousin.
George and Laurie are second cousins-twice removed because Lawrie's grandfather Harold is George's second cousin.

Ian and Laurie are third cousins-once removed because Laurie's father Joshua is Ian's third cousin.

The concept of "cousins" and "cousins-removed" isn't very easy to figure out off the top of your head, but written down and taking the 'levels' into account it is easier to understand and figure out. Try writing down the above example and hopefully it should all fall into place.

Go to Google and key in
first cousin once removed

Cheers.

The point of asking is to have the info here, maybe explained in a different way.

Your uncle is the brother of your father or mother.

Your aunt is the sister of your father or mother.

Your great uncle (or grand uncle) is the brother of your grandfather or grandmother.

Your great aunt is the sister of your grandfather or grandmother.

Your great-great uncle is the brother of your great-grandfather or great- grandmother.

Your great-great aunt is the sister of your great-grandfather or great- grandmother.

Your first cousin is the child of your aunt or uncle.

Your second cousin is the grandchild of your great aunt or great uncle. (If two people are first cousins, the children of each of the people will be second cousins.)

Your third cousin is the great-grandchild of your great-great uncle or great-great aunt. (Children of 2nd cousins, are 3rd cousins to each other.)

Your first cousin, once removed, is the child of your first cousin or is the child of your great uncle or great aunt. (See also REMOVED COUSINS)

If someone is your first cousin, then his or her child is your first cousin once removed. (Once removed means one generation level different from you.) All your regular cousins (first, second, etc.) are at the same generation level as yourself. Those at different levels are "removed." If someone is YOUR first cousin once removed, then you are HIS or HER first cousin once removed also. Your second cousin once removed is the child of your second cousin. Your first cousin twice removed is the child of your first cousin once removed (i.e. the grandchild of your first cousin). Your second cousin twice removed is the child of your second cousin once removed (i.e. the grandchild of your second cousin).

REMOVED COUSINS: If two people are some type of cousins, but they are at different generation levels, then here is the way to compute their relationship.
Count how many generation levels they are apart. This is the number they are "removed."

Start with the one at the highest generation level (the older level) and count how many generations up you must go to find the brothers or sisters that are the ancestors of these cousins. This is the "FIRST" or "SECOND" or "THIRD" part of the cousin relationship.

gee janilye, glad Scott didn't ask for a "hard to remember explanation of this"

haha lol

Well you know how I like to simplify things NG :0

ha!

Janilye's explanation is actually the clearest explanation I think I've ever read. I'm looking for true understanding here, not just following a chart.

I'm going to just repeat what I understand, just to say it another way...

So the thing about cousins is that at some point you have common ancestors, obviously. These are your shared grandparents.

They have children who are also each of your grandparents who are siblings of each other. These are your aunts/uncles, with an extra "great" on it than your grandparent at that level (I need to think about why that is to internalize that one).

Their children are your first-cousins, removed the number of times that you are generations below their first cousin(s). Cousins are "removed" if they are not at the same level as you.

Your first-cousin's children are your second cousins, and their children are your third cousins, and so-on. (removed, or not)

These cousins are removed until you go down the number of levels to match your own at which you become nth-cousins, where n is the number of levels down from the children of your shared grandparents.

I don't know if it sounds it, but I get it. :)

By George I think he's got it Ng

OK, so now which ones can you kiss? ;)

now that we have mastered all that ;)
we can move on to this ...

DOUBLE COUSIN
Double cousins arise when two siblings of one family mate with two siblings of another family. The resulting children are related to each other through both of their parents and are thus doubly related. Double first cousins share both sets of grandparents and have twice the degree of consanguinity of ordinary first cousins; genetically, they are as related as half-siblings. Double second cousins can arise in two ways: from two first-cousin relationships among their parents or from one double-first-cousin relationship between their parents

HALF COUSIN
Half-cousins are the children of two half-siblings, and their respective spouses

STEP COUSIN
Step-cousins are either stepchildren of an individual's aunt or uncle or nieces and nephews of one's step-parent

COUSIN IN LAW
A cousin-in-law is the spouse of an individual's cousin or the cousin of one's spouse

PATERNAL or MATERNAL COUSIN
A term that specifies whether one individual is a cousin of another through the mother's side of the family (maternal) or the father's side (paternal). If the relationship is not equally paternal for both or equally maternal for both, then the paternal cousin of one is the maternal cousin of the other

I knew you wouldn't be able to help yourself !!
..and we were supposed to keep it simple

To ScottJ: I'm afraid you still don't have it. You say: "Your first-cousin's children are your second cousins, and their children are your third cousins, and so-on. (removed, or not)" That is not true. Your first cousin's children are the second cousins of YOUR children, not of you. For you, they are first cousins once removed.
Just remember that "removed" indicates a different generational level. It doesn't matter whether that is up or down.

Thanks @hrthompson, I do get that. I don't know what I was thinking when I wrote it.

It's the match between 2 families
Parent v Parent = Cousin
Grandparent v Grandparent = 1st Cousin
2Gt Grandparent v 2Gt Grandparent = 2nd Cousin etc
but if it's Grandparent v Gt Grandparent = 1st Cousin 1 removed
Grandparent v 2Gt Grandparent = 1st Cousin 2 removed etc
Like wise Gt Grandparent x 2Gt Grandparent = 2nd Cousin 1 removed
The 1st number is the same as the eldest Generation and the 2nd number is the number of generation differnce between the other generation.

Sorry I said that wrong the 1st number is the younger generation and the 2nd number is the generation difference to the other generation
1st Generation (Parents) Cousin
2nd Generation (Gt Grandparents) 2nd Cousin etc

so if its Grandparent v Gt Grandparent, the younger is 1st Cousin, theres 1 generation difference so thats 1 removed = 1st Cousin 1 removed

When it gets to adding removed all that means is they are of past generations. A 1st Cousin once removed in relation to me would be;

My grandfather's brother, who is my Gr8 Uncle, a child of his would be my 1st cousin once removed. Any children this cousin had would then become my Second Cousin Twice Removed.

I hope I'm not confusing you.

Cheers
Geoff

To nhartigan50 :--Who is Michael ?