The rule for computing cousins is as follows.
1. Identify the first common ancestor or ancestors. If it is a couple then it is a full-blooded relationship; if it is only a single man or woman, then it is a half-blooded relationship. With cousins of course you can get double-blooded relationships, or in the more remote orders of cousins triple or quadruple-blooded relationships. But let's not go there just for now.
2. Count the number of generations back to the common ancestor(s) on both sides.
3. If the number of generations is EQUAL, then there are no removes. Simply subtract one from the number of generations, and that gives you your order of cousins. Thus if it is two generations back to the common ancestor(s) you are looking at first cousins; if it is three generations you are looking at second cousins; and so on.
4. If the number of generations is UNEQUAL, then you use the LOWER of the two numbers to compute the ORDER of cousins, and the DIFFERENCE BETWEEN the number of generations gives you the number of removes. e.g. two generations on one side, four on the other = first cousins twice removed.
5. You can further differentiate with the terms ASCENDING and DESCENDING. Take "cousin Fred". He is my great grandfather's first cousin (and still alive, the last time I heard

) so it is two generations to the common ancestors on his side, and five on mine. So we are first cousins three times removed. But he is my first cousin three times removed ascending, whereas I am his first cousin three times removed descending.
Cool, isn't it??