"Cousin" and "removed" measure two different things, and mixing them up is the most common mistake in the terminology. The cousin number, first, second, third, and so on, measures how many generations back the shared ancestor sits. The removal measures the gap between your generation and your cousin's, when the two of you are not the same number of generations from that shared ancestor. Older records complicate the picture, since wills and letters from centuries past often used cousin loosely, for a nephew, a grandchild, or nearly any relative outside the immediate household.
Finding the Cousin Number
Start by identifying the most recent ancestor you share with the other person, then count the generations from each of you back to that ancestor. Say a grandparent you share is 2 generations back from you but 3 generations back from your relative, since that same grandparent is also their great-grandparent. Take the smaller of the two numbers and subtract 1: 2 minus 1 leaves 1, so you are first cousins. Take the difference between the two numbers: 3 minus 2 leaves 1, so the relationship is once removed. Your first cousin's child, in other words, is your first cousin once removed, not your second cousin, a mix-up even careful researchers make. When one generation count is 0, you are looking at a direct-line relative rather than a cousin. When it is 1, look for a sibling, aunt, uncle, niece, or nephew instead.
Half Cousins, Double Cousins, and Cousin-German
The same counting method applies no matter how the shared ancestor connects the two of you. Half cousins share one grandparent instead of two, descended from half siblings. Double cousins share two full sets of grandparents, created when two siblings from one family have children with two siblings from another. Both keep the same cousin number and removal as an ordinary cousin, but neither carries the same amount of shared DNA, which sometimes complicates genetic-genealogy match estimates. A first cousin with no removal at all was traditionally called a cousin-german, a term genealogists still run across in old wills and legal papers.
Why Two Counting Systems Exist
The cousin-and-removal system is an English folk system, not a legal one, and it grew up alongside a much older, formal method for counting kinship in degrees. Roman civil law counted a degree for every generational step in a relationship, up to the shared ancestor and back down again. Siblings were 2 degrees apart under this system, and first cousins were 4. The Catholic Church adopted a different computation during the reforms of the 11th and 12th centuries, counting only the longer line back to the shared ancestor instead of summing both. Under this method, siblings were 1 degree apart and first cousins were 2. The Fourth Lateran Council narrowed the prohibition in 1215, cutting it from 7 degrees down to 4. Under the canon system that meant third cousins and closer still needed permission to marry, while fourth cousins did not.
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