What relation is your grandmother's niece to you?

Answer 1

According to the table at http://freepages.genealogy.rootsweb.ancestry.com/~gentutor/chart.html

Your common ancestor is your Great grandparent (you are their Great grandchild - Row 3). Your Grandmother's niece/nephew is their brother/sisters child making them your Great grandparent's grandchild (column 2).

This makes you grandmother's niece/nephew your First Cousin once removed

Answer 2

Your grandmother's niece is your parent's first cousin and your first cousin, once removed. See link.

The 'first' part, the degree, indicates that the common ancestor you share with the niece in question is a grandparent, your grandmother's parent. Whichever connection to the common ancestor is shorter, that is the one you use. So even though the common ancestor is your great grandparent, you figure the kinship based on your cousin's connection: grandparent. The 'once removed' part means that the niece is in the same generation as your parents, if you block out the family tree. In terms of generations, you are one generation removed from (or one generation later than) this niece. This niece is your parent's first cousin, and children of the niece are your second cousins.

Confusing? Yes, it is. It takes getting used to.