When I'm going to cut the binding fabric, I measure the quilt. Two sides and top and bottom. Put those numbers into the calculator and add them. Write that down. Now measure the fabric piece. If it is 44 inches wide, you need to count that as 42, to be sure you have enough after it is seamed. So divide the number of inches around the quilt by 42. That will give you the number of strips you need. No, you don't have to add anything for corners. They don't take anything extra beyond the actual measurement of the quilt. You really need only 2 and a half inches (or the width of the binding) beyond the total number of inches around the quilt. That is the overlap to seam the ends.
If the piece I have chosen for the binding looks like it's almost not large enough, I measure the fold of the binding fabric and divide that by the number of strips I need.
That will tell you how wide you will be able to cut your strips. Sometimes I make a "lining" with trash fabric and put it on so you can't see that.
I never have a whole strip left over.