The problem with that calculator is that it tells you how much binding you can get out a yard, not how much yardage you need for a specific length of binding. Of course you don't want to use a whole yard and get enough binding for a kingsize quilt. But the problem with using a square to get just the right length of bias binding is that you will wind up with lots of seams in the binding, which you probably don't want to work with on a small project.
If you have an extra yard of the binding fabric and don't mind cutting a strip diagonally from it, I would probably do just that. Assuming you're cutting a strip that is 36"x40" (bias doesn't have to be on the true 45 degree line from the selvage). You would wind up with a single strip that is probably long enough for your entire placemat. If you're willing to work with a seam or two, you could use a smaller square, but if you try to optimize your use of fabric you will wind up with lots of seams and difficulty managing the bias square. Hope that helps.
Edited to add - here's a bias calculator that might help determine how much fabric you need, but it doesn't tell you how many seams you will wind up with!
http://www.quiltersparadiseesc.com/C...Calculator.php