Calculate max font size that fits in a rect?

Question

I\'m attempting to find the maximum font size that will fit in a given rect for a given string. The goal of the algorithm is to fill as much of the rect as possible with as

Answer 1

It may be impossible to fill a rectangle completely.

Say at a certain font size you have two lines of text, both filling the screen horizontally, but vertically you have almost but not quite three lines of space.

If you increase the font size just a tiny bit, then the lines don't fit anymore, so you need three lines, but three lines don't fit vertically.

So you have no choice but to live with the vertical gap.