I'm making a 2D GUI for my game. I get screen resolution independence by using percentages for x, y & width, height for the controls relative to it's parent container where the top level is the entire screen. This helps make my GUI look exactly the same on all resolutions of the same aspect ratio.
Now I want to make it aspect ratio independent so that I don't have to make my screens per aspect ratio. So when I initially make the GUI, I use a base screen res/aspect ratio to get it to look just right. I want to take this base and make it look the same (positioning and sizing) on any resolution the player selects for the game. What is the math on something like that?