If we’re just trying to make a proportional change, then the area formula is all you need, since we can assume the height should be roughly the same between them.
It really should be a simple calculation. In fact, you don’t even need pi, since that’s a common factor. All you need is the ratio between diameters squared.
If you want to go from 12" to 16" recipes, you take (16/12)^2 ~= 1.8
So just multiply all the amounts by that factor and it should be about right. If it’s not, adjust it a bit for next time.