Insulating a 2x4 wall with exterior rigid foam

Question

I'm gutting the interior and redoing the siding of my old house. Unfortunately the exterior walls are only 2x4 which makes it challenging to reach R20 code let alone go above it to make a greener more energy efficient home.

So if you fill the 2x4 cavity with rock wool, then mount 4 inches of rigid foam to the sheathing, would that surpass R20? What would others do in my shoes? Double studding and losing square footage could be a possibility but would seem a lot more expensive.

Also where does the house wrap and vapor barrier go?

Climate Zone 5 (cold winters/hot summers)

Answer 1

Given that typical foams are R5 per inch, 4 inches of foam alone will exceed R-19. Rockwool in the stud spaces will help somewhat on top of that (with a thermal break at each stud, but an additional R11 or so between studs.)

Answer 2

Consider a foamed in place product. Then a thin layer of expanded polystyrene under the siding should get you there. Make sure to include a heavy mil vapor barrier.

Answer 3

Your foam is fine, and is a vapor barrier, so don't put another one in there!

Your plan to use 4" of closed cell rigid foam as continuous exterior insulation is sound, and will get your R-20 or thereabouts without any insulation in the stud cavities, so adding rockwool to the stud cavities will get you well above your R-20 target.

However, water gets into walls despite all our best efforts to stop it, so it needs a path out of the wall, either to the inside or the outside. Since the closed-cell foam is an effective vapor barrier, it can't exit to the outside, so it must have a path back to the inside, through the drywall, to exit. In other words, do NOT put poly or any other vapor barrier material on the inside, or else you'll have a soggy mess on your hands when you turn the air conditioner on!