Effective insulation slows the rate that heat flows out of the house in winter or into the house in summer, so less energy is required to heat or cool the house. If your house has no wall insulation, and it has more-or-less continuous wall cavities (such as conventional stud walls), blown-in insulation can greatly improve your comfort and save enough energy to be very cost-effective. (It rarely pays to blow additional insulation into already insulated walls.) If your attic is unfinished, it often pays to upgrade its insulation.
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Your contractor’s expertise is more important than the insulation material you choose. Properly installed fiberglass, cellulose, and most foam insulation materials can all reduce the heat conduction of the completed wall system. The key is “properly installed.” Ideally, the contractor will use an infrared camera during or after installation to look for voids.