Quick Answer — What Does Upgrading R-Value Actually Save?
Heat loss through an insulated surface follows a well-established building-science formula: annual heat loss (BTU) = Area × 24 × Heating Degree Days ÷ R-value. Because R-value is in the denominator, doubling your R-value doesn't halve your heat loss evenly across the range — going from R-11 to R-22 cuts loss in half, but going from R-11 to R-49 cuts it by about 78%, since each additional point of R-value delivers a shrinking marginal benefit once you're already well-insulated.
Quick reference: A 2,000 sq ft area upgraded from R-11 to R-49, in a climate with 4,500 heating degree days, on an 80%-efficient furnace burning $1.20/therm gas, saves about 190 therms and $228 per year — a 78% reduction in heat loss through that surface.
This calculator is the physics-based companion to this site's bill-based home insulation savings calculator, which estimates savings directly from your actual utility bill using a simpler attic-loss-share assumption. Use this one when you know (or can estimate) your actual R-values and want the underlying heat-loss math, not just a bill-percentage estimate.