U-Factor from Total R-Value (U = 1/R)

Insulation is sold by resistance and windows are sold by conductance, so the same envelope gets described two ways: R-20 is U-0.05 in imperial units, and RSI 3.52 is U = 0.284 W/(m²·K) in metric. They are reciprocals of each other within one unit system — and note that the conversion between systems is the same 5.678 factor running the other way, since U in W/(m²·K) equals 5.678 divided by the imperial R. Codes mix the two deliberately: opaque assemblies get a prescriptive R, fenestration gets a U-factor on the NFRC label, and the compliance path adds them up as UA products.

Here is the mistake that costs real money, and it appears in spreadsheets everywhere: U-factors add, R-values add, but never in the same direction. R-values add along the path heat takes, in series through the layers. U-factors add across the wall, area-weighted, when parallel paths share the same ΔT — which is why a wall and its windows combine as ΣUA and not as an average R. Averaging R-values across an elevation of wall and glass gives a wall that looks far better than it is: 90% at R-20 and 10% at R-3 does not average to R-18.3; it averages to U = 0.9 × 0.05 + 0.1 × 0.333 = 0.0783, which is R-12.8. The glass ate a third of the wall's performance, and only the U-side arithmetic showed it.