Effective R-Value with Framing (Parallel Path)

The R-value on a batt is measured at the centre of the cavity, in a guarded hot box, with nothing in the way. The wall you actually build has a stud every 16 inches, and the stud is a parallel path: heat picks whichever route is easier, so the two paths are added as conductances, area-weighted, not as R-values. That is this equation, the parallel-path or isothermal-planes method of ASHRAE Fundamentals. A 2×6 wall with R-19 batts, 6.875 of framing R through 5.5 inches of softwood and a 25% framing factor comes out at 1/(0.25/6.875 + 0.75/19) = R-13.2 — a wall sold as R-19 delivering R-13, and every watt of the difference is real money on a fuel bill.

Framing factors are higher than anyone guesses. Counting studs alone suggests 10–15%, but once you add plates, headers, sills, rim joists, corners and the extra studs around every opening, a conventionally framed wall lands at 23–27% at 16 in on centre, and only careful advanced framing at 24 in on centre gets you near 15%. Two consequences follow. First, you cannot fix a bridged wall by adding cavity insulation — push $R_{\mathrm{cav}}$ to infinity in the equation above and $R_{\mathrm{eff}}$ still cannot exceed $R_{\mathrm{fr}}/f_{\mathrm{fr}}$, which for this wall is 27.5; the studs are a hard ceiling. Second, continuous exterior insulation is added in series with the whole assembly, so it works on both paths at once, and this is exactly why modern energy codes stopped asking for thicker batts and started demanding continuous insulation instead. Steel framing makes the point brutally: steel conducts about 400 times better than wood, so a steel-stud wall filled with R-19 can measure R-7, and the correction there needs the code's tabulated factors rather than a simple two-path split.