How do I convert a U-value to an R-value (and back)?

Invert it: R = 1/U and U = 1/R, in matching units. A wall at U = 0.357 W/m²K has a metric R of 2.80 m²K/W. To express that in American units, multiply the metric R by 5.678 — giving R-15.9 — and never invert an imperial R directly into a metric U without converting first.

Is a US R-value the same as a European R-value?

No. US R-values are in ft²·°F·h/BTU while metric R-values are in m²·K/W, and 1 m²K/W = 5.678 imperial units. An American R-13 batt is R-2.29 metric; a European assembly at 2.80 m²K/W is about R-16 American. The physics is identical — only the unit systems differ — but an unconverted number is off by nearly a factor of six.

Why does continuous insulation count for more than cavity insulation?

Because cavity insulation is interrupted by framing, and the studs short-circuit it: softwood conducts about three times better than mineral wool, and in the worked wall 15% framing raised U from 0.357 to 0.476 W/m²K. Continuous insulation covers the studs too, so no bridge bypasses it — which is why the IECC accepts options like R-0+20ci in place of R-30 cavity fill.

What are Rsi and Rse in a U-value calculation?

They are the resistances of the thin films of still air clinging to the assembly’s two faces, standardized by ISO 6946 rather than measured per project: 0.13 m²K/W inside and 0.04 outside for walls, with the internal value shifting to 0.10 for roofs (upward heat flow) and 0.17 for floors (downward). They join the layer sum before the reciprocal is taken — U = 1/(Rsi + ΣR + Rse) — so leaving them out overstates the U-value.

U-Value vs R-Value — How Thermal Transmittance Is Calculated (ISO 6946)

Two names for the same wall

R-value and U-value describe the identical physical fact from opposite directions. R is thermal resistance — how hard it is for heat to get through a layer or an assembly — so bigger is better. U is thermal transmittance — how much heat actually flows through each unit of area per degree of temperature difference — so smaller is better. Mathematically they are reciprocals: U = 1/R. A wall with a total resistance of 2.80 gives U = 1/2.80 = 0.357, and there is no information in one number that isn’t in the other.

The two names persist because two traditions grew around them. American practice talks R: insulation products are sold by R-value, and the energy code’s prescriptive table (IECC Table R402.1.3) demands R-30 attics or R-20+5ci walls. European practice talks U: regulations cap the transmittance of the whole assembly in W/m²K, computed layer by layer under ISO 6946. An American reads a bigger number as winning; a European reads a smaller one the same way. The confusion starts when the numbers cross the Atlantic — because the units underneath them are not the same.

The unit trap: R-13 is not R-13

A US R-value is measured in ft²·°F·h/BTU; a metric (SI) R-value is in m²·K/W, and one metric unit equals 5.678 imperial units. So an American R-13 batt is R-2.29 in metric, and a European wall computed at R = 2.80 m²K/W is R-15.9 — call it R-16 — in American terms. Quote a metric resistance to a US audience without converting and the wall sounds catastrophically bad; quote an imperial R to a European and it sounds five times better than it is. Whenever an R-value looks surprising, check the units before checking the insulation.

The per-inch ratings on American products live in the same imperial world. Blown cellulose at a representative 3.5 R per inch means 3.5 imperial R per inch of depth — which is why an R-60 attic needs ceil(60/3.5) = 18 inches of it. Run that through the conversion and cellulose comes out around λ ≈ 0.041 W/m·K, right in the family of the mineral wool used in the metric example below — the materials agree; only the bookkeeping differs.

ISO 6946, layer by layer

The metric method stacks resistances like resistors in series. Each material layer contributes R = d/λ — thickness in metres divided by thermal conductivity in W/m·K — and the assembly adds two resistances that surprise newcomers: the air films clinging to each face. ISO 6946 fixes these surface resistances by direction of heat flow: Rsi = 0.13 m²K/W inside and Rse = 0.04 outside for walls, Rsi = 0.10 for roofs (heat flowing up) and Rsi = 0.17 for floors (heat flowing down). The still air at the surfaces is genuinely part of the insulation, and for a poorly insulated assembly it can be a noticeable share of the total.

This guide’s running example is a deliberately simple wall: 100 mm (about 4 inches) of mineral wool at λ = 0.038 W/m·K, alone between the air films. The insulation contributes R = 0.100/0.038 = 2.63 m²K/W; adding Rsi = 0.13 and Rse = 0.04 gives R_total = 2.80 m²K/W, and U = 1/2.80 = 0.357 W/m²K. In American units that’s an R-15.9 assembly. Every number in that chain is auditable — one division per layer, one addition, one reciprocal.

Thermal bridging: the studs tell on you

Real walls aren’t unbroken insulation — timber studs interrupt the batts, and wood conducts heat about three times better than mineral wool (λ = 0.13 W/m·K for softwood against 0.038). ISO 6946 handles this with the combined method: treat the bridged layer as two parallel heat paths and blend them by area fraction, 1/R_combined = f/R_bridge + (1−f)/R_insulation. Give the example wall studs on 15% of its area: R_bridge = 0.100/0.13 = 0.769, so 1/R_combined = 0.15/0.769 + 0.85/2.63 = 0.518, R_combined = 1.93, and the wall drops to R_total = 0.13 + 1.93 + 0.04 = 2.10 m²K/W — U = 0.476 W/m²K.

Read that again: 15% framing raised the transmittance by a third, from 0.357 to 0.476, and knocked the American rating from R-15.9 to R-11.9. This is the quiet math behind the “ci” entries in the IECC wall table — continuous insulation outside the studs blankets the bridges, which is why R-0+20ci can stand in for R-30 cavity fill. It’s also why an honest assembly calculation beats reading the batt label: the U-value calculator applies the ISO 6946 combined method automatically when you set a bridging fraction and bridge conductivity on a layer, reports the upper- and lower-bound resistances, and converts the result between metric and imperial R so both traditions get their number.

What the code tables actually ask for

The two traditions meet in compliance. The US prescriptive path is an R-value table: under the 2021 IECC, attics need R-30 in zone 1, R-49 in zones 2–3, and R-60 in zones 4–8; wood-frame walls run from R-13 in the hot zones to R-30 cavity — or combinations like R-20+5ci — in zones 4–8. But even the IECC concedes the U-side of the coin: Table R402.1.2 offers a U-factor alternative, because U is what the physics of the whole assembly, framing included, actually delivers. A wall of R-20 batts between studs does not perform at R-20, and the U-factor path is where that truth gets counted.

Converting a requirement into material is the last step. R-values of stacked layers simply add, so depth is the requirement divided by the per-inch rating, rounded up — 18 inches of 3.5-R/in cellulose for an R-60 attic, and R = r-per-inch × depth runs the other way if you’re auditing an existing layer. The unit rules stay in force to the end: add imperial R to imperial R, metric to metric, divide by 5.678 to cross over, and invert only once, at the finish line, if a U-value is what your regulation wants.

The example wall, start to finish

One wall told the whole story. As a clean 100 mm mineral wool layer: R = 2.63 from the insulation, plus the ISO 6946 air films (Rsi 0.13, Rse 0.04) for R_total = 2.80 m²K/W, U = 0.357 W/m²K, R-15.9 imperial. With softwood studs bridging 15% of the layer: the combined method blends λ 0.038 against λ 0.13 into R_combined = 1.93, dragging the assembly to U = 0.476 — one-third more heat loss from framing alone, and the entire argument for continuous insulation in one number. R measures the fight against heat flow; U measures the heat that gets through anyway; 5.678 separates the American and metric dialects; and the assembly, not the batt label, is what your building actually does.