Insulation and R-values

Why it matters

Buildings account for a large share of energy use, and most of a building's heating and cooling load passes through its walls, roof and windows. Insulation is rated by R-value, and building energy codes set minimum R-values or maximum U-factors for each part of the envelope. Engineers, architects and energy auditors compare wall assemblies by adding up thermal resistances, exactly the way you add resistors in series in an electric circuit.

Thermal resistance

Rewrite Fourier's law per unit area as "temperature difference divided by resistance":

q/A = ΔT / R

• For a solid layer, R = L / k (thickness divided by conductivity).
• For a surface air film (convection), R = 1 / h.
• In SI, R is in m²·K/W. In the US building trade, R is in ft²·°F·h/Btu. To convert: R_US = 5.678 × R_SI. A product sold as "R-13" in the US is about R 2.3 in SI units.

Layers in series add:

R_total = R_inside_film + R_1 + R_2 + ... + R_outside_film
U       = 1 / R_total            (W/(m²·K))
q       = U · A · ΔT             (W)

The U-factor (or U-value) is the inverse: lower U means better insulation. Windows are usually rated by U-factor, insulation by R-value.

Worked example: two wall assemblies

Compare a 10 m² wall section with and without cavity insulation, for 20 °C inside and 0 °C outside. Typical surface film resistances are about 0.12 m²·K/W inside and 0.03 outside.

Wall A, insulated:

inside air film                         0.120
12.5 mm gypsum board (k = 0.17)         0.0125 / 0.17 = 0.074
90 mm mineral wool (k = 0.04)           0.090 / 0.04  = 2.250
11 mm OSB sheathing (k = 0.13)          0.011 / 0.13  = 0.085
outside air film                        0.030
R_total ≈ 2.56 m²·K/W     U ≈ 0.391 W/(m²·K)
q = 0.391 × 10 × 20 ≈ 78 W

Wall B, empty cavity (an air space instead of insulation, R ≈ 0.17):

R_total ≈ 0.12 + 0.074 + 0.17 + 0.085 + 0.03 ≈ 0.48 m²·K/W
U ≈ 2.09 W/(m²·K)     q ≈ 418 W

The insulation cuts the heat loss through this section by more than 80 %. Notice that the insulation layer provides almost all of wall A's resistance: thin layers of board and the air films matter much less.

Real walls are not uniform

The example treats the wall as continuous layers. Real walls have studs, which conduct heat far better than mineral wool and form thermal bridges. A wood stud wall's whole-wall R can be 10–20 % lower than the centre-of-cavity value, and steel studs are far worse. Engineers use parallel-path or more detailed methods (from ASHRAE handbooks) to account for framing, and they also check for moisture: a wall that is warm on one side and cold on the other can condense water inside if the vapour control is wrong.

Parallel paths in one step

When heat can flow through two different paths side by side (for example studs and insulation), add their conductances weighted by area fraction:

U_wall = f_stud · U_stud_path + f_cavity · U_cavity_path

With 15 % studs, this is often enough for an estimate; detailed design uses software and code-approved values.

Common mistakes

• Adding U-values in series. Add R-values in series; add U × area in parallel.
• Mixing SI and US R-values. Always state which units you mean.
• Forgetting air films. They are small for insulated walls but significant for single glazing.
• Assuming more insulation always pays. Doubling R halves the loss through that layer, so each extra centimetre saves less than the one before.

Codes and professionals

Building energy codes (for example the IECC in many US states, or national codes elsewhere) set the required R-values and U-factors by climate zone. Local building officials enforce them, and envelope designs for real projects are prepared or reviewed by licensed architects or engineers. See ASHRAE for the technical handbooks: https://www.ashrae.org/ (Checked on 2026-10-23.)

Recap

• R = L/k for a layer, R = 1/h for an air film; series resistances add.
• U = 1/R_total, q = U A ΔT.
• R_US ≈ 5.678 × R_SI.
• Thermal bridges and moisture make real walls more complex than the layer model.

Try it

On the Do tab, add thermal resistances in Python and compare the two wall assemblies.