Multilayer Wall U-Value

Combine three material layers and surface resistances into a plane-wall U-value and heat flow.

How this calculation works

A wall's U-value expresses how much heat crosses each square metre for each degree of temperature difference. Enter each material thickness in millimetres and its conductivity in W/(m·K), then supply the inside and outside surface resistances. A zero thickness omits a layer, although its conductivity must remain positive. The calculator converts thicknesses to metres, adds the series resistances and takes the reciprocal to obtain U. Wall area affects total heat flow but does not change the U-value or flux. Positive results mean heat travels from the inside toward the outside; a warmer exterior reverses the sign. This is a steady, one-dimensional layer model. Thermal bridges, air leakage, moisture and contact resistance are excluded, so the result is not a certified whole-building value.

Inputs and units

Layer 1 thickness (mm)
Layer 1 conductivity (W/(m·K))
Layer 2 thickness (mm)
Layer 2 conductivity (W/(m·K))
Layer 3 thickness (mm): Use zero to omit this layer
Layer 3 conductivity (W/(m·K))
Inside surface resistance (m²·K/W)
Outside surface resistance (m²·K/W)
Wall area (m²)
Inside air temperature (°C): Must be above absolute zero
Outside air temperature (°C): Must be above absolute zero

Method and formula

R = Rinside + Σ(thickness/1000/conductivity) + Routside; U = 1/R; q = U(Tinside − Toutside); Q = qA/1000 kW.

Worked example

Example inputs

Layer 1 thickness: 100 mm
Layer 1 conductivity: 0.04 W/(m·K)
Layer 2 thickness: 200 mm
Layer 2 conductivity: 1 W/(m·K)
Layer 3 thickness: 10 mm
Layer 3 conductivity: 0.2 W/(m·K)
Inside surface resistance: 0.13 m²·K/W
Outside surface resistance: 0.04 m²·K/W
Wall area: 100 m²
Inside air temperature: 20 °C
Outside air temperature: 0 °C

Calculation steps

Convert the layer thicknesses: 100/1000 = 0.1 m, 200/1000 = 0.2 m and 10/1000 = 0.01 m.
Add material and surface resistances: R = 0.13 + 0.1/0.04 + 0.2/1 + 0.01/0.2 + 0.04 = 2.92 m²·K/W.
Take the reciprocal: U = 1/2.92 = 0.342466 W/(m²·K), displayed as 0.3425 W/(m²·K).
Apply the temperature difference: q = (1/2.92) × (20 − 0) = 6.849315 W/m².
Multiply by the 100 m² wall area and convert watts to kilowatts: Q = 6.849315 × 100/1000 = 0.684932 kW, flowing outward.

Example results

Total area-normalized resistance: 2.92 m²·K/W
U-value: 0.3424657534 W/(m²·K)
Signed heat flux, inside to outside: 6.849315068 W/m²
Signed wall heat flow: 0.6849315068 kW

Assumptions

Steady one-dimensional heat transfer; all layers cover the same area
Conductivities and surface resistances are supplied by the user

Limitations

Excludes thermal bridges, air leakage, moisture and contact resistance
Not a certified whole-building or code-compliance U-value

Sources

U.S. DOE Fundamentals Handbook: Heat Transfer, Volume 2: HT-02 pp. 7–10, series thermal resistance; pp. 20–21, combined heat transfer