R-value (insulation) of a multi-layered installation

Description

Formula first contributed by:
zfyl

The R-value is a measure of thermal resistance, or ability of heat to transfer from hot to cold, through materials (such as insulation) and assemblies of materials (such as walls and floors). The higher the R-value, the more a material prevents heat transfer. R-value depends on materials’ resistance to heat conduction, as well as the thickness and (for loose or porous material) any heat losses due to convection and radiative heat transfer. However it does not account for the radiative or convective properties of the material’s surface, which may be an important factor for some applications. R varies with temperature but in construction it is common to treat it as being constant for a given material (or assembly). It is closely related to the thermal transmittance (U-value) of a material or assembly, but is easier to manipulate in some calculations since it can be simply added for materials and assemblies that are arranged in layers, or scaled proportionately if the thickness of a material changes. R-values expressed in United States customary units are about 5.68 times larger than those expressed in metric (SI) units

R is expressed as the thickness of the material normalized to the thermal conductivity, and under uniform conditions it is the ratio of the temperature difference across an insulator and the Heat Flux Density (heat transfer per unit time per unit area through it. The unit thermal conductance of a material is the reciprocal of the unit thermal resistance. This can also be called the unit surface conductance.

In calculating the R-value of a multi-layered installation, the R-values of the individual layers are added like in the shown formula.

To account for other components in a wall such as framing, first calculate the U-value (=1/R-value) of each component, then the area-weighted average U-value. The average R-value will be 1/(this average U-value). For example, if 10% of the area is 4 inches of softwood (R-value 5.6) and 90% is 2 inches of silica aerogel (R-value 20), the area-weighted U-value is 0.1/5.6 + 0.9/20 = 0.0629 and the weighted R-value is 1/0.0629 = 15.9.