Thermal Transmittance (U-value)

Adds up the thermal resistance of each layer of a wall from its thickness and conductivity, and takes the reciprocal to give the U-value. A smaller U-value means better insulation and less heat escaping.

The insulating performance of a wall is expressed as its thermal transmittance, or U-value: the watts lost per square metre for each degree of temperature difference. Smaller is better.

It is found in two steps. The thermal resistance of each layer is added up, and the total is inverted.

R = R_i + \sum \dfrac{d}{\lambda} + R_o \qquad U = \dfrac{1}{R}

$R$ is the total thermal resistance
$d$ is the thickness of a layer and $\lambda$ its conductivity
$R_i$ and $R_o$ are the surface resistances inside and outside
$U$ is the thermal transmittance

A layer's resistance being thickness divided by conductivity is intuitive: thicker resists more, and a material that conducts well resists less.

The surfaces resist too. A thin film of still air clings to each face and insulates in its own right. Indoors, with little air movement, 0.11 is used; outdoors, where wind strips the film away, 0.04.

Example

The default input is a wall built up from the inside as 12 mm of plasterboard, 100 mm of glass wool and 12 mm of plywood.

Adding the resistances gives 0.15 for the surfaces, 0.055 for the plasterboard, 2.632 for the glass wool and 0.075 for the plywood, a total of about 2.911. The U-value is its reciprocal, about 0.3435.

Over 20 square metres with a 20 degree difference, the heat loss is about 137 W.

The insulation does almost all of it

Look at the breakdown: the 100 mm of glass wool alone contributes 2.632, ninety percent of the total. The plasterboard and plywood barely register for their thickness.

Strip the insulation out and leave only the 12 mm of plywood, and the U-value leaps to 4.44 — about thirteen times the original 0.3435, meaning thirteen times the heat through the same wall. Whether insulation is present essentially determines the performance.

Points to watch

Posts and studs run right through the wall and conduct better than the insulation around them. These thermal bridges make a real wall perform worse than this calculation suggests.

Windows have U-values of 2 to 6, far above any wall. Losing nearly ten times as much per square metre, they dominate a building's heat loss, and thickening the walls alone achieves less than it seems.