01What a U-value is
One number for the whole roof.
A U-value is the rate of heat loss through one square metre of a building element, per kelvin of temperature difference, in W/m²K. It describes the roof as built, every layer together, not any one product. The lower the number, the less heat the roof loses.
The roof worked through below comes out at 0.14 W/m²K. Every step of how that number was reached is shown.
For engineers: how the figure is built
Four steps, from the material to the roof.
01 · The materialλW/mKThermal conductivityHow readily a material lets heat through. A property of the material alone. Closed-cell spray foam: 0.027. Mineral wool: 0.042. Softwood: 0.13.
02 · The layerR = d ÷ λm²K/WThermal resistanceA layer resists heat in proportion to its thickness d and in inverse proportion to its λ. Thicker, or lower λ, means more resistance.
03 · The build-upRT = ΣR + Rsi + Rsem²K/WTotal resistanceEvery layer's resistance added up, plus the thin films of still air on the inside and outside surfaces (Rsi and Rse).
04 · The roofU = 1 ÷ RTW/m²KThe U-valueThe reciprocal of the total resistance. Lower is better. Approved Document L sets the target it is checked against.
Why the roof's U-value is never the foam's λ.
Timber and fixings cross the insulation, and heat takes the easier path through them. BS EN ISO 6946 combines the two paths (the clear path through the insulation and the bridged path through the timber, weighted by the area of each) into one total resistance for the roof. That is why a roof insulated with a 0.027 material does not perform at 0.027, and why the figure has to be calculated for each roof rather than read off a datasheet.