A U-value is the rate at which heat passes through one square metre of a building element for each degree of temperature difference across it, in W/m²K. A lower figure is better. For a wall, floor or roof the calculation is made to BS EN ISO 6946; for a ground floor or a heated basement, where the ground is part of the construction, to BS EN ISO 13370. A specification that states a U-value should be able to show the working to one of those standards.
The layer-by-layer sum, and where it stops being enough
For an element of uniform layers, the calculation is a sum. Each layer contributes a thermal resistance, its thickness divided by its conductivity. Add the surface resistances inside and out, add the layers, and the U-value is one over the total. A cavity wall with an unbroken 90mm of insulation board in the cavity is close to this case, and the sum gets close to the answer.
Most elements are not uniform. A timber frame wall is insulation between studs; a pitched roof is insulation between rafters; a suspended floor is insulation between joists. Timber conducts heat several times faster than a high-performance board, and at 400mm centres the studs or rafters are roughly an eighth of the area. Heat takes both paths. A sum through the insulation alone ignores the timber and gives a figure that is simply wrong.
The combined method
BS EN ISO 6946 handles a bridged layer by calculating two limits and taking their mean. The upper limit treats the element as parallel paths through the insulated part and through the bridging part, each with its own resistance. The lower limit treats each layer as a single averaged layer. The true resistance lies between them, and the standard takes the average of the two. The working a specification prints shows both limits and the mean, so that a plan checker can see the bridging fraction and the conductivities that went into it rather than take the result on trust.
The example that caught us. 100mm of a 0.019 W/mK board between 47 × 150mm rafters at 400mm centres, with 37.5mm of insulated plasterboard below, was carried in our library at 0.15 W/m²K, which is the target for a new roof in an existing dwelling. Calculated by the combined method it achieves 0.20. The rafters roughly halve the effective resistance of the board between them. The clause now specifies the thicker under-rafter board that reaches the target, and the working is printed beside it.
The same thing was true of every framed wall in the library, where the studs were bridging 140mm of board. Seven figures were corrected the day the calculation was run. The lesson is not that the figures were careless: at the level of a layer-by-layer sum every one of them was right. It is that a framed or rafter-level U-value must never be stated without running it through the combined method.
The Annex F corrections
The calculated figure is then corrected for two things a clean sum leaves out. Air gaps around and between boards, which depend on how well the boards are fitted: the standard defines levels, and a full-fill cavity board fitted to the manufacturer's instructions typically warrants a correction of around 0.01 W/m²K. Wall ties passing through cavity insulation, which each carry heat across it; the correction depends on their number, cross-section and conductivity, and stainless steel ties at the usual centres add a small but real amount. A specification that prints its working should print these corrections as lines of their own.
Ground floors and basements
A ground floor loses heat to the ground, and the ground is not a layer of known thickness. BS EN ISO 13370 accounts for it through the floor's perimeter-to-area ratio: a small floor with three exposed edges loses proportionally more than a large one with one. So a floor build-up does not have one U-value; it has one for each plan. An extension floor that meets 0.18 W/m²K at a ratio of 0.5 may not at a ratio of 0.7, and a specification that offers two insulation thicknesses "depending on the ratio" has left the designer's decision to whoever orders the boards. The ratio is to be calculated for the job and one thickness stated. A heated basement wall is treated the same way, with the depth below ground entering the figure.
What the working should show
- Every layer, its thickness, its conductivity and the resistance it contributes, with the source of the conductivity: a manufacturer's declared value, a BBA certificate, or a standard tabulated figure.
- For a bridged element, the bridging fraction and the upper and lower limits, and the mean.
- The Annex F corrections as lines of their own, and the corrected U-value.
- The target the element has to beat, and whether it does.
Printed in the specification as its own section, that working is what makes a stated U-value defensible. Without it, the figure is an assertion, and a plan checker is entitled to ask for the working.