Thermal Resistance in Series

Resistances add; conductances do not

Heat passing through a wall crosses each layer in turn, and each layer resists it. Because they are in series, their resistances add directly — plasterboard plus insulation plus sheathing plus cladding, plus the thin but real resistance of the still air films on each face.

The U-value is the reciprocal of that total. It is a conductance, and conductances in series emphatically do not add: two layers of U = 0.5 do not make U = 1.0, they make U = 0.25. Adding U-values is a common and large error, and it always errs toward claiming better performance than exists.

Run backwards, the same sum sizes the insulation. The total resistance a target asks for is 1 ÷ U; take away the surface resistances and every other layer, and the remainder times the insulation's conductivity is its thickness. Which way the heat flows sets the inside film — 0.10 m²K/W (0.57 hr·ft²·°F/BTU) under a ceiling, 0.13 (0.74) on a wall, 0.17 (0.97) on a floor — and a well-ventilated cavity counts for nothing, taking every layer outside it with it.

Thermal bridging: the parallel path

The series model assumes heat crosses uniform layers. A framed wall is not uniform: at every stud there is a parallel path of much lower resistance, and heat preferentially takes it. A wall with insulation rated R-19 between studs does not perform at R-19, because the studs occupy a meaningful fraction of the area and conduct several times better.

This is why continuous insulation outboard of the framing is disproportionately effective. It is the only layer with no bridge through it, so it raises the whole assembly rather than only the cavity.

Where a bridge is a line or a point rather than a share of the area — a window reveal, a slab edge, a floor junction, a cladding bracket — it is counted by its own transmittance instead: ψ for each metre of junction and χ for each bracket, from a model to BS EN ISO 10211, added to the plane elements' heat loss as Σψ·L + Σχ. Spread over the element's area, that sum is what the bridges add to its U-value.

And then there is air

R-value describes conduction. It says nothing about air moving through or around the insulation, and air movement can dominate. A well-insulated wall with an interrupted air barrier can underperform a modest wall that is properly sealed, because convection carries heat past the insulation rather than through it.

The practical consequence is that measured performance is found with a blower door, not with a specification. Several calculators on this site size the air-sealing side of that pair for exactly this reason.

Adding to the best layer is worth less than removing the worst

Because resistances add, the total is dominated by whichever layer contributes most — and the return on adding to that layer diminishes steadily, because each increment is a smaller fraction of a growing total.

Doubling the insulation in an already well-insulated element makes a modest difference to the assembly. Adding the FIRST equivalent thickness to an element that had none makes an enormous one. This is the whole economic case for treating the worst element in a building before improving the best, and it is why loft insulation and draught sealing keep appearing at the top of measure lists while marginal upgrades to already-good walls do not.

It also explains a result that looks wrong on paper: two assemblies with the same total resistance perform the same in steady state regardless of how the resistance is distributed between their layers. Where the layers sit changes the temperature profile through the element — and therefore where condensation forms — but not the heat lost.

A parallel path does not add; it short-circuits

Series arithmetic assumes the heat has one route. Where a conductive element passes through the insulation — a stud, a joist, a lintel, a balcony slab, a fixing — it provides a parallel route with far less resistance, and heat takes it.

The effect is out of proportion to the area involved. A steel stud conducts on the order of a thousand times better than the timber it replaced, so a lightweight steel-framed wall can deliver a fraction of the resistance its material layers suggest even though the steel occupies a small percentage of the elevation. This is why insulation continuous OVER the framing outperforms a thicker layer between it, and why the effective resistance of a framed wall has to be computed with the framing fraction rather than at its centre.

The consequences are not only thermal. A bridge is a cold spot on the interior surface, so it is where condensation and mould appear first, and it is where a thermal image of a building shows the frame through the finish. A wall meeting its calculated performance and growing mould at every stud is behaving exactly as its parallel paths dictate.

R-values are measured under conditions your building is not in

A declared resistance is a laboratory measurement at a stated MEAN TEMPERATURE, usually around ten or twenty-four degrees depending on the standard, and materials do not all hold that value elsewhere.

Some closed-cell foams perform worse as they get colder, which means their resistance is lowest exactly when it is needed most. Others change over time as their blowing agent diffuses out and is replaced by air — which is why aged or long-term values are declared separately from initial ones, and why using an initial figure for a lifetime calculation overstates the result.

Installation moves the number as much as chemistry does. Batt insulation compressed into a space thinner than its nominal thickness loses resistance in proportion; blown insulation settles over years and loses depth; a gap left at the edge of a batt creates a convection loop that carries heat past the insulation rather than through it. Installed performance is a workmanship property, and it is the reason inspection grades exist.

Where steady-state resistance is the wrong model entirely

This whole calculation describes a steady state: constant temperatures inside and out, and heat flowing at a constant rate. Real weather does neither, and for heavyweight construction the difference matters.

A massive element absorbs heat, holds it and releases it later, so its response to a daily temperature swing is both delayed and reduced. Two walls with identical resistance and very different mass behave differently in a hot climate with cool nights — one follows the outside temperature, the other lags it by hours — and neither their resistance nor their transmittance captures that.

The properties that do are dynamic ones: decrement factor for how much of the swing gets through, and time lag for how long it takes. They matter for summer comfort and for buildings that are intermittently heated, and they are outside the arithmetic on this page. Where a building is continuously conditioned in a cold climate, steady-state resistance remains the right model — which is most of what these calculators are used for, and the pages say so.

The inside surface sits where the chain puts it

The same chain sets how warm the inside surface stays. The internal surface film takes its share of the whole temperature difference — Rsi as a fraction of the total resistance, which is U × Rsi — so the surface sits the fraction 1 − U·Rsi of the way from the outdoor temperature to the indoor one. That fraction is the temperature factor, fRsi, and it describes the construction rather than the weather.

BS EN ISO 13788 assesses mould and condensation on opaque surfaces with a deliberately larger film, 0.25 m²K/W (1.42 hr·ft²·°F/BTU), to stand for corners, furniture and curtains, and keeps the ordinary values for windows and doors. BRE IP 1/06 sets the factor a surface should reach by the humidity of the building's use: 0.75 for dwellings, residential buildings and schools, less for drier buildings and more for wetter ones. At a junction the heat flow is two- or three-dimensional, and the factor comes from a model or a measured surface temperature rather than from a U-value.