Inputs
Direction of heat flow, what the outer side faces, the material layers with thickness and thermal conductivity λ, the component area and the indoor and outdoor temperatures.
Fluid & thermodynamics · ISO 6946
U-value of a building component
Calculate the U-value of a wall, ceiling or roof from its layer build-up to ISO 6946: RT = Rsi + Σ(d/λ) + Rse and U = 1/RT. Besides the U-value the calculator returns the resistance of each individual layer, the heat flow, and the inside surface temperature and temperature factor fRsi from which the mould risk can be read.
One-dimensional steady-state layer model for the undisturbed component. Thermal bridges at corners, reveals and junctions are colder and are assessed separately; moisture content, air layers, penetrating fasteners and the ISO 6946 correction terms are not included.
UISO 6946
02
U-value and surface temperature
Set the layers and calculate.
Inputs and method
U-value to ISO 6946
Calculate the thermal transmittance of a layered component and the inside surface temperature that governs the mould risk.
Calculation
The layers are thermally in series, so their resistances add: RT = Rsi + Σ(d/λ) + Rse with the ISO 6946 surface resistances (inside 0.10 upward, 0.13 horizontal, 0.17 downward; outside 0.04 against outdoor air). The U-value is the reciprocal, U = 1/RT. The inside surface temperature follows from θsi = θi − U·Rsi·(θi−θe), and the temperature factor from it as fRsi = 1 − U·Rsi.
Example
An uninsulated 240 mm solid brick wall with λ = 0.79 W/(m·K) has R = 0.304, RT = 0.474 and therefore U = 2.11 W/(m²K); at 20 °C inside and −5 °C outside its surface sits at 13.1 °C and fRsi at 0.73 – just above the mould limit.
Sources and limits: ISO 6946, series connection of the resistances with the table 1 surface resistances; the limit fRsi ≥ 0.70 corresponds at 20 °C/−5 °C to a surface temperature of 12.5 °C; the 12.6 °C also quoted corresponds exactly to fRsi = 0.704. One-dimensional and steady-state; thermal bridges, moisture, air layers, penetrating fasteners and the standard's correction terms are not included.
U-value to ISO 6946 in detail
Calculate the thermal transmittance of a layered component and the inside surface temperature that governs the mould risk.
What is the U-value?
The U-value states how much heat passes through per square metre of component and per kelvin of temperature difference. It arises from the series connection of all resistances: the two surface resistances and the d/λ resistances of the individual layers. Because resistances in series add while the U-value is their reciprocal, it is the thickest insulating layer, not the weakest one, that dominates the result.
Formula and variables
U = 1 / (Rsi + Σ(d/λ) + Rse)
Rsi: 0.10 upward · 0.13 horizontal · 0.17 downward (m²K/W)Rse: 0.04 against outdoor air; against an unheated space Rse = Rsiθsi = θi − U · Rsi · (θi − θe)fRsi = (θsi − θe)/(θi − θe) = 1 − U · Rsi
| Symbol / input | Meaning |
|---|---|
| d, λ | Thickness and design thermal conductivity of each layer. |
| Rsi, Rse | Inside and outside surface resistances per ISO 6946 table 1. |
| RT, U | Total resistance and its reciprocal, the thermal transmittance. |
| θsi, fRsi | Inside surface temperature and the temperature-independent factor formed from it. |
Choose the inputs correctly
Direction of heat flow, what the outer side faces, the material layers with thickness and thermal conductivity λ, the component area and the indoor and outdoor temperatures.
How to use the calculator
Choose the direction of heat flow – horizontal for walls, upward for ceilings and roofs, downward for floors – and state whether the outer side faces outdoor air or an unheated space. Then enter each material layer with its thickness and thermal conductivity λ, from inside to outside. Add the component area and the two air temperatures; the calculator returns the U-value, the resistance of each layer, the heat flow and the surface temperature.
Worked example
An uninsulated 240 mm solid brick wall with λ = 0.79 W/(m·K) has R = 0.304, RT = 0.474 and therefore U = 2.11 W/(m²K); at 20 °C inside and −5 °C outside its surface sits at 13.1 °C and fRsi at 0.73 – just above the mould limit.
Which value decides what?
The U-value alone says what the component costs in energy. Whether it is also sound in building-physics terms is decided by the surface temperature: it follows directly from U and Rsi and is the quantity that governs mould risk and comfort. The resistance per layer additionally shows which layer really carries the insulating effect – often more than 90 % of the total resistance sits in a single layer.
Thicknesses in millimetres, λ in W/(m·K), resistances in m²K/W, U in W/(m²·K), temperatures in degrees Celsius. The R-value on an insulation datasheet corresponds to the layer resistance reported here, not to the total resistance RT.
Typical applications
Assessing existing wall, roof and ceiling build-ups before a refurbishment, comparing insulation options and thicknesses, estimating the heat loss of individual components, and – via the surface temperature – judging whether a wall will stay free of mould after the work.
Assumptions, limits and common mistakes
ISO 6946, series connection of the resistances with the table 1 surface resistances; the limit fRsi ≥ 0.70 corresponds at 20 °C/−5 °C to a surface temperature of 12.5 °C; the 12.6 °C also quoted corresponds exactly to fRsi = 0.704. One-dimensional and steady-state; thermal bridges, moisture, air layers, penetrating fasteners and the standard's correction terms are not included.
Common mistake: Do not enter the surface resistances as a layer of their own – the calculator already inserts them from the heat flow direction. Do not use a headline conductivity from a brochure but the design value from the datasheet or approval, which includes moisture and ageing allowances. And keep the reciprocal in mind: doubling the insulation thickness does not halve the U-value, it only doubles the resistance contributed by that one layer.
Frequently asked questions
Why does Rsi depend on the direction of heat flow?
Because part of the surface heat transfer is convective and warm air rises. With upward heat flow this buoyant flow assists the transfer, so the resistance is smallest at 0.10 m²K/W; with downward heat flow it works against it and the resistance rises to 0.17.
Why is Rse outside so much smaller than Rsi inside?
Because there is wind outside. Forced convection improves the surface transfer considerably, so the standard uses only 0.04 m²K/W against outdoor air. If the component faces an unheated space with no wind, the indoor value applies on both sides.
What does the temperature factor fRsi tell me?
It is the surface temperature normalised to the temperature difference and therefore independent of the temperatures chosen. At 20 °C inside and −5 °C outside, 0.70 means a surface temperature of 12.5 °C; the 12.6 °C quoted as the mould limit – the temperature at which the relative humidity right at the wall reaches the critical 80 % range – corresponds exactly to 0.704. The 0.70 requirement is the rounded form of it.
Is a good U-value enough against mould?
For the open area yes, for the edges not automatically. This calculator describes the undisturbed, one-dimensional component. Corners, window reveals, ceiling junctions and penetrating elements are thermal bridges and therefore colder than the open area; they are assessed separately and with a less favourable inside surface resistance.
Why does the second half of the insulation achieve so little?
Because the U-value is the reciprocal of a sum. The first centimetres of insulation add resistance to a small starting value and cut U sharply; once 4 m²K/W is already present, the same thickness barely shifts the sum in relative terms. That is why the first layer of insulation always pays back the most.