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Calculating the U-value to DIN EN ISO 6946: method and sources of error

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The U-value is the reciprocal of the total thermal resistance. The method is set out in DIN EN ISO 6946, 2018-03 edition, “Bauteile – Wärmedurchlasswiderstand und Wärmedurchgangskoeffizient – Berechnungsverfahren” (Building components and building elements – Thermal resistance and thermal transmittance – Calculation methods). The edition replaces that of 2008-04 and is corrected by Corrigendum 1 of 2023-04. The calculation itself is short; the errors arise in the input values, and they weigh particularly heavily in existing buildings, because the build-up and condition of the layers are rarely documented there.

The calculation in three steps

  1. Layer resistance: R = d / λ, that is the layer thickness in metres divided by the thermal conductivity in W/(m·K).
  2. Total resistance: RT = Rsi + R1 + R2 + … + Rse, that is the sum of the layer resistances plus the two surface resistances inside and outside.
  3. U-value: U = 1 / RT in W/(m²·K).

The surface resistances are not calculated; they are taken from the tables of the standard. They differ only by the orientation of the building element and cannot be influenced by the choice of material or the thickness of the element. For an external wall, the Fraunhofer IBP (Fraunhofer Institute for Building Physics) in a 2022 publication calculates with Rsi = 0.13 and Rse = 0.04 m²K/W and calls this the currently usual calculation.

Worked example: single-leaf wall, uninsulated and insulated

The thermal conductivities are assumptions for this example; in a project, the design values from the standard or product documents apply.

Layer d [m] λ [W/(m·K)] R [m²K/W]
Surface resistance inside (Rsi) – – 0.13
Internal plaster 0.015 0.70 0.021
Masonry 0.365 0.40 0.913
External render 0.020 0.87 0.023
Surface resistance outside (Rse) – – 0.04
Sum RT 1.127

From this follows U = 1 / 1.127 ≈ 0.89 W/(m²·K). If 12 cm of insulation with λ = 0.035 W/(m·K) is added on the outside, the resistance rises by 0.12 / 0.035 = 3.43 m²K/W. Then RT = 4.555 m²K/W and U ≈ 0.22 W/(m²·K).

Variant with a ventilated façade: the cladding stands behind a strongly ventilated air layer and is disregarded, the external render is omitted, and for Rse the value of Rsi applies. Then RT = 0.13 + 0.021 + 0.913 + 3.429 + 0.13 = 4.623 m²K/W and U ≈ 0.22 W/(m²·K). The result is almost the same here because the insulation dominates the build-up; with thin or no insulation the difference would be greater.

What the figure means: the U-value describes the heat flow that passes through the building element per square metre of element area and per kelvin of temperature difference. With 100 m² of wall area and a 20 K difference, that would be around 1,770 W in the uninsulated example and around 440 W in the insulated one. This is a snapshot under steady-state assumptions and not an annual balance.

Conversely, the insulation thickness needed for a target value can be determined: d = (1/Unew − 1/Uexisting) · λ. For Unew = 0.24 W/(m²·K) this gives (4.167 − 1.127) · 0.035 ≈ 0.106 m. The formula assumes homogeneous layers; corrections for fixings and other influences are added.

The value 0.24 is the maximum value that Annex 7 of the Building Modernisation Act (Gebäudemodernisierungsgesetz, GModG) gives for external walls of residential buildings when insulation layers are applied to the outside of an existing wall. When this requirement applies and which exceptions exist is explained in the article GEG is now GModG.

Typical sources of error

  • Wrong internal surface resistance: The mould proof uses Rsi = 0.25 instead of 0.13 m²K/W at thermal bridges. Anyone who carries this value over into the U-value calculation underestimates the U-value: in the example 0.80 instead of 0.89 W/(m²·K) uninsulated, 0.21 instead of 0.22 insulated. Why the mould proof uses the higher value is explained in the article on the mould criterion.
  • Ventilated façade: With a strongly ventilated air layer, the resistance of the air layer and of all layers outside it is omitted; for Rse the value of Rsi of the same building element applies. This is how the BAFA list of technical FAQs on the BEG (version 5.0, 03/2023) summarises it. The current version is always the one that counts.
  • Nominal value instead of design value: The method is based on design values of thermal conductivity. Thermal conductivity also depends on moisture; an existing building material that has become damp has a different value from the table value.
  • Inhomogeneous layers: Timber rafters next to an insulated bay or metal fixings require the approximation method of the standard. The correction in Annex F covers metal fixings; other cases in which metal bridges the insulation lie outside the standard.
  • Wrong scope: Windows, curtain walls and building elements with heat exchange with the ground are excluded.
  • Expecting thermal bridges in the U-value: They are not included. In the balance they are taken into account through an allowance on the entire envelope area.
  • Units: Entering thicknesses in centimetres or millimetres with thermal conductivity in W/(m·K): the error is a factor of 100 or 1,000 and is noticed only if the result is implausible.
  • Rounding too early: Round layer resistances only at the end. Anyone who rounds every intermediate value to one decimal place distorts precisely the uninsulated wall: in the example the U-value would then be 1.0 instead of 0.89 W/(m²·K).

Existing buildings: the build-up is the biggest unknown

With existing walls, the calculation formula is rarely the problem; the question is what is in the wall. In § 38(4), the Building Modernisation Act allows, for the energy assessment of existing buildings, the use of established empirical values for building elements of comparable age classes where characteristic values are missing. This is a simplification for the balance, not a substitute for knowledge of layer thicknesses and condition.

A worked example like the one above shows the method but does not replace a proof. Its informative value is only as great as the assumptions about the thickness, thermal conductivity and moisture condition of the layers present.

Sources

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