# How to calculate the thermal transmittance

## Thermal insulation calculation and U-value - Made understandable for the client

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If you want to carry out thermal insulation properly, you have to work your way through a mountain of terms and formulas. Without a degree in natural sciences, this can hardly be done. We therefore try to reduce everything to the essentials so that even the layman can carry out a thermal insulation calculation.

The terms that keep appearing in connection with thermal insulation are thermal conductivity, thermal resistance, heat transfer coefficient, heat transfer resistance and heat transfer coefficient. As you can see, you can work up a sweat! But don't panic, you don't have to memorize everything you have just read. For the most part, we spare ourselves precise definitions and formulas at this point, because these are at most irritating to the layperson.

The most important key figure in connection with the thermal protection of an individual component is U-value (heat transfer coefficient, heat permeability, U-value used to be the k-value). It indicates the amount of heat (in kWh) transported through a component area of ​​100 m² in one hour if there is a temperature difference of 10 degrees between inside and outside. The smaller the value, the better. (Please do not report physicists and engineers, we know that the exact definition is slightly different).

To give you a feeling for the difference between well and poorly insulated components, the following table lists reference values ​​for the U-value of various components. The values ​​listed under the heading "very good" are the values ​​of a low-energy house and have therefore been the standard since the EnEV (Energy Saving Ordinance) came into force in February 2002.

 U-value Component very bad bad medium Well very good top, roof ≥ 1,00 0,60 0,30 0,22 ≤ 0,15 example None ormaximum 4 cm Between-raftersinsulation 6 to 10 cmBetween-raftersinsulation 12 to 16 cmBetween-raftersinsulationor 9 cm PUROver-rafterinsulation 18 to 20 cmBetween-raftersinsulationor 12 cm PURRecessinsulation 27 to 30 cmBetween-raftersinsulationor 18 cm PUROver-rafterinsulation Solid wall ≥1,50 0,80 0,40 0,30 ≤ 0,20 example 24 cmSolid brickmasonrywith plaster 36.5 cmSlightly highperforated brickmasonrywith plaster 36.5 cmAerated concrete 600 [kg / m³] with plaster,inside gypsum plaster 36.5 cmAerated concrete 400 [kg / m³] with plaster,inside gypsum plaster 36.5 cmBrick wallwork with13 cm PURinsulation window 5,20 3,50 1,80 1,40 ≤ 1,20 example Single-discGlass Doubleglazing Heat protection-glazing ModernHeat protection-glazing Low-energy housewindow

Walls of prefabricated houses were not mentioned in the above list, but they have very interesting U-values. Outer walls of the latest generation of prefabricated houses in timber frame or timber frame construction come with a thickness of only 25 cm - 27 cm and a U-value of 0.17. For comparison: A 36.5 cm solid wall made of brick masonry with an additional 13 cm PUR insulation comes to a comparable U-value, although the wall is about twice as thick.

The prefabricated house manufacturers argue quite correctly that with a floor space of 9 x 12 m for an average single-storey house, the living space with this wall structure is around 9 m² larger than with the solid masonry plus insulation variant.

### This is what the Energy Saving Ordinance says about the U-value

In the case of a new building or changes to existing buildings, minimum requirements for the U-value of the component must be met. There is no general obligation for home owners to retrofit. The top floor slabs are an exception. Owners of residential buildings must insulate non-accessible, but accessible top floor ceilings above heated rooms by December 31, 2006 so that the U-value of the floor ceiling of 0.30 W / (m²K) is not exceeded. Otherwise the following values ​​apply:

### Calculation of the U-value

The most important term related to thermal insulation is thermal conductivity. This is a thick, independent material property and should not be confused with the U-value. The thermal conductivity of a material indicates what amount of heat (in kWh) is transported through a building material surface of 100 m² and 1 m thick in one hour if there is a temperature difference of 10 degrees between inside and outside. As with the U-value, the smaller the value, the better.

In Germany, insulation materials are classified in a "thermal conductivity group" (thermal conductivity group, WLG) depending on their thermal conductivity. This group corresponds to the decimal places of the thermal conductivity. Example: Insulation with a thermal conductivity of 0.030 has the thermal conductivity group WLG 030.

In order to be able to calculate the thermal permeability (U-value) of a component, you also need the insulation value of the individual layers. In technical jargon, this thermal insulation value is called thermal resistance. This indicates the resistance of a layer to the flow of heat. To determine it, the thickness of the relevant layer (in meters) must be divided by the material-related thermal conductivity. In the case of multi-layer components, the individual value must be determined for each layer using this calculation method. The sum of all individual values ​​then gives the thermal transmittance or thermal insulation value for the entire component. The greater the resistance, the better the thermal insulation.

Even calm air layers (no flowing rear ventilation) have a certain insulation value depending on the thickness and incline. This resistance is 0.16 for static layers of air up to an incline of 60 degrees. If the layer is inclined more than 60 degrees 0.18. These values ​​must be taken into account when calculating the total resistance.

The calculation of the U-value becomes more complicated if the thermal insulation of components is interrupted. This is the case with roofs, e.g. with insulation between the rafters. Two areas need to be examined here. On the one hand the compartment where the thermal insulation is located and on the other hand the rib that interrupts the thermal insulation. The ribs (i.e. the rafters or the beams) are only taken into account in the thickness of the thermal insulation lying on the side. Vapor barriers and waterproofing membranes are not taken into account in the thermal insulation calculation.

The following formulas for calculating the thermal protection of a component result from the above explanations:

The insulation value of a layer, called resistance (thermal resistance), is calculated using the following formula:

If the component has several layers, all layers (including static air layers, see above) must be added to the total resistance (thermal resistance):

The thermal permeability (the U-value) of a component is calculated from the reciprocal of the total resistance:

If the compartment and rib are added, the following formula results for the heat permeability:

You should now be able to carry out a thermal insulation calculation yourself.

The thermal conductivity of some important component layers can be found in the table below. If you are missing values, take a look at the relevant construction tables or ask the manufacturer or supplier of the building material.

 description Thermal conductivity Claddings / panels Plasterboard 0,25 Wooden formwork (softwood) 0,13 Chipboard (flat press) 0,13 (Standard clothing) 0,35 Interior plasters Gypsum plaster 0,70 Gypsum plaster without surcharge 0,35 (Standard interior plaster) 0,90 Structure Sand-lime brick masonry, 1600 [kg / m³] 0,79 Light vertical perforated brick masonry, 900 [kg / m³] 0,42 Aerated concrete 350 [kg / m³] 600 [kg / m³] 0,090,16 Rafters / ribs made of softwood 0,13 Reinforced concrete 2,1 Solid brick masonry, 1600 [kg / m³] 0,68 (Standard masonry) 1 Vapor retarders > Glass fleece bitumen roofing membranes V 13 0,17 Thermal insulation Wood fiber insulation boards, WLG 050 0,050 Mineral wool WLG 035 ("glass or stone wool") 0,035 Mineral wool WLG 040 ("glass or stone wool") 0,040 Polystyrene (PS 20 SE) ("Styrofoam") WLG 040 0,040 PUR rigid foam, WLG 030 0,030 FOAMGLAS® sheets T4-040 0,040 isofloc cellulose insulation material WLG 040 0,040 Sheep wool insulation mats DWS 8/90 0,044 (Standard thermal insulation) 0,040 Exterior plasters Cement-lime plaster 0,87 Synthetic resin plaster 0,70 Standard exterior plaster) 0,90