UWE

U values and Calculations

Contents

1 Introduction

2 Simple U value calculation

3 Typical K values

4 Typical U values

5 Floor Insulation

6 More Complex U Values - Walls

7 Adjusting/Comparing U Values

1 Introduction

Decisions regarding uprating insulation are much easier if you have a basic understanding of U values. A U value is a measure of thermal transmittance through a building element; walls, floors, roof etc. It's the amount of energy in watts transmitted through one square metre of the element for every degree Kelvin (same as Celsius for our purposes) between the internal and external air temperature.  So if a wall has a U value of 2.5 and the temperature difference is 10 degrees the heat flow per m2 is 25 watts.

U values - W/m2K

Definition: The amount of heat which will flow through 1 square metre of a wall for every degree in temperature difference between the inside and outside.

Another example - If a wall has a U value of 1.6 W/m2K (typical of a 1930's cavity wall) the heat loss through the wall (say 100m2) on a cold winter's day (20 degree difference between inside and outside temperature) could be 100 x 1.6 x 20 = 3200 watts. If the wall is well insulated, say U value of 0.30, the heat loss will be 600 watts.   Simple U values are quite easy to calculate; ones for building control purposes are a bit more complex but unnecessary for following this part of the web site.

Typical U values

1890 solid wall 1 brick thick.
1925 cavity wall, both leaves brick (100mm).
late 1970s cavity wall, brick and lightweight block (both 100mm).
mid 1990s cavity wall, brick outer leaf, 50mm cavity batts, 100mm aerated block inner leaf.
2002  - brick cavity wall with aerated block inner leaf and 75mm cavity batts, 100mm aerated bock.
2.1 W/m2K 1.8 W/m2K 1.00 W/m2K 0.45 W/m2K 0.35 W/m2K

You can find U values in published tables (there are some more examples on a later page). You can also calculate them from K values. 

Thermal Conductivity - W/mK (K values)

Definition: This is the measure of the ability of a material to transmit heat.

Good insulators have lower values. It is measured as the heat flow in watts across a thickness of 1 metre of material for a temperature difference of 1 degree and a surface area of 1 m2. Some modern lightweight blocks, for example, have a value of about 0.11W/mK. U and K values are easily confused but remember that a K value assumes a thickness of 1 metre and is related to an individual material. A U value measures heat flow though a combination of materials, each of them of varying thickness.  So, if we know which material are in the wall and we know their individual thicknesses we can work out the overall U value of the wall.

Thermal Resistance  - m2K/W

Definition: The measure of the resistance to heat flow of a material of a given thickness. This is the thickness (in metres) divided by the K value. The higher the number the better the resistance. This is calculated for each material within a wall or other building element.

In a U value calculation we also need to add in some other resistances. These are a bit complicated; for example the thermal resistance of a surface (ie the face of a brick) depends on the conduction, convection and radiation at that surface. The air next to the surface forms a stationary layer which limits heat flow. Similarly, the thermal resistance of a cavity also depends on conduction, convection and radiation within the cavity.

For our purposes in calculating wall U values we can use the following constants.

To calculate the U value we add up all the resistances (individual materials and constants above) and then work out the reciprocal. In other words the U value is 1 divided by the sum of all the resistances. Try and follow the two examples on the next page. 

2 Simple U value calculation

From April 2002, U values have had to be calculated using the Combined method. This is much more complex than the method shown here and takes into account thermal bridging effects of bedding mortar, wall ties, built-in timber joists etc. However, the method shown here shows the principles and is accurate enough for comparative purposes.

To calculate a U Value for a cavity wall we need to know.
  • The thermal conductivity value for each material in the wall 
  • The thickness of each material 
  • The thermal resistance of any enclosed air space 
  • The surface resistance values 

NB. The thermal conductivity (W/mK) values can be obtained from manufacturers. Surface resistance values (which vary by location and exposure) can be obtained from the CIBSE. The surface resistance is caused by air in contact with the material surface which opposes the flow of heat. Values vary in relation to direction of heat flow (up or down), exposure, and surface properties. The ones in the calculation below (outside & inside wall surface, cavity) are typical - in any event their affect on the overall calculation is not normally significant..

The U value calculation 

Note: thickness divided by thermal conductivity = thermal resistance

Material

Thickness

Thermal Conductivity

Thermal Resistance

Outside wall surface
n/a
n/a
0.06
Brick outer leaf
0.10
0.84
0.12
Cavity air space
n/a
n/a
0.18
Aerated block (Solar)
0.125
0.11
1.14
Gypsum plaster
0.013
0.16
0.08
Inside wall surface

n/a

n/a

0.12

Total Thermal Resistance
1.70

U value = reciprocal of 1.70 = 1/1.70

0.59W/m2K

If the cavity is filled with mineral wool insulation the U value will drop. Notice that in the calculation below the thermal resistance of the cavity air space has been replaced with the thermal resistance of the mineral wool (K value is 0.04).

Material

Thickness

Thermal Conductivity

Thermal Resistance

Outside wall surface
n/a
n/a
0.06
Brick outer leaf
0.10
0.84
0.12
Cavity insulation
0.05
0.04
1.25
Aerated block (Solar)
0.125
0.11
1.14
Gypsum plaster
0.013
0.16
0.08
Inside wall surface n/a n/a

0.12

Total Thermal Resistance
2.77

U value = reciprocal of 2.77 = 1/2.77

0.36W/m2K

More K values are shown on the next page.

3 Typical K values

We have listed below some of the most common building materials and their K values. These can be used to calculate U values as shown on the previous page. Note that there is some variation in specific materials - brick and stone vary, for example, depending on their density.

 

Conductivity

W/mK

 

Conductivity

W/mK

Walls Brickwork (dense)  0.90 Finishes Plasterboard 0.21
  Brickwork (common)  0.56   Fibreboard 0.10
  Blocks - lightweight aggregate 0.57   Tiles (ceramic)  1.20
  Blocks - aerated concrete  0.18   Render - sand-cement (external) 1.00
  Block - standard concrete 0.70   Plaster (dense) 0.57
  Concrete dense 1.25   Plaster (lightweight) 0.18
  Mortar 0.90 Roofs Aerated concrete slab 0.16
  Sandstone 1.30   Asphalt 0.70
  Limestone (soft) 1.10   Felt/bitumen layers 0.23
  Limestone (carboniferous)  1.70   Screed 0.41
  Timber (softwood) 0.12   Stone chippings 2.00
  Timber (hardwood)  0.18   Tiles (clay)  1.00
  Glass 0.90   Tiles (concrete)  1.50
Wall ties 17.00 Wood wool slabs 0.10
Floors Concrete slab (cast) 1.35  Insulants Expanded polystyrene 0.035
  Screed 0.41 Mineral wool 0.04
  Chipboard 0.11   Polyurethane Foam  0.025
    Phenolic foam 0.025

4 Typical U values

We have listed some typical U Values below - theses typical values should always be regarded with caution because we don't know the exact nature of the construction. Floor U values can be found on the next page. 

 

Element

W/m2K

Windows Single glazed steel/aluminium 5.8
  Single glazed wood/plastic  4.7
  Double glazed aluminium 4.2
  Double glazed wood/plastic 3.0
  G Argon filled, Low 'e' glass 2.0
     
Walls Half brick wall 3.2
  One brick solid (225mm) 2.1
  Stone 300mm 1.9
  Brick (and brick) cavity wall 1.6
  Brick and 100mm lightweight block 1.0
  Brick and 100mm aerated block 0.7
  Brick and 125mm aerated block, 50mm cavity insulation 0.4
  Brick and 125mm aerated block, 75mm cavity insulation 0.3
     
Roofs Pitched no insulation        3.3
  Pitched 25 - 50mm insulation 2.6
  Pitched 75mm insulation 1.0
  Pitched 100mm insulation 0.5
  Pitched 200mm insulation 0.3
  Flat uninsulated 2.0
  Flat 50mm insulation 0.7

5 Floor Insulation

Unlike walls and roofs, the heat loss through a ground floor varies with its size and shape. This is because most heat is lost around the edges of the floor. So, a house with a high perimeter to floor area ratio will suffer most.

NB: calculating U values for floors in accordance with The Building Regulations is complex and far beyond the nature and scope of this section.

Thermal bridges are a significant source of heat loss. They may also cause localised condensation and mould growth. Correct detailing at the junction of the floor slab and external wall will reduce thermal bridging and thus the risk of condensation.

Where insulation is placed between timber joists, the joists have the potential to act as thermal bridges. However, where joists are at least 150mm deep and the space between them is fully filled with insulation, the timber does not constitute a thermal bridge.

With suspended timber ground floors, care is needed to minimise air leakage from the ventilated sub floor void into the heated space. As well as gluing the joints between the floor deck panels, the floor perimeter should be sealed by applying expanded foam tape under the skirting and a continuous bead of sealant to the back of the skirting prior to fixing.

Typical U values

P/A Floor ratio

Uninsulated Concrete

Uninsulated timber

0.30 0.50 0.75
0.50 0.73 0.98
0.80 1.0 1.30
1.0 1.10 1.40

U values of insulated floors obviously vary according to the nature and type of insulation. The values below are typical of what can be achieved by adding 100mm insulation roll between a joist floor and 50mm foam insulation in a concrete floor. Note that uprating a timber floor is fairly easy; uprating a concrete one can be complex and expensive.

P/A Floor ratio

Insulated Concrete

Insulated timber

0.30 0.22 0.30
0.50 0.28 0.35
0.80 0.33 0.45
1.0 0.45 0.60

6 More Complex U Values - Walls

In some forms of construction it's worth calculating two U Values to allow for differences in construction. In the example below we have calculated U values through the wall at the studding and at the insulation.  The U value through the wall at the point of the insulation is 0.23 (it would have been 0.32 if 100mm insulation had been used - this was more common until recently). The U value through the studs is 0.52. If the studs are 50mm wide and are at 600mm centres then the ratio of insulation to studding is 10:1. Thus the average U value is (10x0.23 + 1x0.52)/11 = 0.27 W/m2K. In the examples below we have had to work to three decimal places due to the thin nature of the vapour check and breather paper - in fact their effect on the U value is virtually insignificant.  

7 Adjusting/Comparing U Values

If you are unsure about the effect of differing thicknesses of insulation it's worth setting up a simple spreadsheet. In the example below we have included an estimate of the heat loss and its impact on heating costs over a year to give the figures a bit more meaning. The first example shows a solid wall with cement based plaster on the inner face. The U value is 2.17 - typical for a one brick sold wall. In a modest 3 bed detached house this could account for, say, 250 of the overall annual heating cost.

If the wall is insulated internally with foam backed plasterboard (40mm foam) the U value drops dramatically - to about 0.47. The heat loss through the wall is now only about 55. If the thermal board has an 80mm backing of foam the U value drops to about 0.27 and the annual heat loss is now only about 34. Is the extra thickness  of insulation worth its capital cost - maybe an additional 300 or so.

Whichever thickness is chosen remember this work could be very expensive (probably 5,000 or so), it will make the room substantially smaller and it will cause a lot of inconvenience.   

You could also adapt the spreadsheet to work out the required thickness of insulation to give a required U value. When improving properties it's difficult knowing what the optimum U values are - there are many variables to consider. The Energy Saving Trust recommend walls should be insulated to give a U value of at least 0.30 W/m2K. This may not always be practical.

©2006 University of the West of England, Bristol
except where acknowledged