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What is a U-value?

When we talk about the U-Value of a particular component of a building such as a wall, roof or window, we’re describing how well or how badly that component transmits heat from the inside (usually) to the outside. On a cold day in the UK when we’re warm and cosy on the inside of the building, we will be happier the lower the U-Value is – because it means that our wall or roof or window is quiet good at holding-up the heat getting to the outside.

A 'Component' might be a homogeneous material (such as a concrete retaining wall) or a series of materials in contact (such as in a cavity wall).

The technical name for which we use the shorthand ‘U-Value’ is Thermal Transmittance.

The **U-value** of a building component like a wall, roof or window, measures the amount of energy (heat) lost through a square metre (m^{2}) of that material for every degree (K) difference in temperature between the inside and the outside.

Before we start looking at what that means, lets sort out the units we use to define it.

**• Energy** flows along in watts (which is a measure of energy in ‘joules’ flowing over a period of time in ‘seconds’ ).

**• Temperature** is measured in degrees Kelvin – which practically is degrees Celsius to the rest of us.

The actual equation involves a few more ‘values’ which when put together gives us the U-value of our wall or window. We’ll look at those in a moment, but the essential equation is this:

**U = 1/R** in W/m^{2}K or Watts per square metre per degree Kelvin

### Example of how U-values work:

• The U-value of a single sheet of glass as found in a traditional window pane is 6.0W/m2K – which means that for every degree of temperature difference between the outside and the inside, a square metre of the glazing would lose 6 watts. So for example, if the temperature difference on a typical cold day was 15 degrees, then the amount of heat loss would be 15x6 = 90 watts per square metre. That’s a lot of heat!

• By comparison, the U-value of a modern piece of triple-glazing can be as low as 0.7W/m2K – which is not very much heat at all.

The ‘R-value’

‘R-value’ (reciprocal of U-value) means the Thermal Resistance or how much of a fight the material puts up against the heat passing through it, for a given thickness and area. The R-value is expressed as m^{2}K/W

The heat flow through a building construction depends on the temperature difference across it, the conductivity of the materials used and the thickness of the materials. Of course the temperature difference is an external factor. The **thickness** and the **conductivity** are properties of the material. A greater thickness means less heat flow and so does a lower conductivity. Together these parameters form the thermal resistance of the construction.

If the component is a composite (consisting of several material elements), the overall resistance is the total of the resistances of each element.

A construction element with a high thermal resistance (e.g. rock wool), is a good insulator; one with a low thermal resistance (e.g. concrete) is a bad insulator.

### Example of R-values:

• 100mm of wood fibre insulation board would have has an R value of 2.6 m^{2}K/W whereas in comparison

• 100mm of glass fibre insulation batt would have has an R value of 2.2 m^{2}K/W – which makes the wood fibre more resistant to heat loss.

The ‘R-Value’ too has its own equation that picks up on yet another ‘value’:

**R = t/ λ** where ‘t’ is the thickness of the material in metres and λ is the Thermal Conductivity (sometimes known as the ‘k-value)

## The 'Lambda (λ) value'

The lambda (λ) value, or the Thermal conductivity, or 'k-value' of a material, is a value that indicates how well a material conducts heat. It indicates the quantity of heat (W), which is conducted through 1 m² wall, in a thickness of 1 m, when the difference in temperature between the opposite surfaces of this wall equals 1 K (or 1 ºC). In practice λ is a numerical value expressed in terms of W/(mK). The lower the λ value, the better the insulation property of the material.

### Examples of Thermal Conductivity:

• Wood fibre insulation has Thermal Conductivity of 0.038 W/mK

• Glass fibre insulation has Thermal Conductivity of 0.044 W/mK

• And the Thermal Conductivity of dense concrete is around 1.5 W/mK

• In comparison, the Thermal Conductivity of copper is a whopping 401 W/mK – which is why some of your kitchen pans might have copper bottoms.

That’s quite enough ‘values’ for now!

## Calculating a building element's U-value

• Below is an example of how to calculate a rough U-value of a typical UK cavity wall, though with a 100mm cavity.

• More accurate calculations will involve extra data including loss through thermal bridging; thermal bypass as well as extra materials such as mortar joints.

• There are several U-value calculators available on-line, though they tend to be provided by the product manufacturers.

• The two main commercial U-value calculators are supplied by Build Desk (Windows only) and BRE (Windows only). The Build Desk calculator is about as comprehensive and user-friendly as they come, but at a hefty annual licence fee. Both applications come as Windows-only which is a pain to Mac users.

• Two** free** handy Apps for **IoS** are: U-Value Calculator from Mark Stephens of TeachPassiv, which needs manual entries; and U-Value Insulation Calculator from Dorada App Software.

**Example calculation:**

Layer & Material |
Thickness and conductivity |
R value |

1 External surface resistance | - | 0.40 K m²/W |

2 Clay bricks | 0.105 m; 0.710 W/mK | 0.15 K m²/W |

3 Glass mineral wool |
0.100 m; 0.035 W/mK | 2.85 K m²/W |

4 Concrete blocks | 0.100 m; 0.18 W/mK | 0.55 K m²/W |

5 Plaster | 0.013 m; 0.16 W/mK | 0.08 K m²/W |

6 Internal surface resistance | - | 0.13 K m²/W |

TOTAL |
- | 4.16 K m²/W |

Therefore the overall wall element **U-value = 1 / R = 1 / 4.16 = 0.24 W/m^{2}K**

## Read more about Building Physics:

- Heat transfer: Conduction, Convection & Radiation MORE
- Insulation materials: thermal properties MORE
- Air tightness MORE
- Air barrier design MORE
- Thermal bypass MORE
- Decrement Delay & Thermal buffering MORE
- Thermal mass MORE

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