# Heat loss

This article provided a basic description of how to calculate the heat loss through a part of a building's structure (say a wall or roof), or from a complete building.

Doing these calculation can greatly help:

- When choosing a replacement boiler or heating system
- When working out where to best spend money improving insulation
- Deciding on construction details of new extensions or other alterations
- Calculating pay back times on any expenses incurred on "energy saving" measures.

## Contents

## Causes of heat loss

Mother nature dictates that overall, heat will flow from hotter objects to cooler ones. Generally there is not much we can do about this, but we can change how quickly it happens. Most heat lost from a house is initially via conduction - through walls, floors, and ceilings. These losses will tend to heat the outer surfaces of the building where the heat is then convected away to the atmosphere. The second major loss of heat is through air changes; every time a draft allows cold air in from outside (and conversely warm air out), that cold air will need to be re-heated.

It is worth bearing in mind however, that while a set of heat loss calculations are very useful, they are not the complete story. Some additional rules of thumb can also be applied to better qualify the results. For example:

- One can take into account the exposure of outside walls. More heat may be lost through one wall that is subject to high wind exposure that the heat loss calculation alone would initially suggest. This may mean that two otherwise identical houses in different locations would benefit most from different remedial work. One on a hill top in an exposed location may get most gain from cavity wall insulation, where as the sheltered one may get more immediate gain from extra loft insulation.
- Damp walls conduct heat better than dry ones.
- Rooms with large south facing windows will receive more solar gain than others - this may alter the relative priorities when deciding where to insulate.
- Windy locations also increase losses due to air changes (i.e. drafts).

## Calculations

It is relatively easy (although a bit tedious!) to do a full set of heat loss calculations in a spread sheet. One works through the property room by room computing a loss (or gain) for each room.

### Heat loss via conduction

To calculate the rate of loss of heat through a wall or other component of a building, we need some basic information about it. The rate of heat loss:

- The total area of the surface (A) - the larger it is, the faster heat will flow through it.
- The temperature difference (ΔT) - the bigger the difference in temperature from one side to the other, the faster the heat flow
- The thermal conductivity of the component (U) - the more insulating the material, the slower the rate of heat flow.

The rate of heat flow (F) is simply:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F = A \times \Delta T \times U}**

**To get sensible answers, we need to use consistent units for all measurements. So sticking to SI units, the rate of heat loss will be given in Watts. Areas need to be measured in square metres, and the thermal conductance in W/m²K - where K is the temperature difference in Kelvins or degrees Celsius**

The area is generally easy to compute, although you may need to break a surface down into a number of parts if the construction is not consistent over the whole area. So for example an outside wall of 10 m², may include 2 m² of window. The window will need to have its heat loss computed separately to allow for the different thermal resistances.

The temperature difference is simply the difference between the rooms normal temperature and whatever is the other side of the wall etc. Now with an outside wall, the chances are the outside temperature will be significantly lower that inside. When computing worst case losses for the depths of winter one would typically use and assumed outside temperature of -3°C. Note that with inside walls, there may actually be a heat gain from the adjoining room rather than a loss - it depends on which room is hotter. If you have a party wall shared with a neighbour, you may get heat loss or even heat gain through that depending on how warm they keep their place.

The U value will vary with the building material and the type of construction. Usually you can look these up in a table to find a suitable figure. So a single skin brick wall will lose more heat than a cavity wall. Thermal blocks are better than standard bricks etc. See the tables at the end of this page for more information.

### Heat loss due to air changes

Talking about "air changes" is a way of quantifying the effects of drafts, and of doors being opened and people moving about a house.

The simplest way to deal with air changes is to make an assessment of the number of times the complete volume of air in the room will be changed. There are standardised tables for these values which vary for the type of room (see below). However in the absence of a suitable value you can assume 3 changes an hour is a typical worst case for a room with some draft proofing.

If one knows the volume of the room, the number of cubic metres changed per hour is easy to work out. Once you have this you multiply by a standardised constant figure of 0.36 W/m³h

The air change heat loss constant is derived from multiplying the number of cubic meters of air by the mass of 1 cubic meter to convert from m³ to kg Then multiplying the mass in kg by the specific heat capacity or air to get a total in Joules (J) Finally dividing by 3600 to convert figure in J/h to one in J/Sec (Watts)

### Worked Example

Lets take a very simple "house" with two rooms:

We will assume it has:

- 9" solid brick walls
- decent argon fill double glazed windows and door
- The partition wall is a plasterboard
- There is a pitched roof over with tiles and felt, and 100mm of loft insulation
- The floor is a concrete slab
- Outside temperature is -3°C
- The left hand room is warmest at 21°C, and the smaller room is 18°C
- Air changes in the left room are 1 per hour, and 2 per hour in the right hand one
- and finally the rooms are all 2.2m tall

If we slap all the above figures into a spereadsheet, and take the u values from the table at the end, we get:

Room | Surface | Width | Height | Area | Tdelta | u-value | Loss | Air Cng | Vol | Total |

Left Room | Front Wall | 3800 | 2200 | 2.37 | 24 | 2.2 | 125 | 1.00 | 25 | |

Window | 2722 | 2200 | 5.99 | 24 | 1.7 | 244 | ||||

Left wall | 3000 | 2200 | 6.60 | 24 | 2.2 | 348 | ||||

Partition wall | 3000 | 2200 | 6.60 | 4 | 1.8 | 48 | ||||

Rear Wall | 3800 | 2200 | 8.36 | 24 | 1.2 | 241 | ||||

Floor | 3800 | 3000 | 11.40 | 24 | 0.8 | 219 | ||||

Ceiling | 3800 | 3000 | 11.40 | 24 | 0.3 | 82 | ||||

Total | 1307 | 217 | 1524 | |||||||

Right Room | Front wall | 2806 | 2200 | 3.01 | 21 | 2.2 | 139 | 2.00 | 19 | |

Window | 1318 | 1318 | 1.74 | 21 | 1.7 | 62 | ||||

Door | 762 | 1865 | 1.42 | 21 | 1.7 | 51 | ||||

Partion walll | 3000 | 2200 | 6.60 | -4 | 1.8 | -48 | ||||

Back wall | 2806 | 2200 | 6.17 | 21 | 2.2 | 285 | ||||

Right wall | 3000 | 2200 | 6.60 | 21 | 2.2 | 305 | ||||

Floor | 2806 | 3000 | 8.42 | 21 | 0.8 | 141 | ||||

Ceiling | 2806 | 3000 | 8.42 | 21 | 0.3 | 53 | ||||

Total | 989 | 280 | 1269 | |||||||

Total loss | 2793 |

**(A downloadable Excel spreadsheet for the above example is available here)**

Notes:

- Remember to subtract window / door sizes from the front wall area
- We are assuming that the partition wall door is the same u value as the stud wall
- The right hand room gets a nett gain of heat from the left

ConclusionsTotal heat loss is just under 2.8kW on the coldest of days. If you redo the sums for an more typical average outside temperature of 10°C, then you get a total heat loss of only 1.2kW

## Full calculations - Downloadable Example

For a full working example of calculations for a three bed semi-detached house with a loft conversion (adding an additional 3 rooms), you can download this Excel Spreadsheet.

There are some U values on the first tab of the sheet. The second tab has the actual calce. More U values are available in the tables below.

You can play with the room temperatures and air changes on the first tab, and also the reference temperature (i.e. the outside temp).

*To make sense of some of the Tdelta columns you need to know which walls back onto each other (hence start with a quick sketch when doing your own). This example is for a basic 3 bed semi with loft conversion. The layout has the living room side attached to its neighbour. The lounge at the front backs onto dining room. The hall to its right, backing onto the kitchen. Master bedroom is above the lounge, backing onto bed 2 (listed as "office" in the sheet). Bed 3 is over the hall, and the bathroom over kitchen. At that stage of the calcs the loft has been calculated as one big space rather than individual rooms although the outer insulation is included in the sums. *

## Tables of figures

### Air changes and typical room temperatures

Room type | Room temp | Air Changes |
---|---|---|

Lounge | 21 | 1 |

Dining Room | 21 | 2 |

Bedroom | 18 | 0.5 |

Hall and Landing | 16 | 1.5 |

Bathroom | 22 | 2 |

Kitchen | 18 | 2 |

### Alphabet soup - K, R, and U Values

#### K Values

The K value (aka known as a "lambda value") is a measure of how well a material conducts heat. The bigger the number the better it conducts. The value is a specific property of the material - you also need the thickness of the material to make practical use of this value. The standard units of a k value are W/m·k (watts per metre per kelvin).

#### U Values

The U value of the material is a measure of its thermal conductivity that does take into account the depth of it. It is calculated as:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle U Value = \frac { K value }{ depth }}**

The units are W/m²K

So for example you can work out the approx U value for a PIR foam board (e.g. products like Celotex or Kingspan) if you know the thickness. Start with the k value (from the table below) of 0.025, and divide by the depth expressed in metres. So say its an 80mm thick board, you get:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle U Value = \frac { 0.025 }{ 0.08 }}**

U Value = 0.31 W/m²K

#### R Values

For completeness one ought to mention the R value. This is simply the reciprocal of the U value, and hence is a measure of the thermal resistance rather than the thermal conductivity. It can sometimes be useful when calculating the overall U value for a wall etc made from a number of layers of material - each with different insulating properties - since the R values can be added together to arrive at a total thermal resistance. Taking the reciprocal of that gives the U value.

For example, if you wanted to know the overall U value for a solid brick wall with a U value of 2.2, combined with 80mm of PIR board insulation with a U value of 0.3, you would calculate it like this:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle U Value = \frac { 1 } {\frac { 1 }{ 2.2 } + \frac { 1 }{ 0.3 } } = 0.264 W/m^2 K}**

Beware when searching for thermal properties of building materials that R values are commonly quoted by US based web sites and suppliers. However they will usually be quoted in imperial units ft²·°F·h/BTU. To covert imperial units to SI, you can multiply by 0.1761

#### Computing u values for more complex walls

When dealing with complicated wall constructions it can be handy calculate a U value by taking into account the properties of several layers of different materials.

The following question and explanation (provided by a local authority building control officer (BCO) was posted to uk.d-i-y:

Two of the walls are external and stone structure. Can someone give me a usable U figure for a stone wall that is 560mm thick and consists of an inner and out stone skin with loose rubble in the middle. Inside this is 50mm of rockwool and then p/b.

From the top of my head: Outside surface resistance = 0.04m²K/W Limestone: conductivity = 1.13W/mK; divide the thickness by this value to give resistance. Mortar (and presumably loose fill): conductivity = 0.84W/mK [1] Rockwool: conductivity = 0.05m/0.038W/mK = 1.32m²K/W [2] Plasterboard resistance = 0.06m²K/W Inner surface resistance = 0.13m²K/W Add up all the resistances, then take the reciprocal to give your U-value. [1] It depends on the proportions of wall to rubble-fill, but I would have thought about 75% stone to 25% mortar and crap, which gives an average conductivity of about 1.04W/mK. [2] If you want a precise figure, you should also include for the studs in the dry-lining. R = 0.04 + 0.56/1.04 + 1.32 + 0.06 + 0.13 = 2.09m²K/W. Therefore U-value = 1/2.09 = 0.48W/m²K. To work out heating, probably best to use 0.6-0.8 unless you can put actual values to the thicknesses of the leaves of the wall.Hugo Nebula

### Tables of U Values

#### Common walls and ceilings

Materials | u-Value | Comments |
---|---|---|

Wall - outer 9" solid brick | 2.2 | |

Wall - outer 11" brick (unfilled) cavity | 1.0 | |

Wall - outer 11" brick insulated cavity | 0.6 | |

Wall - internal plaster over 4" block | 1.2 | |

Wall - internal PB over stud | 1.8 | No insulation in void |

Floor (ground) - solid concrete | 0.8 | |

Floor - PB + joist + FB flow up | 1.9 | Flow from downstairs to upstairs is faster than the other way |

Floor - PB + joist + FB flow down | 1.5 | |

Roof pitched with felt + 100 insulation | 0.3 | |

Window - Single Glazed | 5.6 | |

Window - wood DG | 2.9 | float glass, air fill |

Window - wood - low E | 1.7 | Argon fill, Pilkington K glass |

Door single glazed | 3 | |

Wall Insulated | 0.6 |

#### Double Glazing Units

Glass specification | Cavity | ||
---|---|---|---|

12 mm | 16 mm | 20 mm | |

float/air/float | 2.9 | 2.7 | 2.8 |

float/argon/float | 2.7 | 2.6 | 2.6 |

float/air/Pilkington K Glass | 1.9 | 1.7 | 1.8 |

float/argon/Pilkington K Glass | 1.6 | 1.5 | 1.5 |

Overall thickness of unit(mm) | 20 | 24 | 28 |

### Table of K values

Material | Type | K value (W/mK) |
---|---|---|

Asphalt | 19mm |
0.50 |

Blocks | lightweight |
0.38 |

mediumweight |
0.51 | |

heavyweight |
1.63 | |

Bricks | exposed |
0.84 |

protected |
0.62 | |

Calcium silicate | board |
0.17 |

Chipboard | standard |
0.15 |

Concrete | aerated slab |
0.16 |

lightweight |
0.38 | |

dense |
1.40 | |

Felt/bitumen | 3layers |
0.50 |

Fibreboard | Standard |
0.06 |

Fibreglass | quilt |
0.04 |

Glass | sheet |
1.05 |

Hardboard | standard |
0.13 |

Mineral Wool | quilt |
0.04 |

slab |
0.035 | |

Mortar | normal |
0.80 |

Phenolic foam | board |
0.020 |

Plaster | gypsum |
0.46 |

sand/cement |
0.53 | |

vermiculite |
0.19 | |

Plasterboard | gypsum |
0.16 |

Polystyrene | expanded |
0.035 |

Polyurethane | board |
0.025 |

Rendering | external |
0.50 |

Roofing tiles | clay |
0.85 |

concrete |
1.10 | |

Screed | 0.41 | |

Stone | reconstructed |
1.30 |

sandstone |
1.70 | |

limestone |
~1.30 | |

granite |
2.30 | |

Stone | chippings |
0.96 |

Timber | softwood |
0.14 |

Vermiculite | loose |
0.65 |

Woodwool | loose |
0.11 |

Another large list can be found here