Calculation of U-value
The heat transmission coefficient or U-value is the value that shows
how much heat is transferred through different surfaces in a building. The
reciprocal of the U-value or
!
"
equals to the thermal resistance, R, of that
construction. Furthermore, it is known that each object has its own thermal
resistance. Therefore, to calculate the U-value of external wall (or any other
het transfer element), thermal resistance of each layer must be added, then
its reciprocal will equal to the U value of external wall (or any other heat
transfer element).
𝑅$%&'( = 𝑅*'+,- ! + 𝑅*'+,- 0 + 𝑅*'+,- 1 + 𝑅*'+,- 2 + 𝑅*'+,- 3 + ⋯
+ 𝑅*'+,- 5
𝑈=
1
𝑅$%&'(
Table 1: Thermal resistance (R) for commonly used materials in building construction
Description
Outdoor
Surface
Resistance
Indoor
Vertical
Surface
Resistance
Indoor
Horizontal
Surface
Resistance
Wall Air
Space
Resistance
Ceiling Air
Space
Resistance
Stone
Acoustic Tile
Carpet
Thickness
(inches)
Density
(lb/ft3)
-
-
Thermal
Resistance
(ft2٠°F٠h/Btu)
0.25
-
-
0.68
-
-
-
-
0.92
-
-
-
-
0.87
-
-
-
-
1.00
-
-
1
¾
½
160
23
18
0.05
1.79
1.23
0.19
0.14
0.33
2.53
0.20
0.25
Page 1 of 12
Specific
Heat
(Btu/lb٠°F)
-
Thermal Mass
(Btu/h.ft2.°F)
-
Description
Thickness
(inches)
Density
(lb/ft3)
Terrazzo
Gyp Board
1
5/8
Fiber Glass
Roll
1
Fiber Glass
Rigid Slab
1
Extruded
Polystyrene
Rigid Foam
1
Expanded
Polystyrene
1
Whiter Block
(AAC)
1
Brick
Heavyweight
Concrete
Heavyweight
Concrete
Heavyweight
Concrete
Sand Cement
Roofing Tile
Sand Cement
Screed
Specific
Heat
(Btu/lb٠°F)
0.19
0.26
4
6
160
50
0.63
0.75
1.00
1.13
1.25
1.50
2.00
2.25
3.00
1.5
2.00
2.25
3.00
4.00
4.50
5.00
6.25
1.3-1.5
1.6-1.7
2.2
2.4-2.6
2.8-3
1.1-1.2
1.4-1.6
1.7-1.9
28
31.2
34.3
37.5
120
140
Thermal
Resistance
(ft2٠°F٠h/Btu)
0.08
0.56
3.23
3.45
3.70
3.85
4.00
4.12
4.37
4.51
4.65
4.12
4.37
4.51
4.65
4.51
4.12
4.12
4.12
4.5
4.8
5.0
5.3
5.6
4.0-3.45
4.17-3.57
4.35-3.70
1.14
1.07
1.00
0.95
0.65
0.44
0.19
0.22
2.53
0.68
0.02
0.02
0.03
0.03
0.04
0.05
0.06
0.07
0.09
0.05
0.06
0.07
0.09
0.12
0.14
0.15
0.19
0.04
0.05
0.06
0.07-0.08
0.08-0.09
0.03-0.04
0.04-0.05
0.05-0.06
0.58
0.65
0.71
0.78
7.6
15.4
8
140
0.48
0.22
20.53
12
140
0.89
0.22
30.80
1
111.9
1.00
0.2
1.87
1
111.9
0.25
0.2
1.87
Page 2 of 12
0.36
0.36
0.35
0.35
0.25
Thermal Mass
(Btu/h٠ft2٠°F)
Description
Thickness
(inches)
Density
(lb/ft3)
Thermal
Resistance
(ft2٠°F٠h/Btu)
Specific
Heat
(Btu/lb٠°F)
Thermal Mass
(Btu/h٠ft2٠°F)
Sand Cement
1
111.9
0.25
0.2
1.87
Plaster
Sand Cement
1
126
0.16
0.19
2.00
Block
Sand Cement
1
126
0.16
0.19
2.00
Brick
Foamed
1
70
1.02
0.2
1.17
Concrete
Concrete Slab
1
140
0.10
0.2
2.33
Mortar bed
1
116
0.25
0.2
1.93
Sand Lime
1
111.9
0.21
0.21
1.96
Brick
Elastomeric
Waterproofing
on
0.29
Bituminous
Primer
Where 1 in. = 2.54 cm; 1 lb/ft3 = 16.02 kg/m3; 1 ft2٠°F٠h/Btu = 0.176 m2٠K/W
Note: 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑚𝑎𝑠𝑠 = 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 ∗ 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 ∗ 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 (𝑖𝑛 𝑓𝑒𝑒𝑡)
For thermal resistance of other materials, refer to ASHRAE Handbook of
Fundamentals, or any other reliable source.
Page 3 of 12
Example # 1:
Figure 1: External wall layers
Page 4 of 12
Table 2: Calculation of 𝑹𝑻𝒐𝒕𝒂𝒍 and the Total Thermal Mass for Example 1
Description
Indoor
Vertical
Surface
Resistance
SandCement
Plaster
SandCement
Block
Extruded
Polystyrene*
Sand Lime
Brick
Outdoor
Surface
Resistance
Thickness
(inches)
Density
(lb/ft3)
Thermal
Resistance
(ft2٠°F٠h/Btu)
Specific
Heat
(Btu/lb٠°F)
Thermal Mass
(Btu/h٠ft2٠°F)
-
-
0.68
-
-
2 ÷ 2.54 =
0.79
111.9
0.79 * 0.25 =
0.2
0.2
0.79 * 1.87 =
1.48
20 ÷ 2.54 =
7.87
126
7.87 * 0.16 =
1.26
0.19
7.87 * 2 =
15.7
5 ÷ 2.54 =
1.97
11 ÷ 2.54 =
4.33
-
1.3
111.9
4.5 * 1.97 =
8.87
0.12 * 4.33 =
0.52
0.35
0.21
1.97 * 0.04 =
0.08
4.33 * 1.96 =
8.49
-
0.25
-
-
𝑅$%&'(
11.78
ft2٠°F٠h/Btu
Total
Thermal
Mass
25.75
Btu/h٠ft2٠°F
* Density of extruded polystyrene is not given therefore take the lowest
density as a precaution.
𝑅$%&'( = 𝑅*'+,- ! + 𝑅*'+,- 0 + 𝑅*'+,- 1 + 𝑅*'+,- 2 + 𝑅*'+,- 3 + 𝑅*'+,- S
𝑈=
𝑈=
1
𝑅$%&'(
1
11.78
𝑈 = 0.085
Check with the latest R6 to see whether the U-value of the surface is within
the limit. If not, add/increase the thermal insulation.
Page 5 of 12
Steps for the checking procedure
1. Open the latest R6 and search for the below given table, “Maximum
Allowable U-values for Different Types of Walls and Roofs.”
Table 6.1 Maximum Allowable U-values for Different Types of Walls and Roofs.
Description
Very light construction,
Light construction,
Medium construction (3)
Heavy construction,
Walls, columns and Beams
Thermal
U-value(2)
Mass(1)
< 50
≤ 0.227
(<2.4)
≤ (0.04)
50 - 220
≤ 0.369
(2.4 - 10.8)
≤ (0.065)
221 – 440
≤ 0.439
(10.9 - 21.5)
≤ (0.070)(4)
> 440
≤ 0.483
> (21.5)
≤ (0.080)
Roof
Thermal
U-value(2)
Mass(1)
< 25
≤ 0.155
(<1.2)
≤ (0.027)
25 – 110
≤ 0.170
(1.2 - 5.4)
≤ (0.03)
111 – 220
≤ 0.199
(5.5 - 10.8)
≤ (0.035)
> 220
≤0.256
> (10.8)
≤ (0.045)(5)
Notes:(1) Figures are given in kJ/m2.°C (Btu/ft2٠°F).
(2) Figures are given in W/m2.°C (Btu/h٠ft2٠°F).
(3) Walls built with AAC white Azel block are categorized as medium construction.
(4) Achievable for walls using 30 cm-thick white aerated blocks with density of ≤ 500
kg/m3 and conductivity k ≤ 0.93 Btu.in/ft2.h.°F
2. Calculate the total thermal mass of wall that is being checked.
3. So, from “Table 1: Calculation of RTotal and the Total Thermal Mass
for Example 1” the total thermal mass is 25.75 Btu/h٠ft2٠°F
4. From “Table 6.1 Maximum Allowable U-values for Different Types
of Walls and Roofs.” it indicates that this wall construction is
considered Heavy therefore the Max. U-value is 0.080 Btu/h٠ft2٠°F
5. From our calculation the U-value is 0.085 Btu/h٠ft2٠°F which is
greater than 0.080 Btu/h٠ft2٠°F
6. Therefore, the thermal insulation of the wall must increase.
7. So, add 1 more inches of insulation and recalculate the RTotal and the
Total Thermal Mass
Page 6 of 12
Table 3: Recalculation of 𝑹𝑻𝒐𝒕𝒂𝒍 and the Total Thermal Mass for Example 1
Description
Indoor
Vertical
Surface
Resistance
SandCement
Plaster
SandCement
Block
Extruded
Polystyrene*
Sand Lime
Brick
Outdoor
Surface
Resistance
Thickness
(inches)
Density
(lb/ft3)
Thermal
Resistance
(ft2٠°F٠h/Btu)
Specific
Heat
(Btu/lb٠°F)
Thermal Mass
(Btu/h٠ft2٠°F)
-
-
0.68
-
-
0.79
111.9
0.2
0.2
1.48
7.87
126
1.26
0.19
15.7
1.97+1 =
2.97
1.3
4.5 * (2.97) =
13.37
0.35
(2.97) * 0.04 =
0.12
4.33
111.9
0.52
0.21
8.49
-
-
0.25
-
-
Total
25.79
Thermal
Btu/h٠ft2٠°F
Mass
* Density of extruded polystyrene is not given therefore take the lowest density as a
precaution.
𝑅$%&'( = 𝑅*'+,- ! + 𝑅*'+,- 0 + 𝑅*'+,- 1 + 𝑅*'+,- 2 + 𝑅*'+,- 3 + 𝑅*'+,- S
𝑅$%&'(
16.28
ft2٠°F٠h/Btu
𝑈=
𝑈=
1
𝑅$%&'(
1
16.28
𝑈 = 0.061
8. From the additional thermal insulation, the wall is now within R6
limits.
Page 7 of 12
Example # 2:
Figure 2: Roof layers
Page 8 of 12
Table 4: Calculation of 𝑹𝑻𝒐𝒕𝒂𝒍 and the Total Thermal Mass for Example 2
Description
Thickness Density
(inches)
(lb/ft3)
Outdoor
Surface
Resistance
Sand Cement 2 ÷ 2.54 =
Roofing Tile
0.79
2 ÷ 2.54 =
Mortar Bed
0.79
Elastomeric
Waterproofi
ng on
Bituminous
Primer
Sand Cement 2 ÷ 2.54 =
Screed
0.79
Foamed
Concrete 2%
5 ÷ 2.54 =
Slope (5 cm
1.97
at lowest
point)
1000 Gauge
Polythene
Sheet
Extruded
5 ÷ 2.54 =
Polystyrene*
1.97
Concrete
12 ÷ 2.54
Slab
= 4.72
Indoor
Horizontal
Surface
Resistance
111.9
116
Thermal
Resistance
(ft2٠°F٠h/Bt
u)
Specific
Heat
(Btu/lb٠°F)
Thermal Mass
(Btu/h٠ft2٠°F)
0.25
-
-
0.2
0.79 * 1.87 =1.48
0.2
0.79 * 1.93= 1.52
0.79 * 1 =
0.79
0.79 * 0.25 =
0.20
-
0.29
-
-
111.9
0.79 * 0.25 =
0.20
0.2
0.79 * 1.87 = 1.48
70
1.97 * 1.02 =
2.01
0.2
1.97 * 1.17 = 2.30
-
-
-
-
1.3
4.5 * 1.97 =
8.87
0.1 * 4.72 =
0.47
0.35
0.04 * 1.97 = 0.08
0.2
4.72 * 2.33 = 11.00
0.92
-
-
140
-
Total
17.86
𝑅$%&'(
Thermal
Btu/h٠ft2٠°F
Mass
* Density of extruded polystyrene is not given therefore take the lowest density as a
precaution.
14.00
ft2٠°F٠h/Btu
𝑈=
𝑈=
1
𝑅$%&'(
1
14.00
Page 9 of 12
𝑈 = 0.071
Check with the latest R6 to see whether the U-value of the surface is within
the limit. If not, add/increase the thermal insulation.
Steps for the checking procedure
1. Open the latest R6 and search for the below given table, “Maximum
Allowable U-values for Different Types of Walls and Roofs.”
Table 6.1 Maximum Allowable U-values for Different Types of Walls and Roofs.
Description
Very light construction,
Light construction,
Medium construction (3)
Heavy construction,
Walls, columns and Beams
Thermal
U-value(2)
Mass(1)
< 50
≤ 0.227
(<2.4)
≤ (0.04)
50 - 220
≤ 0.369
(2.4 - 10.8)
≤ (0.065)
221 – 440
≤ 0.439
(10.9 - 21.5)
≤ (0.070)(4)
> 440
≤ 0.483
> (21.5)
≤ (0.080)
Roof
Thermal
U-value(2)
Mass(1)
< 25
≤ 0.155
(<1.2)
≤ (0.027)
25 – 110
≤ 0.170
(1.2 - 5.4)
≤ (0.03)
111 – 220
≤ 0.199
(5.5 - 10.8)
≤ (0.035)
> 220
≤0.256
> (10.8)
≤ (0.045)(5)
Notes:(1) Figures are given in kJ/m2.°C (Btu/ft2٠°F).
(2) Figures are given in W/m2.°C (Btu/h٠ft2٠°F).
(3) Walls built with AAC white Azel block are categorized as medium construction.
(4) Achievable for walls using 30 cm-thick white aerated blocks with density of ≤ 500
kg/m3 and conductivity k ≤ 0.93 Btu.in/ft2.h.°F
2. Calculate the total thermal mass of roof that is being checked.
3. So, from “Table 1: Calculation of RTotal and the Total Thermal Mass
for Example 2” the total thermal mass is 17.86 Btu/h٠ft2٠°F
4. From “Table 6.1 Maximum Allowable U-values for Different Types
of Walls and Roofs.” it indicates that this roof construction is
considered Heavy construction therefore the Max. U-value is 0.045
Btu/h٠ft2٠°F
From our calculation the U-value is 0.071 Btu/h٠ft2٠°F which is
greater than 0.045 Btu/h٠ft2٠°F
5. Therefore, the thermal insulation of the roof must increase.
Page 10 of 12
6. So, add 2 more inches of insulation and recalculate the RTotal and the
Total Thermal Mass
Table 5: Recalculation of 𝑹𝑻𝒐𝒕𝒂𝒍 and the Total Thermal Mass for Example 2
Description
Outdoor
Surface
Resistance
Sand-Cement
Roofing Tile
Mortar bed
Elastomeric
Waterproofing
on
Bituminous
Primer
Sand -Cement
Screed
Foamed
Concrete 2%
Slope (5 cm at
lowest point)
1000 Gauge
Polythene
Sheet
Extruded
Polystyrene*
Concrete Slab
Indoor
Horizontal
Surface
Resistance
Thickness
(inches)
Density
(lb/ft3)
Thermal
Resistance
(ft2٠°F٠h/Btu)
Specific
Heat
(Btu/lb٠°F)
Thermal Mass
(Btu/h٠ft2٠°F)
-
-
0.25
-
-
0.79
111.9
0.79
0.2
1.48
0.79
116
0.20
0.2
1.52
-
-
0.29
-
-
0.79
111.9
0.20
0.2
1.48
1.97
70
2.01
0.2
2.30
-
-
-
-
-
1.97+2 =
3.97
4.72
1.3
0.35
140
4.5 * 3.97 =
17.87
0.47
0.2
0.04 * 3.97 =
0.16
11.00
-
-
0.92
-
-
Total
17.94
𝑅$%&'(
Thermal
Btu/h٠ft2٠°F
Mass
* Density of extruded polystyrene is not given therefore take the lowest density as a
precaution.
23.00
ft2٠°F٠h/Btu
𝑈=
1
𝑅$%&'(
𝑈=
1
23
𝑈 = 0.043
Page 11 of 12
7. From the additional thermal insulation, the roof is now within R6
limits
For More Clarifications Contact
Design and Supervision Department
The Technical Services Sector
Page 12 of 12