System Total R-value Calculations (CIBSE Guide A)

The Better Building Floor System R-Value calculation approach has been derived from CIBSE Guide A Section 3.5 Ground Floors and Basements. The system calculates thermal resistance (R-value, in m²·K·W⁻¹), which is the inverse of thermal transmittance (U-value, in W·m⁻²·K⁻¹).

Floor Classification

Following the guidelines of CIBSE Guide A, there are four floor configurations:

• Ground Contact with edge insulation (Section 3.5.3, Equation 3.22)

• Ground Contact without edge insulation (Section 3.5.2, Equation 3.21)

• Suspended Floor - insulated (Section 3.5.5.2, Equation 3.31)

• Suspended Floor - uninsulated (Section 3.5.5.1, Table 3.20 or Equations 3.28-3.30)

Calculation Procedure

The calculation follows this hierarchical approach:

1. Initialise as ground contact floor - establish base parameters

2. Collect relevant components for the specific floor type

3. Check for edge insulation or suspension - determine if CIBSE Equation 3.22 (edge insulated) or Equations 3.28-3.31 (suspended) apply

4. Apply appropriate calculation method to determine the final U-value, then convert to R-value (R = 1/U)

Parameter Collection

Ground Contact Parameters

Required Inputs

All floor types require the following fundamental inputs:

Parameter	Symbol	Unit	CIBSE Reference
Floor area	A_fg	m²	Equation 3.19
Floor perimeter (exposed)	p_f	m	Equation 3.19
Ground thermal conductivity	λ_g	W·m⁻¹·K⁻¹	Table 3.17
Surrounding wall thickness	d_w	m	Equation 3.23
Floor thermal resistance	R_f	m²·K·W⁻¹	Section 3.3

Critical Definitions

Characteristic Dimension (B′)

CIBSE Equation 3.19:

B′ = A_fg / (0.5 × p_f)

Where:

• B′ = characteristic dimension of the floor (m)

• A_fg = floor area (m²)

• p_f = exposed perimeter of floor (m) - includes only perimeter exposed to external (unconditioned) conditions

Floor Thermal Resistance (R_f)

• For ground contact floors: Includes only continuous insulation layers above, below, or within the floor slab, excluding the structural slab itself and surface resistances (CIBSE Section 3.5.2)

• Surface resistances (R_si and R_se) are handled separately in the U-value calculation

Total Equivalent Thickness (d_ef)

d_ef = d_w + λ_g × (R_si + R_f + R_se)

Where:

• d_ef = total equivalent thickness (m)

• d_w = thickness of wall surrounding the floor (m)

• λ_g = thermal conductivity of ground (W·m⁻¹·K⁻¹)

• R_si = 0.17 m²·K·W⁻¹ (internal surface resistance)

• R_f = thermal resistance of floor insulation (m²·K·W⁻¹)

• R_se = 0.04 m²·K·W⁻¹ (external surface resistance)

Edge Insulation Parameters

Edge insulation is evaluated via two mechanisms per CIBSE Equation 3.22:

Option 1: Direct Edge Insulation

Horizontal or vertical insulation applied at the floor perimeter, characterized by:

• Edge insulation width (D) or depth (D′), in metres

• Edge insulation thermal resistance (R_n), in m²·K·W⁻¹

Note: Currently unavailable in Better Building

Option 2: Thermally Improved Wall

The surrounding wall provides edge insulation effect when:

λ_w < λ_g

Where:

• λ_w = thermal conductivity of wall (W·m⁻¹·K⁻¹)

• λ_g = thermal conductivity of ground (W·m⁻¹·K⁻¹)

Collected Parameters

• Wall thermal resistance (R_w) in m²·K·W⁻¹

• Wall thickness (d_w) in m

• Wall depth below ground (D′) in m - as shown above.

Equivalent Edge Insulation Width

D_eq = λ_g × R_w

This check is automatically performed for all non-suspended floors.

Suspended Floor Parameters

Floor Classification Criteria

A floor is classified as suspended when the user specifies:

h_f > 0 m

Where h_f = height of floor above external ground level (m), as shown above.

Additional Required Inputs

Per CIBSE Equation 3.30:

Parameter	Symbol	Unit	Typical Values
Wind speed at 10m height	v_w	m·s⁻¹	3 m·s⁻¹ (UK average)
Wind shielding factor	f_w	-	0.02 (sheltered), 0.05 (suburban), 0.10 (exposed)
Ventilation opening area per unit perimeter	α	m²·m⁻¹	0.0015 or 0.003
Wall U-value (underfloor space)	U_u	W·m⁻²·K⁻¹	1.7 (uninsulated masonry)
Height of floor above ground	h_f	m	Typically 0.5 m

Suspended Floor Types

Uninsulated Suspended Floor

Reference: CIBSE Table 3.20 or Equations 3.28-3.30

• Calculate U_fs using combined thermal transmittance approach

• Floor thermal resistance (R_f) treated as center-of-panel calculation

• Include surface resistances: R_si = R_se = 0.17 m²·K·W⁻¹ on both sides

• U_f calculated from: U_f = 1 / (R_si + R_f + R_se)

Insulated Suspended Floor

Reference: CIBSE Equation 3.31

• First calculate uninsulated U_fs (as above, assuming R_f = 0.2 m²·K·W⁻¹)

• Then apply actual floor thermal resistance

• Floor R_f calculated as thermally-bridged assembly per AS/NZS 4859.2:2018

• Exclude surface resistances from R_f (these are accounted for in Equation 3.31)

• Final U_fsi calculated per Equation 3.31

---

Complete CIBSE Equations

Ground Contact Floor Equations

Equation 3.21: Ground Contact (No Edge Insulation)

U_g = (2λ_g) / (πB′ + d_ef) + 1100 × A_fg / p_f²

Where:

• U_g = thermal transmittance of ground floor (W·m⁻²·K⁻¹)

• λ_g = thermal conductivity of ground (W·m⁻¹·K⁻¹)

• B′ = characteristic dimension (m) from Equation 3.19

• d_ef = total equivalent thickness (m)

• A_fg = floor area (m²)

• p_f = exposed perimeter (m)

R-value conversion:

R = 1 / U_g

Equation 3.22: Ground Contact with Edge Insulation

U = (2λ_g) / [πB′ + d_ef + λ_g × Ψ_ge] + 1100 × A_fg / p_f²

Where all parameters are as Equation 3.21, plus:

• Ψ_ge = linear thermal transmittance for edge insulation (m)

Equation 3.23: Horizontal Edge Insulation

Ψ_ge = -0.5 × ln[1 + (D / (d_ef + 0.5λ_g × R_n))]

Where:

• D = width of horizontal edge insulation (m)

• R_n = thermal resistance of edge insulation per unit area (m²·K·W⁻¹)

• d_ef = total equivalent thickness as before (m)

• λ_g = thermal conductivity of ground (W·m⁻¹·K⁻¹)

Equation 3.24: Vertical Edge Insulation

Ψ_ge = -0.5 × ln[1 + (D′ / (d_ef + 0.5λ_g × R_n))]

Where:

• D′ = depth of vertical edge insulation below floor level (m)

• Other parameters as above

Low Conductivity Foundation Wall

For walls shown in Figure 3.12:

D′ = depth of wall below ground
R_n = R_w (thermal resistance of wall)

Suspended Floor Equations

Equation 3.28: Combined Thermal Transmittance

U_fs = [(1 / U_f) + 1 / (U_fg + U_eu)]⁻¹

Where:

• U_fs = combined thermal transmittance of uninsulated suspended floor (W·m⁻²·K⁻¹)

• U_f = thermal transmittance of the floor itself (W·m⁻²·K⁻¹)

• U_fg = thermal transmittance for heat flow through ground (W·m⁻²·K⁻¹)

• U_eu = equivalent thermal transmittance for wall and ventilation losses (W·m⁻²·K⁻¹)

---

Equation 3.29: Equivalent Ground Thickness (Suspended Floors)

d_eg = d_w + λ_g × (R_si + R_ig + R_se)

Where:

• d_eg = total equivalent thickness of ground for suspended floor (m)

• d_w = thickness of wall surrounding floor (m)

• λ_g = thermal conductivity of ground (W·m⁻¹·K⁻¹)

• R_si = internal surface resistance = 0.17 m²·K·W⁻¹

• R_ig = thermal resistance of insulation between floor and ground (m²·K·W⁻¹) - typically 0 for uninsulated

• R_se = external surface resistance = 0.17 m²·K·W⁻¹ (note: 0.17 for both sides in suspended floor)

Equation 3.30: Wall and Ventilation Losses

U_eu = (2 × h_f × U_u) / B′ + (1450 × α × v_w × f_w) / B′

Where:

• U_eu = equivalent thermal transmittance for walls and ventilation (W·m⁻²·K⁻¹)

• h_f = height of floor above external ground level (m)

• U_u = thermal transmittance of walls surrounding underfloor space (W·m⁻²·K⁻¹)

• B′ = characteristic dimension (m)

• α = area of ventilation openings per unit perimeter (m²·m⁻¹)

• v_w = average wind speed at 10 m height (m·s⁻¹)

• f_w = wind shielding factor (dimensionless)

Wind Shielding Factor (f_w) Values

• Sheltered location (city centre): f_w = 0.02

• Average location (suburban): f_w = 0.05

• Exposed location (rural): f_w = 0.10

Floor Thermal Transmittance (U_f) for Uninsulated Suspended Floors

For uninsulated suspended floors, surface resistances are applied to both sides:

U_f = 1 / (R_si + R_f + R_se)

Where R_si = R_se = 0.17 m²·K·W⁻¹

Ground Thermal Transmittance (U_fg) for Suspended Floors

Calculate using Equation 3.21 format but with d_eg from Equation 3.29 substituted for d_ef:

U_fg = (2λ_g) / (πB′ + d_eg) + 1100 × A_fg / p_f²

Equation 3.31: Insulated Suspended Floor

U_fsi = [(1 / U_fs) - 0.2 + R_f]⁻¹

Where:

• U_fsi = thermal transmittance of insulated suspended floor (W·m⁻²·K⁻¹)

• U_fs = combined thermal transmittance of uninsulated floor from Equation 3.28 (W·m⁻²·K⁻¹)

• R_f = thermal resistance of actual floor excluding surface resistances (m²·K·W⁻¹)

• 0.2 = assumed thermal resistance used in standard uninsulated calculation (m²·K·W⁻¹)

Calculation Procedure

1. Calculate U_fs using Equations 3.28-3.30 with R_f = 0.2 m²·K·W⁻¹

2. Calculate actual R_f for the insulated floor (excluding surface resistances)

3. Apply Equation 3.31 to determine U_fsi

4. Convert to R-value: R = 1 / U_fsi

Thermal Bridging Calculations

Bridged Thermal Resistance

For thermally bridged floors (e.g., timber joists with insulation between):

R_b = [(P_m / R_m) + (P_n / R_n)]⁻¹

Where:

• R_b = combined thermal resistance of bridged section (m²·K·W⁻¹)

• P_m = proportion of area occupied by insulation (dimensionless)

• R_m = thermal resistance of insulation section (m²·K·W⁻¹)

• P_n = proportion of area occupied by structural members (dimensionless)

• R_n = thermal resistance of structural section (m²·K·W⁻¹)

Note: P_m + P_n = 1

Total Floor Resistance

R_f = R_surface_layers + R_b

As calculated per AS/NZS 4859.2:2018 methodology, excluding surface resistances.

CIBSE Table 3.20: U-values for Uninsulated Suspended Floors

Table Assumptions

This table provides U-values for uninsulated suspended floors based on the following fixed parameters:

Parameter	Value	Unit
Thermal resistance of floor	R_f = 0.2	m²·K·W⁻¹
Average wind velocity	v_w = 3	m·s⁻¹
Wind shielding factor	f_w = 0.05	-
Wall U-value (underfloor space)	U_u = 1.7	W·m⁻²·K⁻¹
Height of floor above ground	h_f = 0.5	m
Exposure	Average (suburban)	-

Table 3.20 Data

U-values (W·m⁻²·K⁻¹) for stated soil type and ventilation opening

Ratio p_f / A_fg (m⁻¹)	Clay/silt		Sand/gravel		Homogeneous rock
	α = 0.0015	α = 0.003	α = 0.0015	α = 0.003	α = 0.0015	α = 0.003
0.05	0.16	0.17	0.19	0.20	0.27	0.28
0.10	0.27	0.29	0.32	0.33	0.43	0.44
0.15	0.36	0.38	0.42	0.43	0.54	0.55
0.20	0.44	0.46	0.49	0.51	0.63	0.64
0.25	0.50	0.52	0.56	0.58	0.70	0.71
0.30	0.56	0.58	0.62	0.64	0.76	0.77
0.35	0.61	0.63	0.67	0.69	0.81	0.82
0.40	0.65	0.68	0.72	0.74	0.85	0.87
0.45	0.69	0.72	0.76	0.78	0.89	0.91
0.50	0.73	0.76	0.79	0.82	0.92	0.94
0.55	0.76	0.79	0.83	0.85	0.95	0.97
0.60	0.79	0.83	0.86	0.88	0.98	1.00
0.65	0.82	0.85	0.88	0.91	1.00	1.02
0.70	0.85	0.88	0.91	0.94	1.03	1.05
0.75	0.87	0.91	0.93	0.96	1.05	1.07
0.80	0.90	0.93	0.95	0.98	1.06	1.09
0.85	0.92	0.95	0.97	1.00	1.08	1.11
0.90	0.94	0.97	0.99	1.02	1.10	1.12
0.95	0.96	0.99	1.01	1.04	1.11	1.14
1.00	0.98	1.01	1.03	1.06	1.13	1.15

Note: The row for p_f/A_fg = 0.45 is highlighted in bold as this value is used in the worked example below.

Using Table 3.20

Step-by-Step Procedure

1. Calculate the perimeter-to-area ratio:

   p_f / A_fg = exposed perimeter (m) / floor area (m²)

2. Identify the soil type:

   • Clay/silt

   • Sand/gravel

   • Homogeneous rock

3. Determine ventilation opening area:

   • α = 0.0015 m²·m⁻¹ (standard ventilation)

   • α = 0.003 m²·m⁻¹ (increased ventilation)

4. Look up U_fs value from the appropriate column and row

5. For insulated floors: Use the looked-up U_fs in Equation 3.31

Interpolation Guidelines

If your calculated p_f/A_fg ratio falls between table values:

• Linear interpolation is acceptable for intermediate values

• For greater accuracy, use the full equations (3.28-3.30)

Example Lookup

For the worked example:

• p_f/A_fg = 0.45 m⁻¹

• Soil: Clay/silt

• Ventilation: α = 0.0015 m²·m⁻¹

• Result: U_fs = 0.69 W·m⁻²·K⁻¹

Calculation Methodology

Decision Flowchart

Step 1: Determine Floor Type

Is h_f > 0?
├─ NO → Ground Contact Floor
│   └─ Is λ_w < λ_g OR is edge insulation present?
│       ├─ YES → Use Equation 3.22 (with edge insulation)
│       └─ NO → Use Equation 3.21 (no edge insulation)
│
└─ YES → Suspended Floor
    └─ Is R_f > 0.2?
        ├─ NO → Use Table 3.20 or Equations 3.28-3.30 (uninsulated)
        └─ YES → Use Equation 3.31 with Table 3.20 lookup (insulated)

---

Ground Contact Floors

Method 1: No Edge Insulation

1. Calculate B′ using Equation 3.19

2. Calculate d_ef: d_ef = d_w + λ_g × (0.17 + R_f + 0.04)

3. Calculate U_g using Equation 3.21

4. Convert: R = 1 / U_g

Method 2: With Edge Insulation

1. Calculate B′ using Equation 3.19

2. Calculate d_ef as above

3. Calculate Ψ_ge using Equation 3.23 or 3.24 (or equivalent for low-conductivity wall)

4. Calculate U using Equation 3.22

5. Convert: R = 1 / U

---

Suspended Floors

Method 3: Uninsulated Suspended Floor

Option A: Using Table 3.20 (if parameters match)

1. Calculate p_f / A_fg ratio

2. Look up U_fs from Table 3.20

3. Convert: R = 1 / U_fs

Option B: Using Full Equations (if parameters differ)

1. Calculate B′ using Equation 3.19

2. Calculate d_eg using Equation 3.29 (typically R_ig = 0)

3. Calculate U_fg using Equation 3.21 format with d_eg

4. Calculate U_eu using Equation 3.30

5. Calculate U_f = 1 / (0.17 + R_f + 0.17)

6. Calculate U_fs using Equation 3.28

7. Convert: R = 1 / U_fs

Method 4: Insulated Suspended Floor

1. Obtain U_fs for uninsulated case using Table 3.20 or Equations 3.28-3.30 (with R_f = 0.2)

2. Calculate actual R_f (thermally-bridged if applicable, excluding surface resistances)

3. Apply Equation 3.31 to determine U_fsi

4. Convert to R-value: R = 1 / U_fsi

Technical Implementation Notes

Surface Resistance Treatment

Floor Type	Internal (R_si)	External (R_se)	Application Method
Ground contact	0.17	0.04	Included in d_ef calculation
Suspended uninsulated	0.17	0.17	Included in U_f calculation
Suspended insulated	-	-	Handled by Equation 3.31 adjustment factor

Thermal Bridging Considerations

Ground Contact Floors

• Not typically considered

• Continuous insulation assumed in R_f

• Structural elements ignored in thermal resistance calculation

Suspended Insulated Floors

• Must calculate bridged R_b for joists/beams

• Use AS/NZS 4859.2:2018 methodology

• Account for proportion of structural elements vs. insulation

---

Perimeter Definition Guidelines

What to Include

• All perimeter exposed to unconditioned space

• External walls

• Walls to unheated spaces

What to Exclude

• Party walls between conditioned spaces

• Internal divisions within heated area

• Walls to heated adjacent rooms

Measurement Location

• Measure at floor level

• Not at foundation level

• Use internal dimensions

Table 3.20 Usage Guidelines

When to Use Table 3.20

Use the lookup table when ALL of these conditions are met:

• R_f = 0.2 m²·K·W⁻¹

• α = 0.0015 or 0.003 m²·m⁻¹

• v_w = 3 m·s⁻¹

• f_w = 0.05 (suburban exposure)

• U_u = 1.7 W·m⁻²·K⁻¹

• h_f = 0.5 m

• Soil type matches one of the three columns

When to Use Full Equations

Use Equations 3.28-3.30 when parameters differ significantly from table assumptions:

• Different floor heights (h_f ≠ 0.5 m)

• Different exposures (f_w ≠ 0.05)

• Different wind speeds (v_w ≠ 3 m·s⁻¹)

• Different ventilation rates (α not 0.0015 or 0.003)

• Different wall constructions (U_u ≠ 1.7 W·m⁻²·K⁻¹)

• Non-standard floor thermal resistance (R_f ≠ 0.2)

Unit Conversions

U-value to R-value

R (m²·K·W⁻¹) = 1 / U (W·m⁻²·K⁻¹)

Examples

U-value (W·m⁻²·K⁻¹)	R-value (m²·K·W⁻¹)
0.20	5.00
0.30	3.33
0.50	2.00
0.69	1.45
1.00	1.00

Worked Example

Example: Insulated Suspended Timber Floor

Given Parameters

Floor Geometry:

• Dimensions: 9.5 m × 8.2 m

• Construction type: Suspended timber floor

Floor Construction:

• 19 mm chipboard (λ = 0.14 W·m⁻¹·K⁻¹)

• 50 mm × 100 mm joists at 400 mm centers (λ = 0.14 W·m⁻¹·K⁻¹)

• 100 mm insulation between joists (λ = 0.04 W·m⁻¹·K⁻¹)

Site Conditions:

• Ventilation: α = 0.0015 m²·m⁻¹

• Soil type: Clay

• Exposure: Average (suburban)

Step 1: Calculate Floor Parameters

A_fg = 9.5 × 8.2 = 77.9 m²
p_f = 2(9.5 + 8.2) = 35.4 m
p_f / A_fg = 35.4 / 77.9 = 0.45 m⁻¹

Step 2: Obtain U_fs from Table 3.20

Lookup parameters:

• Clay/silt soil

• α = 0.0015 m²·m⁻¹

• p_f/A_fg = 0.45 m⁻¹

From Table 3.20:

U_fs = 0.69 W·m⁻²·K⁻¹

Note: Since all parameters match the table assumptions (h_f = 0.5 m, v_w = 3 m·s⁻¹, f_w = 0.05, U_u = 1.7 W·m⁻²·K⁻¹), we can use the table lookup directly.

Step 3: Calculate Actual Floor Resistance

Chipboard Layer

R_chipboard = thickness / λ
R_chipboard = 0.019 / 0.14
R_chipboard = 0.136 m²·K·W⁻¹

Bridged Section (Joists + Insulation)

Insulation path:

P_m = 350/400 = 0.875 (proportion)
R_m = 0.1/0.04 = 2.5 m²·K·W⁻¹

Joist path:

P_n = 50/400 = 0.125 (proportion)
R_n = 0.1/0.14 = 0.714 m²·K·W⁻¹

Combined bridged resistance:

R_b = [(P_m/R_m) + (P_n/R_n)]⁻¹
R_b = [(0.875/2.5) + (0.125/0.714)]⁻¹
R_b = [0.350 + 0.175]⁻¹
R_b = [0.525]⁻¹
R_b = 1.90 m²·K·W⁻¹

Total Floor Resistance

R_f = R_chipboard + R_b
R_f = 0.136 + 1.90
R_f = 2.04 m²·K·W⁻¹

Step 4: Apply Equation 3.31

U_fsi = [(1/U_fs) - 0.2 + R_f]⁻¹
U_fsi = [(1/0.69) - 0.2 + 2.04]⁻¹
U_fsi = [1.449 - 0.2 + 2.04]⁻¹
U_fsi = [3.289]⁻¹
U_fsi = 0.304 W·m⁻²·K⁻¹

Final Result

U-value:

U_fsi = 0.30 W·m⁻²·K⁻¹ (rounded)

R-value:

R = 1 / 0.304
R = 3.29 m²·K·W⁻¹

Quick Reference Summary

Equation Selection Guide

Floor Type	h_f	Edge Insulation	Equation/Table to Use
Ground contact, no edge insulation	0	No	3.21
Ground contact, with edge insulation	0	Yes	3.22 + 3.23/3.24
Suspended, uninsulated	>0	N/A	Table 3.20 or 3.28-3.30
Suspended, insulated	>0	N/A	3.31 (uses Table 3.20 or 3.28-3.30)

Key Parameter Values

Parameter	Symbol	Typical Value	Unit
Internal surface resistance	R_si	0.17	m²·K·W⁻¹
External surface resistance (ground)	R_se	0.04	m²·K·W⁻¹
External surface resistance (suspended)	R_se	0.17	m²·K·W⁻¹
Wind speed	v_w	3	m·s⁻¹
Wind shielding (suburban)	f_w	0.05	-
Ventilation opening	α	0.0015 or 0.003	m²·m⁻¹
Underfloor wall U-value	U_u	1.7	W·m⁻²·K⁻¹
Floor height	h_f	0.5	m