> For the complete documentation index, see [llms.txt](https://docs.betterbuilding.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.betterbuilding.io/support-and-training/other-support/testing-and-verification/system-total-r-value-calculations-cibse-guide-a.md).

# 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

{% hint style="danger" %}
*Note: Currently unavailable in Better Building*
{% endhint %}

#### Option 2: Thermally Improved Wall

<figure><img src="/files/ANQLBGPn7dcPzVnT7yj1" alt=""><figcaption></figcaption></figure>

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

<figure><img src="/files/YeFp7qgGu4mSnXC8d7x9" alt=""><figcaption></figcaption></figure>

#### 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 parameter&#x73;**:**

| 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         |


---

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