Buildup | Dew Point & R-Value Calculator

Understanding the Physics

This tool models steady-state 1D heat flow and vapor pressure through a specified wall assembly to predict condensation risks. Before launching the application, review the core mathematical models and underlying assumptions that drive the analysis.

1. Thermal Resistance (R-value)

The foundational metric is the R-value, measuring a material's resistance to heat flow. For a single layer, it is calculated as thickness divided by thermal conductivity:

\[ R = \frac{d}{k} \]

\( R \) = Thermal resistance (\( m^2 \cdot K / W \))
\( d \) = Thickness of the material in meters (\( m \))
\( k \) = Thermal conductivity (\( W / (m \cdot K) \))

The total thermal resistance of an assembly includes the sum of all layers plus interior and exterior surface film resistances (\( R_{si} \) and \( R_{se} \)):

\[ R_{total} = R_{si} + R_1 + R_2 + \dots + R_n + R_{se} \]

2. The Temperature Gradient

To find the dew point, the model calculates the exact temperature at every interface between material layers. The temperature drop across any given layer is proportional to its R-value relative to the total R-value of the assembly.

The temperature at any given interface (\( T_x \)) is:

\[ T_x = T_{x-1} - \left( \frac{R_x}{R_{total}} \times (T_{inside} - T_{outside}) \right) \]

3. Calculating the Dew Point

The application uses the Magnus-Tetens approximation to determine saturation vapor pressure and dew point. First, we calculate the Saturation Vapor Pressure (\( P_s \)) for a given temperature (\( T \) in °C):

\[ P_s(T) = 6.1078 \times \exp\left(\frac{17.27 \times T}{T + 237.3}\right) \]

Next, we determine the Actual Vapor Pressure (\( P_a \)) using the relative humidity (\( RH \)):

\[ P_a = P_s(T_{air}) \times RH \]

Finally, we reverse the Magnus formula to find the precise Dew Point Temperature (\( T_{dp} \)):

\[ T_{dp} = \frac{237.3 \times \ln(P_a / 6.1078)}{17.27 - \ln(P_a / 6.1078)} \]

Note: When the calculated temperature at any interface drops below this \( T_{dp} \) threshold, condensation is predicted to occur.

Key Assumptions & Limitations

Steady-State 1D Heat Flow

Assumes constant indoor and outdoor temperatures and models heat moving in a single straight line. Does not account for thermal bridging unless specifically averaged into a layer.

No Air Leakage

Calculations assume a perfectly airtight assembly. In real-world scenarios, convective moisture transport (air leaks) can deposit far more moisture than vapor diffusion.

Standard Surface Resistance

Static values are used for interior and exterior surface resistances, which do not account for localized wind speeds or microclimates.

Homogeneous Materials

Material properties (like thermal conductivity) are assumed to be uniform throughout the layer and do not degrade as moisture content increases.