Thermal bridges are paths of least resistance that allow heat to flow through a building envelope more readily than through surrounding insulated areas. They occur at structural elements like balcony slabs, window frames, or metal fasteners that penetrate insulation layers. This calculator estimates the seasonal energy loss associated with such bridges using the linear transmittance, or psi-value, combined with the component length, temperature difference, and heating season duration. The governing equation is , where represents heat in watt-hours, is the linear thermal transmittance in watts per meter-kelvin, the length in meters, the temperature difference in kelvins, and the time in hours.
While entire wall assemblies may boast low U-values, localized bridging can undermine their performance. For example, a reinforced concrete balcony that extends through exterior insulation creates a direct path from interior to exterior, bypassing insulation. In cold climates this leads to significant heat loss and can form cold spots that encourage condensation and mold. Builders often install thermal break connectors or separate structural supports to minimize these effects. By inputting typical psi-values, this tool reveals how much energy a design might waste if such mitigations are ignored.
The psi-value combines material properties and geometry. It is typically derived from two- or three-dimensional heat flow simulations following standards like ISO 10211. Values can range from below 0.1 W/m·K for high-performance window frames to over 1 W/m·K for uninsulated steel beams. Because psi-values account for the difference between actual junction performance and the idealized assembly, they complement but do not replace area-based U-values. Many energy codes now require designers to include thermal bridge calculations in compliance reports, recognizing that these small linear elements can constitute a large portion of overall heat loss.
Length is straightforward: it is the total run of the bridge. For example, if a window frame extends around a perimeter of 6 meters, that length factors into the equation. Temperature difference reflects the average gradient between indoors and outdoors during the heating season. In climates with wide swings, designers may use a degree-hour approach to integrate varying conditions, but a simple average suffices for this calculator. Heating season hours represent the total number of hours when heating is active; multiplying by the other variables yields the total energy flowing through the bridge.
After calculating in watt-hours, the script converts the value to kilowatt-hours by dividing by 1,000 and multiplies by the energy cost to estimate monetary impact. This provides a clear sense of how much a single overlooked detail can cost over a winter. For example, a 0.2 W/m·K bridge spanning 5 meters, facing a 20 °C gradient for 2,000 hours, leaks = 40,000 Wh, or 40 kWh. At 15 cents per kWh, that single detail costs six dollars each season. Multiply across dozens of junctions and the losses become significant.
The sample table displays representative psi-values for common assemblies. Concrete balcony slabs, common in mid-century buildings, are notorious thermal bridges with psi-values approaching 0.85 W/m·K. Steel beam penetrations, such as those supporting canopies, can exceed 1.3 W/m·K if left uninsulated. Conversely, modern insulated window frames may achieve 0.04 W/m·K, illustrating the improvements possible through thoughtful design. Engineers can modify these values based on manufacturer data or simulation results for their specific projects.
Beyond energy loss, thermal bridges can affect structural integrity and occupant comfort. Cold spots on interior surfaces may cause interstitial condensation, promoting mold growth and damaging finishes. Thermal movement differences between bridged and unbridged regions can induce stresses that lead to cracking. In extreme cases, ice can form on exterior surfaces, posing safety hazards. By quantifying heat flow, designers can justify the cost of thermal break materials or alternative details that interrupt the conductive path.
The calculator also serves educational purposes. Students learning building science often struggle to connect abstract concepts with tangible outcomes. By experimenting with psi-values and lengths, they can see how an otherwise efficient envelope can be compromised. Environmental policymakers may use the tool to illustrate the importance of holistic design in energy codes. Homeowners retrofitting older buildings can estimate potential savings from adding thermal breaks or insulating exposed concrete.
Although this model simplifies reality by assuming constant temperatures and one-dimensional conduction, it captures the dominant variables governing linear heat loss. More advanced analyses might integrate varying outdoor temperatures, account for thermal mass, or include two-dimensional conduction at intersections of multiple bridges. Such refinements are beyond the scope of a lightweight browser tool but are handled by specialized energy simulation software. Nevertheless, the simplicity of the formula makes it accessible to non-specialists and supports quick what-if scenarios during the design process.
To use the calculator, enter the psi-value obtained from manufacturer documentation or simulation, specify the length of the thermal bridge, and provide average temperature difference and heating hours. The script instantly computes energy loss and cost, displaying results that you can copy for reports. Adjusting inputs allows you to compare design alternatives, such as adding thermal break materials or reducing bridge length. By understanding the hidden penalties of thermal bridges, you can design buildings that conserve energy, reduce operating costs, and improve comfort for occupants.