Thermal Formula Library
Thermal Formula Library
Reference formulas for R-value, RSI, U-value, U-factor, lambda, R per inch, total layers, heat loss, and unit conversions.
Reference
Thermal calculator formulas
This formula library collects the relationships used across the calculators. It is designed for quick extraction: each formula shows variables, units, a compact example, and a calculator link. The formulas assume one-dimensional heat flow unless a page explicitly describes a whole-assembly or area-weighted method.
Typical values are educational planning references. Always check local code, product documentation, and project-specific constraints.
Formula library
These formulas use the same constants as the calculators.
| Formula | Variables and units | Example | Calculator |
|---|---|---|---|
R_SI = thickness_m / lambda | thickness in m; lambda in W/mK; result m²K/W | 0.10 / 0.035 = 2.86 | Lambda to R |
R_US = R_SI * 5.678263337 | RSI to US R-value | 2.86 * 5.678263337 = R-16.2 | Lambda to R |
U_SI = 1 / R_total_SI | total SI resistance in m²K/W | 1 / 4.0 = 0.25 W/m²K | U-value |
U_factor = 1 / R_US | US R-value in h·ft²·°F/Btu | 1 / 19 = 0.0526 | R to U-factor |
R_US = 1 / U_factor | US U-factor in Btu/(h·ft²·°F) | 1 / 0.25 = R-4 | U-factor to R |
lambda = thickness_m / R_SI | thickness in m; RSI in m²K/W | 0.10 / 2.86 = 0.035 | Formula |
R_per_in = 1 / k_US | k in Btu·in/(h·ft²·°F) | 1 / 0.25 = R-4/in | k vs R |
thickness_in = target_R / R_per_in | target US R and R per inch | 38 / 3.8 = 10 in | Thickness |
R_total = Rsi + sum(R_layers) + Rse | surface and layer resistances | 0.68 + 13 + 5 + 0.17 = 18.85 | Total R |
heat_loss = U * area * deltaT | U, area, and temperature difference | 0.30 * 20 * 40 = 240 Btu/h | Window |
U_SI = U_factor * 5.678263337 | US U-factor to SI U-value | 0.0526 * 5.678 = 0.299 | R to U-value |
U_factor = U_SI / 5.678263337 | SI U-value to US U-factor | 0.25 / 5.678 = 0.0440 | U to R |
k_US = lambda * 6.93481276 | W/mK to Btu·in/(h·ft²·°F) | 0.036 * 6.9348 = 0.250 | k vs R |
Thermal calculator formulas
Example: 100 mm at lambda 0.035 W/mK gives RSI 2.86 and about R-16.2 in US units.
Typical values are educational planning references. Always check local code, product documentation, and project-specific constraints.
Practical note
How to interpret the calculator result
Thermal calculator formulas is intended for quick option checks and technical discussion before detailed execution. The result depends on the selected units, declared material values, and chosen surface resistances, so each change in layer or thickness should be treated as a separate variant.
The calculator does not automatically verify every local rule, thermal bridge, moisture condition, structural connection, or installation tolerance. If the result is close to a requirement, treat it as a reason for deeper verification rather than a final decision.
For better comparisons, test several realistic thicknesses, check current product data sheets, and review the complete assembly. A calculated value is most useful when the assumptions are clear: material, thickness, layer order, units, and data source.
For insulation or U-value tools, layer order and correct units are especially important. For concrete, electrical, plumbing, or heating tools, the result should be read as a quick quantity or plausibility check before standards and execution conditions are reviewed.
Save the result with the date, material name, and assumptions. If the product, diameter, cable section, or thickness changes later, do not compare the numbers alone without checking which inputs changed.
For calculator pages, clear separation between inputs and result is essential. If a value looks surprising, check units and default fields first, then review the project assumptions.
Assembly thickness
Assembly thickness
Use the tables and formulas to choose a sensible starting thickness before checking the exact assembly.
U-value
U-value
Keep R-value, U-factor, U-value, lambda, k-value, and unit systems separate before comparing results.
CategoryLambdaLayerMaterialThickness
How it works
Use with care
Constants match the calculator runtime: R_US = R_SI × 5.678263337 and k_US = lambda × 6.93481276.
Next step
Open the linked calculator when you need unit labels, guardrails, and worked outputs.
Thermal Formula Library
Core relation: U = 1 / R_total, with unit conversions kept explicit.
This formula library collects the relationships used across the calculators. It is designed for quick extraction: each formula shows variables, units, a compact example, and a calculator link. The formulas assume one-dimensional heat flow unless a page explicitly describes a whole-assembly or area-weighted method. Example: 100 mm at lambda 0.035 W/mK gives RSI 2.86 and about R-16.2 in US units.
Add layerRestore default setupRemove
Assembly nameThickness unitInternal Rsi (m2K/W)External Rse (m2K/W)
Calculation assumptions
The calculators use visible formulas and explicit unit conversions. Treat the result as a preliminary check, not a complete building design.
- SI and US units are converted separately; R, RSI, U-value, and U-factor are not mixed without the unit factor.
- Enter positive values and compare the result with the selected product datasheet.
- Local codes, thermal bridges, fasteners, and installation quality can change the requirement.
- Last formula review: 2026-04-27.
See how formulas, unit conversions, rounding, and limitations are handled. Methodology details.
Reference FAQ
No. They are educational references for planning, comparison, and calculator input checks.
Use typical values only for early estimates. Product labels, declarations, and local rules should override them.
R-value and U-factor are common in US practice, while lambda and U-value are common in SI reporting. The pages keep unit systems explicit.
Yes. You can print the result or export it to CSV, Excel, or PDF for reports and documentation.
Yes. It is designed for layered assemblies such as external walls, flat roofs, pitched roofs, floors, and slabs. For unusual assemblies, add every relevant layer and treat the result as a planning check before formal verification.
Yes. It is intended for fast concept-stage calculations, insulation comparison, and envelope optimisation before detailed design. It is best used to narrow choices, not to replace a code check or project-specific thermal bridge assessment.
Yes. You can switch between millimeters, centimeters, and inches, and the calculator keeps the values consistent. For fewer mistakes, choose one unit system at the start of a project and review converted thicknesses before export.
Use Thermal calculator formulas as a first-pass reference. Before specifying anything, compare the result with the R per inch, actual project dimensions, product data sheet, and local requirements.