Related tool: Insulation R-Value Calculator - estimate how many bags or rolls of a single insulation material you need to hit a target R-value for a given area.
Unit System:
Panel 1: Structural Assembly Builder

Layers are ordered from the warm (indoor) side on the left to the cold (outdoor) side on the right. Each layer's individual thermal resistance (R = thickness / k-value) is shown on the right. The calculator updates instantly as you change any value.

Panel 2: Environmental Parameters and Thermal Gradient Visualizer
Temperature Gradient Across Assembly
70 F Indoor 20 F Outdoor
Add layers in Panel 1 to see the thermal gradient.
Panel 3: Thermal Telemetry and Energy Output
Total Assembly R-Value
--
Overall U-Value
--
1 / R-total
Heat Loss Rate (Q)
--
Q = U x Area x Delta-T
Per-Layer Thermal Resistance Breakdown
Key Terms Explained
Thermal Conductivity (k-value)
A material property measuring how readily heat flows through it. Units: W/(m-K) in metric, or BTU-in/(hr-ft^2-F) in US. Low k-values (like fiberglass at 0.040 W/m-K) indicate good insulators. High k-values (like concrete at ~1.0 W/m-K) indicate efficient heat conductors.
Thermal Resistance (R-value)
A measure of a material's resistance to heat flow, calculated as R = thickness / k. Higher R-values mean better insulation. R-values are additive across layers: the total assembly R-value is the sum of every individual layer's R-value. US R-values use units of hr-ft^2-F/BTU.
Thermal Transmittance (U-value)
The rate of heat transfer through an assembly per unit area per degree of temperature difference. U-value is the inverse of total R-value: U = 1 / R-total. A lower U-value indicates a better-insulated assembly. It is used directly in the heat loss formula Q = U x A x Delta-T.
Delta T (Temperature Difference)
The driving force for heat conduction. Delta-T is the temperature difference between the warm indoor surface and the cold outdoor surface. A larger Delta-T produces proportionally more heat loss. Doubling the temperature difference doubles the heat flow rate through the same assembly.
Thermal Bridging
When a high-conductivity element (such as a steel stud, concrete tie, or fastener) runs continuously through an insulated assembly, bypassing the insulation. Steel studs can reduce effective whole-wall R-value by 30-50% compared to the cavity R-value alone. This solver models clear-field (cavity) performance, not framing-adjusted values.
Steady-State Heat Transfer
The condition in which temperature at every point in the assembly is constant over time. Heat flowing in equals heat flowing out. This solver uses the steady-state model (Fourier's law), which is the standard for design and code calculations. Real buildings cycle through transient conditions, but steady-state gives the conservative design load used for HVAC sizing.
Heat Loss Rate (Q)
The power continuously flowing through an assembly, measured in Watts (metric) or BTU/hr (US). Q = U x Area x Delta-T. This number tells you how large a heating system must be to continuously replace the energy escaping through that surface when outdoor conditions match the design temperature.
Temperature Gradient
The progressive drop in temperature from the warm side to the cold side of an assembly. Each layer drops a fraction of the total Delta-T in proportion to its share of the total R-value. A highly resistive layer (thick insulation) accounts for most of the temperature drop; a conductive layer (thin concrete) accounts for very little.

The Complete Guide to Wall and Roof Heat Loss Calculations

Whether you are an HVAC engineer sizing heating equipment, a building scientist auditing envelope performance, or a homeowner evaluating insulation upgrades, this tool gives you the complete thermal picture of any multi-layer wall or roof assembly. Understanding how each layer contributes to the total R-value and how that resistance translates into actual heat loss in watts or BTU/hr is the foundation of energy-efficient building design.

How to Use This Solver

Start in Panel 1 by building your wall or roof cross-section. Click "Add Insulation or Structural Layer" and select a material from the dropdown. Enter the layer thickness in the unit system you have chosen (inches for Imperial, meters for Metric). Add as many layers as your assembly has, ordered from the warm indoor side to the cold outdoor side. The per-layer R-value badge on the right of each row updates instantly.

In Panel 2, enter the total surface area of the assembly (for example, one wall face), and set your indoor and outdoor design temperatures. The color-coded cross-section diagram updates in real time, showing each layer colored with a gradient from warm red (indoor side) to cool blue (outdoor side). Temperature labels at each boundary show exactly how the total Delta-T is distributed across the assembly. A thicker insulation layer will capture a proportionally larger share of the temperature drop.

Panel 3 shows the summary output: total R-value, overall U-value, and the final heat loss rate in watts or BTU/hr. The per-layer breakdown table lets you see which layers contribute the most resistance and which are nearly transparent to heat flow. Use "Copy Assembly Report" to export a plain-text summary for documentation or sharing with a client.

The Physics: Fourier's Law of Heat Conduction

This tool implements 1D steady-state heat conduction. For each layer, thermal resistance is:

R_layer = d / k
d = thickness (m or in), k = thermal conductivity (W/m-K or BTU-in/hr-ft^2-F)

Because layers are in series, total assembly resistance is simply the sum:

R_total = R_1 + R_2 + R_3 + ... + R_n
Thermal resistances in series add directly, just like electrical resistances

The overall U-value (thermal transmittance) is the inverse of total resistance:

U = 1 / R_total
Units: W/(m^2-K) in metric, or BTU/(hr-ft^2-F) in Imperial

Finally, Fourier's law gives the steady-state heat loss rate:

Q = U x A x Delta-T
A = surface area, Delta-T = indoor minus outdoor temperature

Reading the Temperature Gradient Visualizer

The cross-section diagram in Panel 2 divides the bar width according to each layer's proportional share of total R-value, not by physical thickness. This is intentional and physically meaningful: a layer's width in the diagram represents how much of the total temperature drop occurs within it. A thick layer with a low k-value (high R, like 6 inches of polyurethane foam) will occupy most of the bar. A thin, conductive layer (like 1/2-inch drywall) will occupy a narrow slice, correctly reflecting that almost no temperature drop occurs across it.

The boundary temperature labels between layers are computed as: T_boundary = T_indoor - (Delta-T x cumulative_R / R_total). This is the exact temperature at the interface between each pair of layers, which is important for condensation risk analysis (dew point calculations) and for selecting vapor barrier placement.

Why R-Values Are Additive but U-Values Are Not

A common source of confusion is whether to add R-values or U-values when combining layers. R-values are always the right thing to add because they represent resistance in series. Adding a layer of R-19 cavity insulation to an R-5 exterior foam board gives a total clear-field R of 24, regardless of materials. U-values do not add - you must sum the R-values first and then take the reciprocal to find U. Trying to add U-values gives a physically wrong answer.

Common Assembly Examples and Their Typical R-Values

A standard 2x4 wood-framed wall with R-13 fiberglass batt, 1/2-inch drywall on one side, and 1/2-inch OSB sheathing on the other reaches a clear-field R of roughly R-15. Adding 1-inch XPS continuous exterior insulation pushes this to approximately R-18. A 2x6 wall with R-21 batt and 2 inches of exterior polyiso can reach R-28 or higher. High-performance "Passivhaus" walls often use 8 to 12 inches of exterior mineral wool or foam, with clear-field R-values above R-40. The tool lets you model any of these assemblies and see exactly how much heat loss changes as you experiment with layer combinations.

Frequently Asked Questions

What is the difference between an R-value and a U-value? +
R-value (thermal resistance) measures how strongly a material resists heat flow. A higher R-value means better insulation. It is calculated as thickness divided by thermal conductivity (R = d / k). U-value (thermal transmittance) is simply the inverse of the total R-value (U = 1 / R_total). A lower U-value means less heat escapes. R-value is additive across layers, so you can sum each layer to get the total assembly resistance. U-value is what engineers use to calculate actual heat flow: Q = U x Area x Delta-T.
How does material thickness impact thermal resistance? +
Thermal resistance (R) scales directly with thickness. If you double the thickness of a layer, its R-value doubles as well, since R = d / k where d is thickness and k is the material's thermal conductivity. This linear relationship means each additional inch of fiberglass batt adds the same fixed R-value per inch, regardless of how much is already installed. However, adding more of the same material yields diminishing returns on total heat loss reduction because U-value is the inverse of R-total. Going from R-10 to R-20 cuts U in half; going from R-20 to R-40 cuts it in half again, but that second doubling requires twice as much added thickness.
Why is trapped air considered an effective insulator? +
Still air has a thermal conductivity (k-value) of approximately 0.025 W/m-K, which is lower than most solid building materials. Insulation materials like fiberglass batt and cellulose work primarily by trapping millions of tiny pockets of air within a fibrous or loose-fill matrix, preventing convective air movement. The solid fibers themselves conduct heat, but they account for such a small fraction of the total volume that the bulk conductivity of the assembly stays close to that of still air. Once air begins moving, this benefit disappears: a ventilated air gap conducts and convects heat far more effectively than a sealed one, which is why poorly sealed wall cavities dramatically reduce real-world R-values compared to laboratory ratings.
What is thermal bridging and how does it compromise insulation? +
Thermal bridging occurs when a highly conductive material creates a continuous path through an insulated assembly, bypassing the insulation entirely. The most common example is a wood or steel stud in a framed wall. Steel studs have a k-value roughly 400 times higher than fiberglass, so heat flows through each stud at a rate far exceeding the surrounding insulation. Even though studs occupy only 10-15% of a typical wall area, they can reduce the effective whole-wall R-value by 30-50% compared to the rated cavity R-value. This solver models layers in series (pure 1D conduction), so it reflects a clear-field R-value between framing members. Real assemblies require a correction factor or a separate framing fraction calculation to account for bridges.
How do engineers use these heat loss metrics to size HVAC systems? +
HVAC sizing begins with a Manual J load calculation that sums the heat loss (in heating season) or heat gain (in cooling season) through every surface of a building: walls, roof, floors, windows, and doors. For each opaque surface, the calculation is Q = U x Area x Delta-T, exactly what this solver computes. Engineers enter the design temperature difference between the coldest outdoor design day and the desired indoor temperature. Summing Q across all surfaces, plus infiltration and ventilation loads, yields the total building heat loss in BTU/hr or Watts. A furnace or heat pump must be sized to supply at least that rate of heat output. Improving the U-value of a wall assembly (by adding insulation layers) directly reduces the required equipment capacity, lowering both installation cost and operating energy.