Calculate heat flow using Fourier law q = kAΔT/L. Find R-value, U-value, and heat flux for 14 materials with visual conductivity comparison.
The **Thermal Conductivity Calculator** applies Fourier's law of heat conduction — q = kAΔT/L — to compute heat flow rate through any material. Thermal conductivity (k) measures how efficiently a material conducts heat: copper at 401 W/(m·K) is 16,000 times more conductive than aerogel at 0.015 W/(m·K).
This property is central to building insulation design (R-values), heat sink engineering, cookware selection, and industrial process equipment. The calculator provides R-values in both SI (m²·K/W) and Imperial (ft²·°F·h/BTU) systems, U-values for building codes, daily energy loss estimates, and a visual comparison across 14 common materials from metals to super-insulators.
Whether you are sizing insulation for a home wall, designing a heat exchanger, or comparing pipe insulation options, this tool gives you the complete picture of steady-state conductive heat transfer. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case. Use the example pattern when troubleshooting unexpected results.
Accurate thermal conductivity calculations prevent energy waste in buildings, ensure proper heat dissipation in electronics, and optimize insulation in industrial piping. R-value comparisons help select the most cost-effective insulation. Keep these notes focused on your current workflow. Tie the context to real calculations your team runs. Use this clarification to avoid ambiguous interpretation. Align the note with how outputs are reviewed.
q = k × A × ΔT / L (Fourier's Law) Where: q = heat flow rate (W), k = thermal conductivity (W/(m·K)), A = cross-section area (m²), ΔT = temperature difference (K or °C), L = thickness (m) R-value = L/k (m²·K/W), U-value = 1/R = k/L (W/(m²·K))
Result: 32,080 W
q = 401 × 0.02 × 40 / 0.01 = 32,080 W. Copper conducts an enormous amount of heat even through a small area, which is why it excels in heat exchangers and heat sinks. R-value = 0.01/401 = 0.0000249 — essentially zero thermal resistance.
Jean-Baptiste Fourier published his theory of heat conduction in 1822, establishing the proportional relationship between heat flux and temperature gradient. In its general form, the heat equation combines conduction with energy storage to describe how temperature evolves in space and time — the foundation of all thermal analysis.
Steady-state conduction (the case this calculator solves) applies when temperatures are constant in time: the heat entering one side equals the heat leaving the other. This is a good approximation for building walls, pipe insulation, and heat sinks under constant load.
**Wall Assemblies:** Building codes specify minimum R-values by climate zone. In climate zone 5 (Northern US), exterior walls need R-20 continuous insulation or R-13 cavity + R-5 continuous. A typical 2×6 wall with fiberglass: R-19 cavity, but accounting for stud bridging (16 OC), the effective R-value drops to about R-14.
**Window Performance:** Windows are rated by U-factor (lower is better). Single pane: U = 5.8 W/(m²·K). Double pane with low-e coating and argon fill: U = 1.4. Triple pane: U = 0.8. Windows are typically the weakest thermal link in a building envelope, accounting for 25-30% of heating/cooling load.
**Heat Sinks:** Electronics cooling requires materials with high thermal conductivity. Aluminum (k=237) is the most common heat sink material. Copper (k=401) is better but heavier and more expensive. Diamond (k=2000) is used in specialized high-power applications. The thermal path from chip to ambient determines junction temperature and device reliability.
**Pipe Insulation:** Industrial piping at 200-500°C uses calcium silicate (k=0.07) or mineral wool (k=0.04). The economic insulation thickness balances the cost of insulation against the value of energy saved. For a steam pipe at 200°C, 50mm of mineral wool reduces heat loss by 95% compared to bare pipe.
R-value is thermal resistance (higher = better insulator): R = L/k. U-value is thermal transmittance (lower = better insulator): U = 1/R. Building codes typically specify minimum R-values for walls/roofs or maximum U-values for windows.
SI R-value uses m²·K/W. Imperial R-value uses ft²·°F·h/BTU, which is 5.678 times larger numerically. US building codes use Imperial (e.g., R-19 walls). European codes use SI (e.g., R-3.3 ≈ R-19 Imperial).
Yes. For metals, k generally decreases with temperature except at very low T. For insulators and gases, k increases with temperature. The values shown are room temperature averages suitable for most engineering calculations.
Add individual R-values: R_total = R_1 + R_2 + R_3. A wall with drywall (R-0.08), fiberglass (R-3.3), plywood (R-0.1), and siding (R-0.05) has R_total = 3.53 SI = R-20 Imperial.
Air has very low thermal conductivity (0.026 W/m·K). Insulation materials like fiberglass and foam trap tiny pockets of still air, preventing convection while exploiting air's low conductivity. Aerogel takes this to the extreme with nanoscale pores.
Installed performance is often 10-30% worse than lab R-values due to installation gaps, thermal bridging through studs, moisture, compression, and air infiltration. Continuous exterior insulation eliminates bridging.