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 estimate steady-state heat flow through a material. Thermal conductivity (k) is the property that describes how easily heat moves through a substance, so high-k materials like copper transfer heat quickly while low-k materials like aerogel resist it.
This page also reports related insulation metrics such as R-value and U-value, which are common in building design, and it shows how different materials compare in a simple reference table. That makes it useful when you need to move between engineering heat-flow calculations and familiar insulation numbers.
Whether you are checking wall insulation, comparing cookware materials, or sizing a heat sink, the calculator keeps the conductivity, resistance, and heat-loss picture in one place.
Thermal conductivity is one of the simplest ways to compare materials when heat flow matters. It helps you tell the difference between a material that conducts heat efficiently and one that is intended to resist it.
Showing the conductivity, R-value, and U-value together makes the same result easier to use in building, appliance, and equipment contexts without reworking the unit conversions by hand.
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.
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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.