Formula and Method for Thermal Conductivity
Thermal conductivity (k) measures how readily a material conducts heat: how much heat flows through it, per unit time, for a given thickness, cross-sectional area, and temperature difference. It is defined by Fourier's Law of heat conduction for steady-state, one-dimensional flow through a flat slab: k = Q·d / (A·∆T), where Q is the heat transfer rate (W), d is the thickness of the material along the direction of heat flow (m), A is the cross-sectional area perpendicular to that flow (m²), and ∆T is the temperature difference across the material (K or °C). This calculator also derives the material's thermal resistance, its per-area (SI) R-value, and the resulting heat flux.
How the calculation works
Enter the steady-state heat transfer rate, the thickness of the material along the heat-flow path, the cross-sectional area the heat passes through, and the temperature difference between the two faces. The calculator converts every value to SI base units (watts, meters, square meters, kelvins) and applies Fourier's law, k = Q·d / (A·∆T), to solve for thermal conductivity. It then derives the total thermal resistance R = ∆T / Q (in K/W), the unit thermal resistance R″ = d / k = A∆T / Q (in m²·K/W, sometimes called the SI R-value), and the heat flux q = Q / A (in W/m²).
Common mistakes
- Not reaching steady state: this form of Fourier's law assumes a constant, unchanging heat flow — measurements taken while a material is still warming up or cooling down will give a misleading k.
- Confusing thickness with area dimensions: d is the distance heat travels through the material (its thickness in the flow direction), not its width or length; A is the face area perpendicular to that flow.
- Mixing temperature scales: a temperature difference (∆T) is numerically identical in °C and K, but not in °F — a °F difference must be multiplied by 5/9 before it matches the metric scale.
Real-world applications
- Insulation and building-envelope design use k (and the derived R-value) to size wall, roof, and window assemblies for a target heat-loss rate.
- Electronics thermal management uses k to choose heat-sink and thermal-interface materials that carry heat away from chips fast enough.
- Cookware and appliance design balances high-k metals (fast, even heating) against low-k handles and housings (safe to touch).
- Materials-testing labs measure Q, d, A, and ∆T directly with a guarded hot plate to determine an unknown material's k experimentally — exactly the calculation this tool performs.