Thermal Conductivity Calculator

Understanding Fourier's Law of Heat Conduction

Fourier's law of heat conduction describes how heat energy transfers through a material due to a temperature gradient. In its one-dimensional steady-state form, the heat flux $q$ is proportional to the temperature difference $\Delta T$ across the material and inversely proportional to the thickness $x$. The constant of proportionality is the material's thermal conductivity $k$, giving the equation $q = k \cdot \Delta T / x$. For related thermal tools, check our Thermal Diffusivity Calculator and Thermal Expansion Calculator.

This fundamental relationship governs heat transfer in building walls, industrial insulation, electronics cooling, and countless engineering applications. Materials with high thermal conductivity (like copper at 401 W/(m·K)) transfer heat quickly, while insulators (like fiberglass at 0.04 W/(m·K)) resist heat flow.

Thermal Conductivity Formula

The calculator uses Fourier's law and its rearrangements to solve for any one variable:

• Heat Flux: $$q = \frac{k \cdot \Delta T}{x}$$
• Thermal Conductivity: $$k = \frac{q \cdot x}{\Delta T}$$
• Temperature Difference: $$\Delta T = \frac{q \cdot x}{k}$$
• Thickness: $$x = \frac{k \cdot \Delta T}{q}$$

Where $q$ is the heat flux in W/m², $k$ is the thermal conductivity in W/(m·K), $\Delta T$ is the temperature difference in °C (or K), and $x$ is the material thickness in meters.

How to Use the Calculator

1. Select the variable you want to solve for from the dropdown menu (Heat Flux, Conductivity, Temperature Difference, or Thickness).
2. Enter the known values in the corresponding input fields. The unknown field will be hidden automatically.
3. The tool instantly calculates the result using Fourier's law, displayed prominently in the results section.
4. Use the Details text area to view all values and copy the output.