Last updated: 2026-06-15

Thermal Conduction

Heat flows through a solid from its warm side to its cool side, and Fourier's law tells you how fast. It is the physics behind a cold windowpane, an insulated wall and the handle of a frying pan. Give this calculator the material's conductivity, the area and thickness of the slab, and the temperatures on each face, and it returns the steady-state heat-flow rate in watts — plus the total heat conducted over a time you choose.

Where the formula comes from

Heat conducts down a temperature gradient: the steeper the temperature drops across a material, the faster heat flows. For a flat slab the gradient is simply the temperature difference $\Delta T$ divided by the thickness $L$. The flow also scales with the area $A$ facing it and with a material property, the thermal conductivity $k$. Putting those together gives Fourier's law for a slab.

Formula

A larger area or temperature difference speeds the flow; a thicker or less conductive slab slows it. The temperature difference is what matters, so it is the same whether you work in kelvin or in degrees Celsius.

Worked example

A single pane of glass, $k = 0.96\ \text{W/(m·K)}$, area $A = 1.5\ \text{m}^2$, thickness $L = 5\ \text{mm}$, with a room at $21\ ^\circ\text{C}$ inside and $4\ ^\circ\text{C}$ outside, over one hour:

Nearly five kilowatts of heat loss through one small pane shows why thin single glazing is such a poor insulator.

Reducing the heat flow

The formula points to every way to cut conduction. Lower the conductivity by choosing an insulating material; increase the thickness, as thicker insulation or a wider double-glazing gap does; or shrink the temperature difference. Doubling the thickness halves the rate, and replacing glass with a trapped layer of air — about forty times less conductive — is what makes a sealed double-glazed unit so much better than a single pane.

Limitations

This is steady-state conduction only: it assumes the temperatures have settled and heat is flowing at a constant rate. It does not capture the warm-up period, nor convection and radiation, which carry heat across the air films on each surface of a real wall. Building energy ratings combine all of these into a single U-value; the conduction computed here is one link in that chain. The formula also assumes one-dimensional flow through a uniform slab, not flow around corners, studs or thermal bridges.