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Fourier Heat Conduction Calculator

Enter conductivity, area, temperature difference and thickness to get the heat flow.

How it is calculated

The tool applies Fourier's law for a flat slab: Q = k × A × ΔT / L. Here k is thermal conductivity in W/(m·K), A is the area in m², ΔT is the temperature difference between the two faces in K (or °C, the same size of step), and L is the thickness in metres. The result is the heat flow in watts, rounded to two decimals. Conductivity and area cannot be negative and the thickness must be above zero. The temperature difference may be negative; that simply gives a negative flow, meaning heat travels the other way. The tool assumes steady state and a single uniform layer: layered walls, surface air films, convection and radiation are not included.

Worked example

A brick wall with k = 0.72 W/(m·K), an area of 12 m² and a thickness of 0.2 m has 20 °C between the inside and outside faces. Multiply the top line: 0.72 × 12 × 20 = 172.8. Divide by the thickness: 172.8 / 0.2 = 864. The wall loses 864.00 W. If the thickness were doubled to 0.4 m, the same wall would lose only half as much, 432 W.

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Common mistakes

  • Entering the thickness in centimetres or millimetres. It must be metres, so a 20 cm wall is 0.2; typing 20 makes the result 100 times too small.
  • Using the outside air and inside air temperatures as ΔT. The law needs the temperature difference between the two surfaces of the slab, which is smaller than the air-to-air difference because of surface films.
  • Using the conductivity of the wrong unit system, such as a value in BTU·in/(hr·ft²·°F). The tool expects W/(m·K); values in other units must be converted first.
  • Applying the result to a multi-layer wall by entering the total thickness with one layer's conductivity. Calculate each layer separately, or combine the layers before using this formula.
  • Reading the output as energy. Watts are a rate; the energy lost over a day is the watts multiplied by hours (864 W for 24 h is 20.7 kWh).

About this calculator

Fourier's law of heat conduction states that steady-state heat flow through a material is Q = k·A·ΔT / L, where k is the thermal conductivity of the material (in W/m·K), A is the cross-sectional area, ΔT is the temperature difference across it, and L is the thickness. Higher conductivity — copper at roughly 400 W/m·K versus fiberglass insulation at around 0.04 — means far more heat escapes for the same temperature gradient.

Mechanical and building-envelope engineers use this exact relationship to size insulation thickness for walls and pipes, estimate heat loss through a wall or window, and check that a heat sink can shed enough wattage in electronics cooling.

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