Heat Conduction (Fourier) Calculator
Heat conduction is the transfer of thermal energy through a material from a hotter region to a cooler one. Fourier's law describes the steady-state rate of conduction through a flat slab in terms of the material's thermal conductivity, the cross-sectional area, the thickness, and the temperature difference across the slab. It is the foundation of building insulation design, heat sink sizing, and process engineering. Enter the conductivity, area, thickness, and the two surface temperatures; this calculator returns the heat flow rate in watts, the heat flux per square metre, and the thermal resistance.
Fourier conduction formula
Temperature difference = T1 - T2
Heat flow rate = k * A * (T1 - T2) / d
Heat flux = k * (T1 - T2) / d
Thermal resistance = d / (k * A)
k is thermal conductivity in W/m/K, A is cross-sectional area in square metres, d is thickness in metres, and the temperature difference is in kelvin (a difference in Celsius equals a difference in kelvin). A positive heat flow means heat moves from the hot side to the cold side.
Heat conduction context
- Fourier's law applies to steady-state, one-dimensional conduction through a uniform slab with constant properties.
- Typical conductivities: copper about 400, aluminium 237, steel 50, glass 1.0, wood 0.15, fibreglass insulation 0.04 W/m/K.
- Thermal resistance adds in series for layered walls, just as electrical resistances add in series.
- A difference in degrees Celsius equals the same difference in kelvin, so either scale works for the temperature inputs.
- For multi-layer or radial geometries, combine resistances rather than applying the slab formula directly.
Heat conduction: frequently asked questions
What is Fourier's law of heat conduction?
Fourier's law states that the steady-state rate of heat conduction through a flat slab is proportional to the thermal conductivity, the cross-sectional area, and the temperature difference, and inversely proportional to the thickness: Q = k x A x (T1 - T2) / d.
What is thermal conductivity?
Thermal conductivity k measures how readily a material conducts heat, in watts per metre per kelvin (W/m/K). Copper is about 400, aluminium about 237, glass about 1.0, and building insulation around 0.04. It is a user-editable input so you can match your material.
What is thermal resistance?
Thermal resistance R equals thickness divided by the product of conductivity and area (d / (k x A)), in kelvin per watt. The heat flow rate equals the temperature difference divided by the thermal resistance, mirroring Ohm's law for electrical circuits.
What is heat flux?
Heat flux is the heat flow rate per unit area, in watts per square metre. It equals conductivity times the temperature difference divided by thickness (k x (T1 - T2) / d), independent of the slab area. This calculator reports both total heat flow and heat flux.
Does this assume steady state?
Yes. Fourier's law in this one-dimensional form applies to steady-state conduction through a uniform slab with constant conductivity and fixed surface temperatures. Transient conduction, where temperatures change over time, requires the heat equation and is outside this calculator's scope.
Official sources
- NIST: Physical Measurement Laboratory (thermal quantities).
- NIST: SI units and conversion factors (SP 811).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.