Fourier's Law of Heat Conduction Calculator
Enter thermal conductivity, area, temperature difference and thickness to compute the conductive heat rate q = k·A·ΔT/L.
Input Data
Results
At a glance:Fourier's law of heat conduction: the conductive heat flux is proportional to the negative temperature gradient, q = −k·A·(dT/dx), and for a flat slab of thickness L with temperature difference ΔT across it, the rate is q = k·A·ΔT/L (W). k is the material's thermal conductivity (W/(m·K)): high for metals (Cu ~400, Al ~237), low for insulators (air ~0.026, fiberglass ~0.04). The heat flux q/A = k·ΔT/L. Thermal resistance R_th = L/(kA), so q = ΔT/R_th, analogous to Ohm's law. This tool computes the steady-state heat rate through a slab.
Formula
Fourier's law: q = k·A·ΔT/L
Thermal resistance: R_th = L/(kA)
Heat flux: q/A = k·ΔT/L
$$Q = \dfrac{k\,A\,\Delta T}{L}$$How to Use
- Enter thermal conductivity k, area A, temperature difference ΔT and thickness L.
- The calculator returns the heat rate q.
Case Studies
Wall heat loss
k = 0.04 W/(m·K), A = 10 m², ΔT = 20 K, L = 0.1 m.
q = 0.04×10×20/0.1 = 80 W.
Adding insulation (lower k or larger L) reduces this.
FAQ
How does insulation work?
Insulation has low k and often traps air (k≈0.026); increasing L and lowering k raises R_th = L/(kA), reducing q for a given ΔT.
Is this steady-state only?
Yes — it assumes constant temperatures at the faces and no heat accumulation. Transient (time-dependent) heating uses the heat equation with thermal diffusivity.
Related Tools
References
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.