Thermal Conductivity Calculator — Fourier's Law of Heat Conduction
Enter the material's thermal conductivity, cross-sectional area, temperature difference, and thickness to get the steady-state heat transfer rate using Fourier's law of heat conduction.
W/(m·K)
m²
K
m
Steady-state thermal power flowing through the material (Fourier's Law)
Formula
Thermal conductivity
Area
Temperature difference
Thickness
Heat transfer rate
- 1
k × A
1 × 5 = 5Conductance across the slab's cross-section. - 2
k × A × ΔT
5 × 20 = 100 - 3
Heat transfer rate Q = k·A·ΔT ÷ d
100 ÷ 0.2 = 500
How does this calculator work?
Fourier's law gives the steady-state heat flow rate through a slab: Q = k·A·ΔT/d, where k is thermal conductivity (W/m·K), A is area (m²), ΔT is the temperature difference (K), and d is thickness (m). Higher k or larger area increases heat flow; greater thickness reduces it. The result is in watts.
Formula
How this is calculated
Fourier's law of heat conduction states that the rate of heat transfer Q (in watts) through a material is proportional to its thermal conductivity k, the area A through which heat flows, and the temperature difference ΔT across it, and inversely proportional to the thickness d. The formula Q = k·A·ΔT/d applies to steady-state conduction — that is, when temperatures at both surfaces are held constant and the heat flow is uniform in one direction (a slab, a wall, a pipe wall approximated as a flat plate).
Thermal conductivity k characterises how easily a material transmits heat: low-conductivity materials such as mineral wool (k ≈ 0.04 W/m·K) or polyurethane foam (k ≈ 0.025 W/m·K) are excellent insulators; high-conductivity materials such as steel (k ≈ 50 W/m·K) or copper (k ≈ 385 W/m·K) conduct heat readily. The SI R-value (d/k, in m²·K/W) is a per-unit-area measure of resistance; multiply by area to get the total thermal resistance R = d/(k·A), used in heat-loss calculations for buildings and electronics cooling.
This calculator assumes one-dimensional, steady-state conduction through a homogeneous material with constant k. It does not account for convective surface resistance (the boundary-layer effect at the surfaces), radiation, or contact resistance between layers. For a multi-layer wall, compute each layer's R-value and sum them before applying the temperature difference.
Frequently asked questions
Fourier's law states that the heat flow rate through a material is Q = k·A·ΔT/d, where k is thermal conductivity (W/m·K), A is area, ΔT is the temperature difference across the material, and d is its thickness. A higher k means the material conducts heat more easily; a greater thickness or smaller area slows heat transfer.
Common values: still air ≈ 0.026, rigid foam ≈ 0.025–0.040, mineral wool ≈ 0.040, wood ≈ 0.1–0.2, brick ≈ 0.6–1.0, concrete ≈ 1.0–1.7, glass ≈ 1.0, water ≈ 0.6, steel ≈ 50, aluminium ≈ 205, copper ≈ 385 W/(m·K). Values depend on material composition, moisture content, and temperature.
The total thermal resistance is R = d/(k·A) in K/W. Heat flow Q = ΔT/R. In building science, the per-area R-value Rʹ = d/k is used (in m²·K/W or ft²·°F·h/BTU in US customary units). A higher R-value means better insulation. The heat loss through a wall is Q = A·ΔT/Rʹ, equivalent to Fourier's law.
Also known as
TG we-Calculate Editorial Team. (2026). Thermal Conductivity Calculator — Fourier's Law of Heat Conduction [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/thermal-conductivity-calculator
TG we-Calculate Editorial Team. "Thermal Conductivity Calculator — Fourier's Law of Heat Conduction." TG we-Calculate. 2026. https://we-calculate.com/calculator/thermal-conductivity-calculator.
TG we-Calculate Editorial Team, "Thermal Conductivity Calculator — Fourier's Law of Heat Conduction," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/thermal-conductivity-calculator
@misc{wecalculate_thermal_conductivity_calculator, title = {Thermal Conductivity Calculator — Fourier's Law of Heat Conduction}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/thermal-conductivity-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?