Heat Conduction Calculator
Calculates the steady-state heat transfer rate through a flat material slab using Fourier's law. Useful for sizing insulation, evaluating wall assemblies, or designing heat sinks.
About this calculator
Fourier's law of heat conduction states that heat flows from hot to cold at a rate proportional to the temperature gradient and the material's ability to conduct heat. The formula is Q = k · A · ΔT / d, where Q is the heat transfer rate in watts, k is thermal conductivity in W/(m·K), A is the cross-sectional area in m², ΔT is the temperature difference across the material in kelvin, and d is the thickness in metres. A higher thermal conductivity (e.g., copper at ~400 W/(m·K)) means much more heat flows compared to an insulator like mineral wool (~0.04 W/(m·K)). The formula assumes one-dimensional, steady-state conduction through a homogeneous material with constant k. It is the foundation for more complex analyses such as multi-layer walls and radial conduction in cylinders.
How to use
Consider a glass window pane: k = 1.0 W/(m·K), area A = 1.5 m², indoor temperature 20 °C, outdoor −5 °C so ΔT = 25 K, thickness d = 0.006 m. Apply Fourier's law: Q = 1.0 × 1.5 × 25 / 0.006 = 37.5 / 0.006 = 6 250 W. This means 6.25 kW of heat is lost through that single pane — equivalent to three electric fan heaters running continuously. Doubling the glass thickness to 12 mm would halve the loss to 3 125 W, illustrating why double glazing is so effective.
Frequently asked questions
What thermal conductivity values should I use for common building materials?
Typical values at room temperature are: concrete 1.0–1.7 W/(m·K), brick ~0.7 W/(m·K), timber ~0.12 W/(m·K), mineral wool insulation 0.03–0.05 W/(m·K), expanded polystyrene ~0.04 W/(m·K), and standard glass ~1.0 W/(m·K). Metals are far higher: steel ~50 W/(m·K), aluminium ~205 W/(m·K), copper ~400 W/(m·K). Always use the value appropriate to the material's temperature and density, as both can affect conductivity noticeably.
How does material thickness affect heat conduction rate?
According to Fourier's law, heat transfer rate is inversely proportional to thickness — doubling the thickness halves Q, and tripling it reduces Q to one-third. This is why thick insulation dramatically cuts heat loss in walls and roofs. The concept of thermal resistance R = d/(k·A) captures this: thicker materials or lower-conductivity materials increase resistance and reduce heat flow for the same temperature difference, just as electrical resistance reduces current.
When does Fourier's law give inaccurate results for heat conduction?
Fourier's law is strictly valid only for steady-state, one-dimensional conduction through a uniform, isotropic material with constant thermal conductivity. It becomes inaccurate during transient conditions (e.g., heating up a wall from cold), in materials where k varies strongly with temperature, in layered or anisotropic composites without proper series-resistance treatment, or when convection or radiation at surfaces contributes significantly to heat transfer. For curved geometries such as pipes, the cylindrical form of Fourier's law must be used instead of the flat-wall version.