Heat Transfer Calculator
Calculate the steady-state heat conduction rate through a flat material layer using Fourier's Law. Use it to evaluate wall insulation, select building materials, or assess thermal management in electronics.
About this calculator
Fourier's Law of heat conduction states that the rate of heat transfer Q̇ through a material is proportional to the temperature difference and cross-sectional area, and inversely proportional to thickness: Q̇ = (k × A × ΔT) / d, where k is thermal conductivity in W/m·K, A is surface area in m², ΔT is the temperature difference across the material in °C (or K), and d is material thickness in meters. The result is in watts. Thermal conductivity k is a material property: metals like copper have k ≈ 400 W/m·K, while building insulation foam may have k ≈ 0.03 W/m·K. The thermal resistance of a layer is R = d / (k × A), analogous to electrical resistance; a higher R means less heat flows for the same temperature difference. This formula applies to one-dimensional, steady-state conduction through a flat slab and is the foundation of building energy codes and heat sink design.
How to use
A concrete wall (k = 0.8 W/m·K) is 0.2 m thick, has a surface area of 10 m², and has an indoor-to-outdoor temperature difference of 15°C. Step 1 — enter Thermal Conductivity = 0.8, Area = 10, Temperature Difference = 15, Thickness = 0.2. Step 2 — Q̇ = (0.8 × 10 × 15) / 0.2 = 120 / 0.2 = 600 W. Step 3 — this wall loses 600 W continuously under these conditions. Step 4 — adding 0.05 m of foam insulation (k = 0.04) in series would dramatically reduce total heat loss, illustrating why insulation matters.
Frequently asked questions
What is thermal conductivity and how does it differ between materials?
Thermal conductivity (k) measures how readily a material conducts heat; it is defined as the heat flux per unit temperature gradient. High-k materials like copper (≈ 400 W/m·K) and aluminum (≈ 200 W/m·K) transfer heat quickly and are used in heat sinks and cookware. Low-k materials like fiberglass insulation (≈ 0.04 W/m·K) or still air (≈ 0.025 W/m·K) are excellent insulators. In building construction, choosing low-k materials for walls and roofs directly reduces heating and cooling energy consumption. The material selector in this calculator provides typical k values to make the comparison straightforward.
How does material thickness affect heat transfer through a wall or panel?
According to Fourier's Law, heat transfer rate Q̇ is inversely proportional to thickness d — doubling the thickness halves the heat loss for the same conditions. This is the physical basis for adding insulation to buildings and wrapping pipes to prevent freezing. Thermal resistance R = d / (k × A) increases linearly with thickness, so each additional centimeter of insulation delivers diminishing but always positive returns. Engineers balance insulation thickness against cost, weight, and space constraints, using this calculation to find the economically optimal thickness.
When does Fourier's Law of conduction not apply or give inaccurate results?
Fourier's Law in the form Q̇ = k × A × ΔT / d applies strictly to steady-state, one-dimensional conduction through a uniform, flat slab. It becomes inaccurate for transient situations where temperatures are still changing over time, for cylindrical or spherical geometries (pipes, tanks) where area varies with radius, or for composite walls where multiple materials are layered (you must sum thermal resistances in series). It also ignores convection and radiation at surfaces, which can dominate in high-velocity airflow or high-temperature environments. For those cases, the full heat transfer equation must include convective coefficients (h) and radiation terms (σεT⁴).