Heat Conduction Calculator
Compute the steady-state heat flow rate through a flat material layer using Fourier's Law. Useful for insulation design, building envelope analysis, and thermal management of electronic components.
About this calculator
Fourier's Law of heat conduction states that the rate of heat transfer through a material is proportional to the temperature gradient and the cross-sectional area. The formula is Q = k × A × ΔT / d, where Q is heat flow rate (W), k is the thermal conductivity of the material (W/m·K), A is the cross-sectional area perpendicular to heat flow (m²), ΔT = T_hot − T_cold is the temperature difference (°C or K), and d is the thickness of the material (m). Materials with high k values, such as copper (~400 W/m·K) and aluminium (~205 W/m·K), are excellent conductors, while insulating materials like mineral wool (~0.04 W/m·K) strongly resist heat flow. Increasing thickness or reducing area decreases heat transfer, forming the basis of insulation engineering.
How to use
A 150 mm thick (d = 0.15 m) concrete wall (k = 1.7 W/m·K) has an area of 20 m². The indoor temperature is 22 °C and the outdoor temperature is −5 °C, giving ΔT = 27 K. Enter k = 1.7, A = 20, T_hot = 22, T_cold = −5, thickness = 0.15. The calculator computes Q = 1.7 × 20 × 27 / 0.15 = 918 / 0.15 = 6,120 W. This means 6.12 kW of heat is lost through that wall, helping you determine how much insulation is needed to meet building energy codes.
Frequently asked questions
What is thermal conductivity and how does it affect heat conduction calculations?
Thermal conductivity (k) is a material property expressing how readily heat flows through it; it is measured in W/m·K. A high k means the material transfers heat easily — metals like copper (400 W/m·K) and steel (50 W/m·K) are prime examples. Insulating materials such as expanded polystyrene (0.035 W/m·K) have very low k values. In Fourier's Law, k appears as a direct multiplier of heat flow: doubling k doubles Q. This is why selecting the right material for either conducting heat away (heat sinks) or blocking it (wall insulation) is the primary design lever.
How does material thickness influence the rate of heat conduction through a wall?
Material thickness d appears in the denominator of Fourier's Law (Q = kAΔT/d), so heat flow rate is inversely proportional to thickness. Doubling the wall or insulation thickness halves the heat transfer rate. This relationship is why adding a second layer of insulation offers diminishing returns: each successive layer reduces absolute heat loss by a smaller amount. In practice, engineers balance the thermal benefit of added thickness against cost, structural weight, and the space consumed by thicker assemblies.
When is Fourier's Law of conduction applicable and what are its limitations?
Fourier's Law in this simple form applies to one-dimensional, steady-state conduction through a homogeneous flat slab with constant material properties. It gives accurate results when temperatures have stabilised and heat flows uniformly in one direction — typical of walls, window panes, and flat insulation panels under stable conditions. It does not account for transient (time-varying) heat flow, multi-dimensional effects at corners and edges, convection, radiation, or materials with temperature-dependent conductivity. For complex geometries or dynamic heating/cooling cycles, finite-element thermal analysis is required.