Calculate the rate of heat transfer through a material using Fourier's Law of Heat Conduction (Q = kAΔT/d)
Last updated: March 26, 2026 | By ForgeCalc Engineering
Ex: Copper 400, Concrete 1.1, Fiberglass 0.04
Watts (W)
Thermal conductivity (k) is a material property that describes its ability to conduct heat through its structure. It measures how quickly heat flows through a unit thickness of material when there is a temperature gradient. Materials with high thermal conductivity (like copper or aluminum) are good heat conductors, while those with low thermal conductivity (like fiberglass or aerogel) are excellent insulators.
The rate of heat transfer through a material is governed by Fourier's Law of Heat Conduction, which states that heat transfer is directly proportional to thermal conductivity, surface area, and temperature difference, and inversely proportional to material thickness. This principle is fundamental to understanding insulation requirements in buildings, industrial processes, and electronic device cooling.
Step 1: Enter the thermal conductivity (k) of your material in W/m·K. Common reference values: copper 400, aluminum 200, concrete 1.1, insulation batts 0.04-0.07, air 0.026.
Step 2: Enter the surface area through which heat flows (in square meters). For a wall, multiply width × height. For a pipe, use the outer surface area.
Step 3: Enter the temperature difference between the two sides of the material, measured in Kelvin or Celsius (the value is the same for a difference).
Step 4: Enter the thickness of the material in meters. The calculator will compute the heat transfer rate in watts.
A homeowner wants to estimate heat loss through their attic insulation during winter. The attic has fiberglass batts with thermal conductivity 0.04 W/m·K, total floor area of 50 m², insulation thickness of 0.1 m (10 cm), and an indoor-outdoor temperature difference of 30°C.
The attic loses 600 watts of heat continuously under these conditions, or about 14.4 kilowatt-hours per 24-hour period.
k-value (conductivity) is the amount of heat (watts) that flows through 1 meter of material per 1°C difference. R-value is the thermal resistance: R = d/k. Thicker materials and lower k-values produce higher R-values (better insulation).
Yes, substantially for gases and slightly for solids. For most solids, k decreases slightly as temperature increases. For gases like air, k increases with temperature. This affects long-term heat transfer predictions.
Air has low thermal conductivity (0.026 W/m·K), but it must be trapped in small pockets to be effective. In open air, convection (air movement) transfers heat rapidly. Foams trap air, preventing convection and using air's low conductivity.
Diamond is the best natural thermal conductor with k ≈ 2300 W/m·K. Among metals, copper (400 W/m·K) and aluminum (200 W/m·K) are excellent. This is why heat sinks in electronics use copper or aluminum.
Water has much higher thermal conductivity (0.6 W/m·K) than air. When insulation becomes wet, water fills air pockets and dramatically increases heat transfer. This is why moisture barriers are critical in building insulation design.
More heat loss means more energy needed to maintain temperature, directly increasing heating/cooling costs. Improving insulation (increasing R-value) reduces this heat loss. Building codes specify minimum R-values for energy efficiency.
Heat always flows from hot to cold. If your calculation shows negative Q, you've reversed the temperature difference (put cold side as T₁ and hot side as T₂). The absolute value represents actual heat flow.
Heat transfer is directly proportional to surface area. A room with larger walls or windows (more A) loses more heat. This is why corner offices and top-floor apartments are typically colder and more expensive to heat.