Heat flows from hot to cold, and through a solid it does so by conduction: faster-vibrating atoms pass energy to their slower neighbors. Joseph Fourier described this in 1822 with a law that is still the starting point for sizing insulation, estimating heat loss through walls and designing heat sinks. This calculator applies Fourier’s law to a flat layer. Give it four of the five quantities and it returns the fifth, along with the heat flux, the layer’s R-value and U-factor, and the energy lost over a day.
How to use the heat conduction calculator
- Choose what to Solve for: heat flow rate, thermal conductivity, area, temperature difference or thickness.
- Pick a Material to use its typical conductivity, or choose “Custom value” and enter it in W/(m·K), W/(cm·K), BTU/(h·ft·°F) or BTU·in/(h·ft²·°F).
- Enter the Area the heat passes through (m², cm², ft², in²), the Temperature difference between the warm and cold faces (°C, K or °F), and the Thickness (mm, cm, m, in, ft).
- When solving for anything else, enter the Heat flow rate in W, kW, BTU/h or mW.
- Read the result plus the heat flux, R-value, U-factor, energy per day and a table comparing the same slab in other materials.
Fourier’s law of heat conduction
P is the heat flow in watts, k the thermal conductivity, A the area, ΔT the temperature difference across the layer and d its thickness. Writing R = d ÷ k gives the form used for buildings: P = AΔT ÷ R, and layers in series simply add their R-values.
Worked example
Heat through a brick wall
A 1.5 m² section of common brick (k = 0.7 W/(m·K)), 200 mm thick, has an inside surface at 20 °C and an outside surface at −8 °C, so ΔT = 28 K.
P = 0.7 × 1.5 × 28 ÷ 0.2 = 147 W
The heat flux is 98 W/m², the R-value is 0.286 m²·K/W (US R-1.6) and the wall section loses 3.53 kWh a day at that steady rate.
Sizing insulation. To cut that same section’s loss to 20 W with fiberglass batts (k = 0.04 W/(m·K)), solve for thickness: d = 0.04 × 1.5 × 28 ÷ 20 = 0.084 m, or 84 mm (3.3 in), which works out to about R-11.9 in US units.
Thermal conductivity of common materials
| Material | k (W/(m·K)) | US R-value per inch |
|---|---|---|
| Copper | 401 | 0.0004 |
| Aluminum | 237 | 0.0006 |
| Carbon steel | 50 | 0.003 |
| Concrete (dense) | 1.4 | 0.10 |
| Window glass | 1.0 | 0.14 |
| Common brick | 0.7 | 0.21 |
| Softwood | 0.12 | 1.2 |
| Fiberglass batt | 0.04 | 3.6 |
| Expanded polystyrene | 0.035 | 4.1 |
| Polyiso foam board | 0.023 | 6.3 |
Figures are typical room-temperature values; manufacturers’ data for a specific product should take priority.
What real walls add
Fourier’s law describes conduction through one uniform layer at steady state. A real wall also has air films on both faces, framing that bridges the insulation, and air leaks, so its actual heat loss is usually higher than the conduction estimate for the insulation alone. The US Department of Energy publishes recommended insulation R-values by climate zone, which the insulation calculator uses. To turn a heat loss into heating equipment size, the BTU calculator is the next step, and the specific heat calculator covers heat stored in a material rather than flowing through it.
Frequently asked questions
What is thermal conductivity?
It measures how easily heat flows through a material: the heat in watts that passes through a 1 m² slab 1 m thick for each kelvin of temperature difference. Copper is about 401 W/(m·K), brick about 0.7, and fiberglass insulation about 0.04.
How does R-value relate to conductivity?
For a single layer, the SI R-value is thickness divided by conductivity, in m²·K/W. Multiply by 5.678 to get the US R-value printed on insulation, in ft²·°F·h/BTU. 84 mm of fiberglass at 0.04 W/(m·K) is R-2.1 SI, or about R-11.9 US.
Does the temperature difference use °C or °F?
Either. A difference of 1 °C equals 1 K, and a difference of 1 °F equals 5/9 K, so the calculator converts the difference directly. Use the difference between the two surface temperatures of the layer.
Why is the heat loss through a single pane of glass so high in the calculator?
Glass itself is a poor insulator: 4 mm of it has an R-value of only 0.004 m²·K/W. In a real window, thin films of still air on each side add about 0.17 m²·K/W, which is why a single-pane window's U-factor is around 5.8 W/(m²·K) rather than 250.
What does the U-factor mean?
It is the inverse of the R-value: the heat flow per square meter for each degree of difference. Lower is better for insulation. Building codes and window labels in the US quote U-factors in BTU/(h·ft²·°F).