Thermal Conductivity Calculator
Work out how fast heat conducts through a wall, window or layer of insulation using Fourier law. Pick a material or type its conductivity, set the area, thickness and the hot and cold face temperatures, and get the heat-transfer rate, heat flux, thermal resistance, R-value and U-value, plus an optional yearly energy cost. You can also reverse the calculation to solve for conductivity, thickness, area or temperature difference.
Formula
Worked example
A 10 m² fibreglass wall (k = 0.04 W/(m·K)), 0.1 m thick, with a 20 K difference: Q/t = (0.04 × 10 × 20) ÷ 0.1 = 8 ÷ 0.1 = 80 W. Its R-value (RSI) is 0.1 ÷ 0.04 = 2.5 m²·K/W, a U-value of 0.4 W/(m²·K). Held for 24 h over 180 days at 0.18 per kWh, that is about 345 kWh, roughly 62 per year.
Fourier law of heat conduction
Conduction is the transfer of thermal energy through a material by molecular collisions, without the material itself moving. Fourier law states that the steady-state rate of heat flow through a flat slab equals the thermal conductivity k multiplied by the cross-sectional area A and the temperature difference ΔT across it, all divided by the slab thickness d: Q/t = k·A·ΔT ÷ d. The result is a power in watts, joules of heat per second. The law assumes one-dimensional, steady-state flow through a uniform material, with the two faces held at fixed temperatures, which is a good approximation for a wall, window or layer of insulation.
Pick a material or solve in reverse
Choose a material from the list to drop in its typical room-temperature conductivity, from still air at 0.026 up to copper at 401 W/(m·K), or pick Custom to type your own. The Solve for menu rearranges the same equation so you can find any single unknown: enter a target or measured heat-transfer rate and the calculator returns the conductivity, the thickness, the area or the temperature difference that produces it. That is handy for sizing insulation to a heat-loss budget or for backing out a material property from a measured power. Switch the unit system to work in feet, square feet and degrees Fahrenheit; the math is done in SI internally and the rate is also shown in Btu per hour.
Thermal resistance, R-value and U-value
The same physics can be written with thermal resistance, R = d ÷ (k·A), so heat flow becomes Q/t = ΔT ÷ R, mirroring Ohm law where temperature difference plays the role of voltage and heat flow the role of current. Builders quote insulation per unit area as the R-value (RSI in metric, d ÷ k), and its reciprocal is the U-value, the heat lost per square metre per degree. A lower U-value or a higher R-value means a better insulator. Resistances of layers in series simply add, which is why a wall assembly total R is the sum of its sheathing, insulation and cladding. To cut heat loss, make a layer thicker, choose a lower-k material, or add more layers in series.
Putting a price on the heat loss
Turn on the energy-cost estimate to see what a steady heat loss costs over a year. The calculator multiplies the heat-transfer rate by the hours per day and days per year you expect the temperature difference to hold, converts watt-hours to kilowatt-hours, and multiplies by your energy price. Divide by a heating or cooling efficiency to reflect the appliance: a resistive heater or gas boiler is close to 1, while a heat pump with a coefficient of performance of 3 to 4 delivers the same heat for a fraction of the energy. The figure is a planning estimate; real losses vary with weather, air leakage and thermal bridging, but it shows how a better-insulated assembly pays back.
Typical thermal conductivities
| Material | k (W/(m·K)) | Conducts heat |
|---|---|---|
| Still air | 0.026 | Low |
| Polyurethane foam | 0.025 | Low |
| Expanded polystyrene | 0.035 | Low |
| Fibreglass insulation | 0.04 | Low |
| Softwood | 0.12 | Low |
| Water | 0.6 | Low |
| Brick | 0.72 | Normal |
| Glass | 0.8 | Normal |
| Concrete | 1.7 | Normal |
| Stainless steel | 16 | High |
| Aluminium | 237 | High |
| Copper | 401 | High |
Approximate values near room temperature, in W/(m·K).
Frequently asked questions
What units does this calculator use?
In metric it uses SI units: conductivity in W/(m·K), area in m² (or cm², ft², in²), thickness in m (or cm, mm, in, ft), and a temperature difference in kelvin, equal to a Celsius difference. The rate is returned in watts and also in Btu per hour. Switch to imperial to enter feet, square feet and a Fahrenheit difference; the conversion is handled for you.
Can I solve for thickness, area or conductivity instead of the rate?
Yes. Use the Solve for menu and enter a known or target heat-transfer rate. The calculator rearranges Fourier law to return the conductivity (k = Q·d ÷ A·ΔT), the thickness (d = k·A·ΔT ÷ Q), the area (A = Q·d ÷ k·ΔT) or the temperature difference (ΔT = Q·d ÷ k·A) that gives that rate.
What is the difference between R-value and U-value?
The R-value (RSI in metric) is the thermal resistance per unit area, thickness divided by conductivity, in m²·K/W; a higher R insulates better. The U-value is its reciprocal, the heat lost per square metre for each degree of difference, in W/(m²·K); a lower U insulates better. They describe the same layer from opposite directions.
How is the yearly energy cost worked out?
It multiplies the heat-transfer rate by the hours per day and days per year the temperature difference holds, divides by 1000 to get kilowatt-hours, then multiplies by your energy price and divides by the appliance efficiency or heat-pump coefficient of performance. Use 1 for resistive or gas heating and 3 to 4 for a heat pump. It is a planning estimate, not a guaranteed bill.