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Physics

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.

Your details

Rearranges Fourier law to find any single unknown from the rest.
Choose a material to fill in its typical conductivity, or pick Custom and type your own.
Material property. Used unless you are solving for k, or a non-custom material is selected.
W/(m·K)
The face through which heat flows.
How far heat must travel across the material.
Hot-side minus cold-side. A kelvin difference equals the same Celsius difference.
K or °C
Currency
Heat-transfer rateModerate heat flow
80W
Heat-transfer rate (imperial)273Btu/hr
Heat flux (per m²)8W/m²
Thermal resistance (R)0.25K/W
R-value (per area, RSI)2.5m²·K/W
U-value0.4W/(m²·K)
80 W
Well insulated<50Moderate50-500High heat loss500+

Heat conducts through at 80 watts.

  • That is 80 joules of heat crossing the material every second, flowing from the hot side to the cold side.
  • The layer R-value (RSI) is 2.5 m²·K/W and its U-value is 0.4 W/(m²·K); a lower U-value means a better insulator.

Next stepTo cut heat loss, add a thicker layer, choose a lower-k material, or stack insulating layers in series to raise the total R-value.

Formula

Qt=kAΔTd,RSI=dk,U=1RSI\frac{Q}{t} = \frac{k \, A \, \Delta T}{d}, \qquad R_{\text{SI}} = \frac{d}{k}, \qquad U = \frac{1}{R_{\text{SI}}}

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

Materialk (W/(m·K))Conducts heat
Still air0.026 Low
Polyurethane foam0.025 Low
Expanded polystyrene0.035 Low
Fibreglass insulation0.04 Low
Softwood0.12 Low
Water0.6 Low
Brick0.72 Normal
Glass0.8 Normal
Concrete1.7 Normal
Stainless steel16 High
Aluminium237 High
Copper401 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.

Sources

Written by Dr. Tomás Okafor, PhD Physicist · Lagos, Nigeria

Physicist specializing in classical mechanics, bringing 17 years of research and applied dynamics expertise to every calculator he reviews.

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