The thermal conductivity calculator above works backwards from a measurement. You supply a steady heat flow through a slab of known thickness and area, together with the temperature difference maintained across it, and the tool returns the material's thermal conductivity in watts per metre-kelvin. That is the direction a laboratory actually works in: conductivity is not something you can read off a specimen, it is something you infer from a controlled heat-flow experiment.
Arb Digital builds free calculators that state their boundary against neighbouring tools, and this one has a clear one. The heat transfer calculator and the heat loss calculator both start from a known conductivity and compute the heat that flows; this page starts from a measured heat flow and computes the conductivity. The thermal conductivity converter does neither — it rescales a value you already have between W/m·K, Btu/h·ft·°F and other units.
What This Thermal Conductivity Calculator Does
In its default mode it rearranges Fourier's law of conduction to isolate k. It also runs in three other directions, because the same four quantities appear in every steady conduction problem and the unknown is not always the same one. Solve for heat flow when the material is known and you want the power crossing a wall. Solve for thickness when you have a target heat flow and need to know how much material delivers it. Solve for temperature difference when the heat flow is fixed by an electrical heater and you want the gradient it will establish.
Whichever mode you use, the results panel completes the set. It reports the conductivity, the heat flux in watts per square metre, and the thermal resistance of that layer in both SI and imperial R-value units, because insulation specifications are quoted in one or the other depending on where you are. Nothing in the grid is left idle in any mode.
How to Use It
- Choose what you are solving for. The hero renames itself to the quantity being computed, so the input and derived figures never blur together.
- Enter the steady heat flow in watts. This is the power actually crossing the sample once temperatures have stopped drifting, which in a guarded hot plate is the electrical input to the metered section.
- Enter the area and thickness. Area is the face the heat crosses; thickness is the distance it travels. Millimetres, centimetres, metres and inches are all accepted for the thickness.
- Enter the temperature difference. Not the two temperatures — the difference between them. It is numerically identical in kelvin and degrees Celsius.
- Read the R-values alongside the conductivity. They express the same physics as a resistance rather than as a material property, and they are what insulation is actually specified by.
The Formula: How Thermal Conductivity Is Calculated
Fourier's law for steady conduction through a plane slab is Q = kA(Th − Tc) ÷ d. OpenStax University Physics Volume 2, section 1.6 on mechanisms of heat transfer, gives it in exactly that form, with k the thermal conductivity, A the surface area, d the thickness and the bracket the temperature difference across the slab.
Rearranged for conductivity it becomes k = Qd ÷ AΔT. Thickness sits in the numerator, which surprises people: a thicker sample passing the same heat at the same temperature difference must be made of a more conductive material, because it is doing more work against a longer path.
Work the default values. A 50 mm slab of one square metre carrying 100 W with 20 K across it gives k = 100 × 0.05 ÷ (1 × 20) = 0.25 W/m·K, which is in the range of dense timber or a plasterboard-like material. The heat flux is 100 ÷ 1 = 100 W/m2, and the thermal resistance is d/k = 0.05 ÷ 0.25 = 0.2 m2·K/W. Multiplying by 5.678263 converts that to 1.136 in imperial R-value units.
The coherent SI unit for conductivity is the watt per metre-kelvin, built from the watt, the metre and the kelvin as set out in the SI Brochure published by the BIPM. Every other unit you will meet — Btu per hour-foot-Fahrenheit, kilocalories per hour-metre-Celsius, watts per centimetre-Celsius — is a rescaling of the same quantity.
Conductivity Versus R-Value: A Property Against an Assembly
Thermal conductivity belongs to the material. A given foam has one value of k whether you buy it as a 25 mm sheet or a 200 mm block. R-value belongs to the layer: it is thickness divided by conductivity, so it scales directly with how much material you install. This is why an insulation product is advertised by R-value while a physics table lists conductivity, and why the two numbers cannot be compared directly.
The relationship is R = d ÷ k in SI units of m2·K/W, and its reciprocal is the U-value, the heat flow per square metre per kelvin. Layers in series add their R-values, which is what makes the resistance form so much more convenient than conductivity for building work — you can total up plasterboard, insulation, cavity and brick by simple addition and then invert once at the end.
The imperial R-value used in North America is a different unit, in h·ft2·°F/Btu, and it is 5.678 times larger for the same physical resistance. An R-13 batt is R-2.29 in SI terms. Quoting one where the other is expected is a factor-of-nearly-six error, which is why this page reports both side by side rather than picking one. The insulation calculator works in the R-value domain directly.
Why a Measured k Rarely Matches the Table Value
Published conductivity figures are measured on dry, homogeneous, defect-free specimens at a stated mean temperature. Real assemblies are none of those things, and the gap between a handbook value and what a wall actually does is usually large enough to matter.
Moisture is the biggest single factor for porous materials. Water conducts roughly twenty-five times better than still air, so filling even a small fraction of the pore volume raises conductivity sharply — a damp insulation batt can lose a substantial part of its rated performance. Density matters too, and not monotonically: very light insulation loses performance because radiation and convection cross the larger voids, while heavy insulation loses it because there is more solid conducting material.
Temperature dependence is real and often ignored. Conductivity of most insulants rises with mean temperature, so a value measured at 10 °C understates performance loss at 40 °C. Metals behave differently again, with conductivity generally falling as temperature rises because increased lattice vibration scatters the electrons that carry most of the heat.
What Gets Measured Wrong in Practice
The most common error in a conductivity measurement is not measuring steady state. Conduction only follows Fourier's law once temperatures have stopped changing, and a sample that is still storing heat gives an apparent conductivity below the true value. Thick or dense specimens can take hours to stabilise, and the temptation to read early is strong.
The second is edge loss. Fourier's law as used here assumes one-dimensional flow straight through the slab, but heat also leaks sideways out of the edges unless the apparatus guards against it. Any of that leakage counted as flow through the sample inflates the conductivity, which is precisely why a guarded hot plate has a guard ring.
The third is contact resistance. A tiny air gap between the sample face and the heater plate adds resistance in series, and the measurement attributes it to the sample. It shows up as a conductivity that is too low and as a dependence on clamping pressure that should not exist. For the transient side of heat storage rather than steady flow, our specific heat calculator and sensible heat calculator cover the energy involved, and Newton's law of cooling calculator handles surface cooling over time.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering two temperatures instead of their difference — the field wants the gap across the slab, and putting an absolute temperature there inflates the denominator enormously.
- Mixing thickness units — a thickness typed in millimetres while the selector reads metres changes the answer by a factor of a thousand, and thickness is in the numerator when solving for k.
- Comparing SI and imperial R-values directly — they differ by a factor of 5.678, so an R-13 batt is R-2.29 in SI units, not thirteen.
- Reading before steady state — a sample still absorbing heat has not reached the condition Fourier's law describes, and the measured conductivity comes out low.
- Treating conductivity as thickness dependent — it is a material property. Doubling the thickness doubles the R-value and leaves k exactly where it was.
Related Free Tools From Arb Digital
Once you have a conductivity, the heat transfer calculator turns it into a heat flow and the heat loss calculator applies it to a building envelope. Rescale the value itself with the thermal conductivity converter, or work in the resistance domain with the insulation calculator. For stored rather than conducted heat use the specific heat calculator or the sensible heat calculator, and for the dimensional change that a temperature gradient causes, the thermal expansion calculator. The full free online tools hub lists everything.
Frequently Asked Questions
Rearrange Fourier's law to k equals heat flow times thickness divided by area times temperature difference. All four inputs must be taken at steady state, with the heat flow being only what actually crosses the sample rather than what the heater consumed.
No. Conductivity is a property of the material and stays the same at any thickness. What changes with thickness is the thermal resistance or R-value, which is thickness divided by conductivity and therefore doubles when the thickness doubles.
They measure the same physical quantity in different units. The SI R-value is in square metre-kelvin per watt, the imperial one in hour-square foot-Fahrenheit per Btu, and the imperial figure is 5.678 times larger for the same resistance. An R-13 batt is R-2.29 in SI terms.
Either, because the field asks for a difference rather than an absolute value, and a difference of one kelvin is identical to a difference of one degree Celsius. Only calculations involving radiation or absolute thermodynamic ratios need true kelvin values.
The usual causes are moisture in a porous material, heat leaking out of the sample edges and being counted as flow through it, or a higher mean temperature than the published value was measured at. Water conducts roughly twenty-five times better than still air, so even modest damp raises the result noticeably.
The heat transfer calculator starts from a known conductivity and computes the heat that flows. This page starts from a measured heat flow and computes the conductivity. One applies a material property, the other derives it, and the thermal conductivity converter simply rescales a value between units.
Not directly. The plane-slab form assumes one-dimensional flow through a constant area. Radial conduction through a pipe wall uses a logarithmic form because the area grows with radius, so applying the flat equation to thick-walled pipe overstates the resistance.
This tool is provided for educational and estimating use. It applies the steady one-dimensional plane-slab form of Fourier's law and does not model transient behaviour, radial geometry, convection, radiation or contact resistance, so treat its output as a physics result rather than a certified material property.
