Thermal Conductivity Calculator – Fourier’s Law, R-Values and U-Values
Heat leaks through everything, and how fast it leaks is set by one material property and one piece of geometry. A thermal conductivity calculatorputs the two together with Fourier’s law of steady-state conduction, Q = k · A · ΔT / L, and then rearranges it for whichever quantity you do not know. Enter a wall, a pipe or a lab sample and you get the heat rate, the heat flux, the thermal resistance and the transmittance — the four ways engineers describe the same physics.
A single wall, and then a real one
Take 10 m² of common brick 100 mm thick, with k = 0.72 W/(m·K), holding 20 °C against 0 °C. The conduction heat loss is 0.72 × 10 × 20 / 0.1 = 1440 W, a heat flux of 144 W/m². Add insulation and the picture changes completely. A plasterboard–mineral wool–brick build-up stacks its resistances in series, R_total = Σ Lⁱ/kⁱ, giving 2.689 m²·K/W and only 96.694 W across the same area at a larger 26 K difference. The 100 mm of wool carries 92.975 % of the temperature drop across 3.7 % of the wall’s thickness, because at equal thickness its resistance is 0.72 / 0.040 = 18×the brick’s.
Interface temperatures and condensation
Because every layer sees the same flux, the calculator can walk the temperature across the build-up and report the value at each interface. In that wall the plasterboard/wool face sits at 20.517 °C while the wool/brick face is at −3.657 °C. Compare those against the dew point and the reason a vapour control layer belongs on the warm side becomes obvious: the cold face of the insulation is far below any indoor dew point, and condensation inside insulation is expensive. Water conducts 0.598 W/(m·K)against still air’s 0.026— 23 times more — so damp insulation is barely insulation at all.
R-13 is not R-13 everywhere
The R-value is resistance per unit area and it comes in two incompatible systems. One h·ft²·°F/BTU equals 0.17611018368230588 m²·K/W, so the two scales differ by 5.678263×. A US batt sold as “R-13” is only R-2.289in SI units. This calculator always prints both with the system in the label, and it also gives the per-inch figure US insulation is actually sold by — mineral wool at k = 0.040 works out at R-3.6 per inch. The U-value is simply U = 1 / R_total, in W/(m²·K) or BTU/(h·ft²·°F).
R_si = 0.13 and R_se = 0.04 m²·K/W for the boundary layers. On a well-insulated wall they change the answer by about 6 %, but on 6 mm single glazing conduction alone predicts U = 166.7 W/(m²·K) against a realistic 5.68— 29.3 times too much heat.Pipes are not flat
Radial area grows with radius, so the flat-plate formula has no single correct area to use. The cylindrical result is Q = 2πkLΔT / ln(r₂/r₁). On 25 mm of lagging over a 60 mm pipe at 80 °C in a 25 °C room, a 10 m run loses 228.051 W, or 22.805 W/m. Approximating it as a slab of the outer area overstates the loss by 33.35 %; using the inner area understates it by 27.26 %. Only the log-mean area, 2πL(r₂ − r₁)/ln(r₂/r₁), reproduces the exact answer.
Working backwards: identify, size and cost
Rearranged for k, the same law identifies a sample: 12 W through a 20 mm, 0.1 m² specimen across 15 K gives k = 0.16 W/(m·K), which the calculator ranks against its material library. Rearranged for L, it sizes insulation to hit a target R-value — always round up to the next stocked thickness. Multiply the U-value by area and heating degree-days and you get seasonal energy, E = U · A · HDD · 24 / 1000kWh, which shows why doubling insulation never halves the bill: the other layers and the films do not change, so a 100 mm to 200 mm upgrade cuts that wall’s loss by 46.65 %, not 50 %.
What the model cannot see
The arithmetic is exact; the assumptions are the limit. This is steady-state, one-dimensional conduction. Studs, ties and fixings are parallel thermal bridgesthat typically make a framed wall’s real U-value 10–30 % worse. Tabulated k values drift with temperature, so each preset carries the temperature it was measured at. Degree-day costs ignore solar gain, internal gains and infiltration, and are best read as the fabric conduction component rather than a heating bill.