Solve conduction for slabs, cylinders, or custom areas. Convert units, then interpret direction and flux. Download clean results, ready for reports and teaching today.
Plane wall, steady one-dimensional conduction
Fourier’s law (rate form): q = k · A · (Th − Tc) / L
This tool reports direction from the sign of (Th − Tc). For layered walls, sum thermal resistances instead of using a single k and L.
| Material | k (W/m·K) | A (m²) | L (m) | Th (°C) | Tc (°C) | q (W) |
|---|---|---|---|---|---|---|
| Aluminum plate | 205 | 0.40 | 0.020 | 120 | 35 | 348500 |
| Glass pane | 1.0 | 1.20 | 0.006 | 25 | 5 | 4000 |
| Foam insulation | 0.03 | 2.00 | 0.050 | 35 | 20 | 18 |
These are illustrative cases. Real systems may require contact resistance and convection on both sides.
Fourier’s law relates steady, one-dimensional conduction to a temperature difference across a solid. In the plane-wall form used here, heat rate rises with conductivity and area, and falls with thickness. It is a fast sizing tool: doubling thickness roughly halves the predicted heat rate when all other inputs stay fixed. It also supports quick back-calculation for unknown parameters safely.
The thermal conductivity k describes how readily a material conducts heat. Metals are typically tens to hundreds of W/(m·K), while glass is about 1 and foams are near 0.02–0.06. Use temperature-appropriate data because k can vary with temperature and composition.
Area must be normal to heat flow, and thickness L must be the true conduction path between the two faces. Small geometry mistakes can dominate the result, especially for thin plates. When solving for required area or thickness, treat the output as a baseline and add margin for tolerances and uncertainty.
Fourier’s law uses temperatures at the two solid faces. Ambient air temperatures can mislead because convection adds resistance. If only ambient values are known, estimate convection first, infer surface temperatures, then apply this calculator to the solid layer.
The calculator reports total heat rate q and heat flux qʺ (W/m²). Flux is the better metric for hotspot checks and allowable thermal loading on coatings or electronics. Two designs can share the same total heat rate yet have very different flux if their areas differ.
The tool converts length and area to SI internally, computes ΔT on an absolute scale, and reports outputs in your selected heat-rate units. With Fahrenheit inputs, conversion is automatic; keep Th and Tc matched to the correct faces.
After computing, do a plausibility check. Large heat rates with insulation usually mean the layer is thin or ΔT is high. If flux is excessive, increase thickness, choose a lower k material, or add layers. For metals, high values can be realistic and may raise thermal stress concerns.
For multilayer assemblies, use resistances: R = L/(kA). Sum series resistances and compute q = ΔT/Rtotal. Add convection terms 1/(hA) where needed. You can still use this page by solving layers individually and recording each step.
A negative result indicates your temperature order is reversed, so heat flows from the side you labeled “cold” to the side you labeled “hot.” The magnitude is still useful for sizing.
If Th equals Tc, the driving force for conduction is zero, so Fourier’s law predicts no net heat transfer. Solving for k, A, or L is undefined because you would divide by zero.
No. It models conduction through a solid between two face temperatures. If your boundary temperatures come from air or fluids, you must account for convection (and sometimes radiation) separately as additional thermal resistances.
Yes. The tool converts your temperatures to an absolute scale internally to compute a consistent temperature difference. Just ensure Th and Tc refer to surface temperatures at the two sides of the solid.
Heat flux is heat rate per area (W/m²). It helps compare designs with different areas, identify localized thermal loading, and check whether coatings, adhesives, or electronics exceed allowable thermal limits.
Compute each layer’s resistance R = L/(kA), sum them in series, then use q = ΔT/Rtotal. You can also solve each layer individually to estimate temperature drops across each material.
If two solids touch with rough surfaces, gaps, or weak clamping, the interface can add significant resistance. This is common in bolted joints, heat sinks, and stacked plates, especially at low contact pressure.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.