Formula and Method for Thermal Resistance
Thermal resistance measures how strongly a material layer opposes the flow of heat, in direct analogy to electrical resistance opposing current. For steady-state conduction through a flat layer, Fourier's law gives the heat flow as Q = k·A·ΔT / L, where k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference across the layer, and L is the layer's thickness. Rearranging ΔT/Q defines the thermal resistance: R = L / (k × A), measured in kelvins per watt (K/W). This calculator computes R directly from a layer's thickness, area, and conductivity, then uses it to find the temperature rise for a given heat (power) flow.
How the calculation works
Enter the layer's thickness and cross-sectional area (the surface through which heat flows, perpendicular to the direction of travel) with their units, plus the material's thermal conductivity in W/(m·K) — pick a common material from the preset list or type in a known value directly. The calculator converts thickness and area to meters and square meters, then applies R = L / (k × A) to get the thermal resistance in K/W and its reciprocal, the thermal conductance G = 1/R in W/K. If you also enter a power dissipation Q (in watts), it multiplies Q by R to estimate the steady-state temperature difference ΔT = Q × R across the layer, and reports the area-normalized resistance R″ = L/k = R × A, a geometry-independent number used to compare materials in datasheets regardless of the size of the actual part.
Common mistakes
- Mixing units: keep the thickness and area unit selections matched to your actual measurements — the calculator converts automatically once the correct unit is chosen, but a wrong unit selection silently produces a wrong answer.
- Confusing conductivity with resistance: thermal conductivity k, in W/(m·K), is a material property alone; thermal resistance R, in K/W, also depends on the thickness and area of the specific piece you are analyzing.
- Ignoring contact resistance: two solids pressed together (for example a heat sink and a chip) never touch perfectly — real assemblies add extra thermal interface resistance on top of R = L / (k × A).
- Celsius vs. Kelvin: because R relates to a temperature difference, and a 1°C change equals a 1 K change, ΔT can be reported in either unit without conversion here.
Real-world applications
- Electronics cooling: heat sink and PCB designers use thermal resistance (junction-to-case, case-to-heatsink, heatsink-to-ambient) to predict component temperature rise and pick adequate cooling.
- Building insulation: wall, roof, and window assemblies are rated by thermal resistance (often as an R-value) to estimate heat loss and size insulation thickness.
- Material selection: the area-normalized resistance R″ = L/k lets engineers compare candidate gaskets, thermal pads, or window panes independent of the specific part's size.
- Series thermal networks: multi-layer assemblies (chip → thermal paste → heat spreader → heat sink → air) sum each layer's resistance to find the total system ΔT for a given power.