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.
Frequently Asked Questions
What is the formula for thermal resistance?
Thermal resistance for conduction through a flat layer is R = L / (k × A), where L is the layer thickness, k is the material's thermal conductivity in W/(m·K), and A is the cross-sectional area heat flows through. R is expressed in kelvins per watt (K/W), and lower values mean heat flows more easily.
How do I find the temperature difference from thermal resistance?
Multiply the thermal resistance by the heat flow: ΔT = Q × R, where Q is the power (in watts) passing through the layer and R is its thermal resistance in K/W. For example, 10 W through a 0.25 K/W resistance produces a 2.5°C temperature rise.
What are typical thermal conductivity values?
Metals conduct heat very well — copper is about 401 W/(m·K) and aluminum about 205 W/(m·K) — while insulators are far lower: fiberglass insulation is about 0.04 W/(m·K), still air about 0.026 W/(m·K), and typical PCB epoxy (FR4) about 0.3 W/(m·K). Choose the value that matches your actual material for an accurate result.
How do thermal resistances combine across multiple layers?
Layers stacked in the direction of heat flow (a series thermal path, like chip → thermal paste → heat sink) add directly: R_total = R1 + R2 + R3 + .... Parallel heat paths (multiple routes for heat to escape at once) combine like resistors in parallel: 1/R_total = 1/R1 + 1/R2 + ....
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
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| Barber / hair salon | 15–20% | On pre-discount total |
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General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |