Thermal Resistance Calculator
Calculate thermal resistance, heat flow rate, and temperature gradient for materials.
Determine the thermal resistance of materials and analyze heat transfer properties for engineering applications, insulation design, and thermal analysis.
Thermal Resistance Calculator
Calculate thermal resistance, heat flow rate, and temperature gradient for materials.
About the Thermal Resistance Calculator
Thermal resistance is a measure of a material's opposition to heat flow, analogous to electrical resistance in circuit theory. Just as electrical resistance (R = V/I) relates voltage to current, thermal resistance (R_th = ΔT/Q) relates temperature difference to heat flow rate. This analogy is powerful: series and parallel combinations of thermal resistances obey the same mathematical rules as electrical networks, allowing complex multi-layer insulation systems to be analysed using simple circuit arithmetic.
The formula for thermal resistance of a flat slab is R = L / (k × A), where L is thickness in metres, k is thermal conductivity in W/(m·K), and A is cross-sectional area in m². The resulting unit is K/W (kelvin per watt). Once R is known, the steady-state heat flow rate is simply Q = ΔT / R, where ΔT is the temperature difference across the material in kelvin. The temperature gradient within the material is ΔT / L, in units of K/m.
Thermal conductivity k characterises the intrinsic ability of a material to conduct heat. Still air has k ≈ 0.024 W/(m·K), making it an excellent insulator — the basis for fiberglass and foam insulation products, which trap air in small cells. High-performance aerogel insulation achieves k as low as 0.015 W/(m·K). At the other extreme, copper has k ≈ 400 W/(m·K) and is used in heat sinks, heat pipes, and heat exchangers where maximum heat transfer is required. Steel (k ≈ 50), concrete (k ≈ 1.4), and wood (k ≈ 0.12) fall between these extremes.
In building construction, insulation performance is often expressed as R-value (per unit area): R_spec = L / k in m²·K/W. This allows direct comparison of different insulation thicknesses and materials without specifying the wall area. UK and European building codes specify minimum U-values (U = 1/R_spec) for walls, roofs, and floors. A well-insulated UK cavity wall might achieve U = 0.18 W/(m²·K), requiring a total R_spec > 5.5 m²·K/W.
In electronics cooling, thermal resistance is the key metric for heat sink and thermal interface material selection. A processor with 100 W power dissipation and a junction-to-case resistance of 0.5 K/W will have its die temperature rise 50°C above the package case temperature. If the thermal interface material and heat sink add another 1.5 K/W, the junction temperature rises 150°C above ambient — potentially exceeding the maximum rated temperature. Minimising every element of the thermal resistance chain from chip to ambient is essential for reliable electronics design.
Thermal Resistance Examples
Practical scenarios illustrating thermal resistance calculations for insulation, construction, and industrial applications.
| Material / Thickness / Conductivity / Area / ΔT | R / Heat Flow | Application |
|---|---|---|
| Fiberglass insulation, L=0.15 m, k=0.04 W/m·K, A=10 m², ΔT=25 K | R = 0.375 K/W | Q = 66.7 W | R-value = 3.75 m²·K/W | Typical residential wall insulation. Good R-value, low heat flux. |
| Concrete wall, L=0.2 m, k=1.4 W/m·K, A=20 m², ΔT=15 K | R = 0.00714 K/W | Q = 2,100 W | R-value = 0.143 m²·K/W | Plain concrete is a poor insulator. Requires additional insulation layers for energy-efficient buildings. |
| Steel heat exchanger plate, L=0.01 m, k=50 W/m·K, A=5 m², ΔT=100 K | R = 0.00004 K/W | Q = 2,500,000 W = 2.5 MW | Steel conducts heat readily. Very low R means extremely high heat transfer rate. |
| Wooden wall, L=0.05 m, k=0.12 W/m·K, A=15 m², ΔT=20 K | R = 0.0278 K/W | Q = 720 W | R-value = 0.417 m²·K/W | Solid wood provides moderate insulation, better than concrete but far below fiberglass. |
How to Use the Thermal Resistance Calculator
- Enter material thickness in metres. For a wall, this is the distance between the two surfaces. For a thin film or coating, use millimetres converted to metres (divide by 1000).
- Enter thermal conductivity in W/(m·K). Lookup values: still air = 0.024, fiberglass = 0.04, wood = 0.12, concrete = 1.4, steel = 50, copper = 400.
- Enter the cross-sectional area in m² perpendicular to the heat flow direction. For a flat wall this is simply length × height.
- Enter the temperature difference across the material in kelvin (K). Note that 1 K difference equals 1°C difference; the units are interchangeable for differences.
- Click Calculate to see thermal resistance (K/W), heat flow rate (W), temperature gradient (K/m), and specific R-value (m²·K/W) for the material.
Thermal Resistance FAQ
What is thermal resistance and how is it measured?
Thermal resistance (R) measures how strongly a material opposes heat flow, defined as R = ΔT / Q in units of K/W. For a uniform slab: R = L / (k × A). It depends on the material's thermal conductivity, thickness, and area. Unlike thermal conductivity (a material property), thermal resistance depends on geometry, just as electrical resistance depends on conductor length and cross-section.
What is the difference between thermal resistance and R-value?
Thermal resistance (K/W) depends on the area of the material. R-value (m²·K/W), also called specific thermal resistance, is area-independent: R-value = L / k. R-values allow fair comparison of different insulation products regardless of the wall size being considered. In the imperial system, R-value is expressed in ft²·°F·h/Btu; to convert: 1 m²·K/W ≈ 5.678 ft²·°F·h/Btu.
How do I add thermal resistances for multiple layers?
For layers in series (e.g., insulation + concrete + plaster), total thermal resistance is the sum: R_total = R₁ + R₂ + R₃ + … This is exactly analogous to resistors in series in an electrical circuit. The total heat flow is Q = ΔT_total / R_total. For parallel paths (e.g., wall studs and insulation side by side), the conductances (1/R) add: 1/R_total = 1/R₁ + 1/R₂.
What thermal conductivity values should I use for common building materials?
Typical values in W/(m·K): still air = 0.024, aerogel = 0.015, fiberglass batt = 0.04, mineral wool = 0.035–0.045, expanded polystyrene (EPS) = 0.033–0.040, extruded polystyrene (XPS) = 0.029–0.036, polyurethane foam = 0.022–0.028, plywood = 0.12–0.15, brick = 0.4–0.9, concrete = 1.0–1.8, gypsum board = 0.17. Values vary with temperature, moisture content, and density; always use measured or certified data for critical design calculations.
How does thermal resistance apply to electronic cooling?
In electronics, thermal resistance is the key metric in the junction-to-ambient thermal model: T_junction = T_ambient + P × (R_jc + R_cs + R_sa), where P is power dissipation and R_jc, R_cs, R_sa are junction-to-case, case-to-sink, and sink-to-ambient resistances respectively. Reducing any resistance in the chain lowers the operating temperature and improves reliability. Thermal interface materials (TIMs) typically have R-values of 0.1–1.0 K·cm²/W.
What is U-value and how does it relate to thermal resistance?
U-value (W/(m²·K)) is the reciprocal of specific R-value: U = k / L = 1 / R-value. It expresses how much heat passes through 1 m² of a construction element per second per kelvin of temperature difference. Lower U-value means better insulation. Building regulations specify maximum U-values: in the UK, external walls ≤ 0.30 W/(m²·K) for new buildings, roofs ≤ 0.20, floors ≤ 0.25, windows ≤ 1.60. A triple-glazed window achieves U ≈ 0.6–0.8 W/(m²·K).