Thermal resistance works like electrical resistance: heat flow equals temperature difference divided by resistance. Pipe and tank insulation are designed with these formulas.
How to use the Thermal Resistance Calculator
- Shape
- Material
- Thermal conductivity k
- Thickness
- Area
- Inner radius r₁
- Outer radius r₂
- Length
- Temperature difference
- Outside convection h (for critical radius)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the shape and material and enter the dimensions and temperature difference.
Tips
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.
Common mistakes to avoid
- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).
Inputs explained
| Field | What to enter |
|---|---|
| Shape | Choose one: Flat plate, Hollow cylinder (pipe), Hollow sphere |
| Material | Choose one: Copper, Aluminium, Carbon steel, Stainless steel … |
| Thermal conductivity k | Units: W/(m·K), BTU/(h·ft·°F) |
| Thickness | Units: mm, cm, m, in, µm |
| Area | Units: m², cm², mm², km², in², ft² |
| Inner radius r₁ | Units: mm, cm, m, in, µm |
| Outer radius r₂ | Units: mm, cm, m, in, µm |
| Length | Units: m, cm, mm, km, in, ft … |
| Temperature difference | Units: K, °C, °F |
| Outside convection h (for critical radius) | Units: W/(m²·K), BTU/(h·ft²·°F) |
Example values
How the main result changes when Thermal conductivity k changes and everything else stays at the example values above:
| Thermal conductivity k (W/(m·K)) | Thermal resistance (K/W) |
|---|---|
| 0.025 | 4.3712 |
| 0.0375 | 4.3712 |
| 0.05 | 4.3712 |
| 0.0625 | 4.3712 |
| 0.075 | 4.3712 |
| 0.1 | 4.3712 |
Formula
Plate: R = L/(k·A) · Cylinder: R = ln(r₂/r₁)/(2π·k·L) · Sphere: R = (1/r₁ − 1/r₂)/(4π·k) · Critical radius: r_c = k/h (cylinder), 2k/h (sphere)Worked example
Inputs — Shape: Hollow cylinder (pipe); Material: Mineral wool; Inner radius r₁: 25 mm; Outer radius r₂: 75 mm; Length: 1 m; Temperature difference: 60 K; Outside convection h (for critical radius): 10 W/(m²·K).
Results — Thermal resistance = 4.37124 K/W; Heat flow = 13.72608 W; Critical insulation radius = 4 mm.
Key terms
- Thermal resistance
- ΔT divided by heat flow.
Frequently asked questions
What is thermal resistance?
Temperature difference per unit heat flow (K/W).
What is the critical radius?
Below it, adding insulation to a small pipe or wire increases heat loss.
How do resistances combine?
In series they add; in parallel their reciprocals add.
Why is the cylinder formula logarithmic?
Heat spreads through a growing area as radius increases.
What formula does the Thermal Resistance Calculator use?
Plate: R = L/(k·A) · Cylinder: R = ln(r₂/r₁)/(2π·k·L) · Sphere: R = (1/r₁ − 1/r₂)/(4π·k) · Critical radius: r_c = k/h (cylinder), 2k/h (sphere).