# Thermal Resistance Calculator

URL: https://speedycalculator.com/calculators/physics/thermal-resistance/
Last updated: 2026-10-30

> The thermal resistance calculator finds the conduction thermal resistance of a flat plate, hollow cylinder (pipe insulation) or hollow sphere, the heat flow for a temperature difference and the critical insulation radius.

## Inputs

- Shape
- Material
- Thermal conductivity k (W/(m·K), BTU/(h·ft·°F))
- Thickness (mm, cm, m, in, µm)
- Area (m², cm², mm², km², in², ft²)
- Inner radius r₁ (mm, cm, m, in, µm)
- Outer radius r₂ (mm, cm, m, in, µm)
- Length (m, cm, mm, km, in, ft, yd, mi)
- Temperature difference (K, °C, °F)
- Outside convection h (for critical radius) (W/(m²·K), BTU/(h·ft²·°F))

## Results

- Thermal resistance
- Heat flow
- Critical insulation radius

## 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)
```

## Explanation

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

FieldWhat to enterShapeChoose one: Flat plate, Hollow cylinder (pipe), Hollow sphereMaterialChoose one: Copper, Aluminium, Carbon steel, Stainless steel …Thermal conductivity kUnits: W/(m·K), BTU/(h·ft·°F)ThicknessUnits: mm, cm, m, in, µmAreaUnits: m², cm², mm², km², in², ft²Inner radius r₁Units: mm, cm, m, in, µmOuter radius r₂Units: mm, cm, m, in, µmLengthUnits: m, cm, mm, km, in, ft …Temperature differenceUnits: K, °C, °FOutside 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)0.0254.37120.03754.37120.054.37120.06254.37120.0754.37120.14.3712

## 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.

## FAQ

**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).


## Sources

- [Incropera – Fundamentals of Heat and Mass Transfer (reference text)](https://www.wiley.com/en-us/Fundamentals+of+Heat+and+Mass+Transfer%2C+8th+Edition-p-9781119320425)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)