# Biot Number Calculator

URL: https://speedycalculator.com/calculators/physics/biot-number/
Last updated: 2026-10-30

> The Biot number calculator compares heat conduction inside a body with convection at its surface, from the heat transfer coefficient, characteristic length (or volume and area) and thermal conductivity, and tells whether a lumped-capacitance model is valid.

## Inputs

- Heat transfer coefficient h (W/(m²·K), BTU/(h·ft²·°F))
- Thermal conductivity k (W/(m·K), BTU/(h·ft·°F))
- Characteristic length from
- Characteristic length L_c (mm, cm, m, in, µm)
- Volume (cm³, m³, L)
- Surface area (cm², m²)

## Results

- Characteristic length
- Biot number
- Lumped-capacitance model

## Formula

```
Bi = h·L_c / k,  L_c = V/A_s
```

## Explanation

A small Biot number means a body heats almost uniformly – you can treat it as one temperature (lumped capacitance). A large Biot number means the inside lags far behind the surface, as in a thick roast in the oven.

### How to use the Biot Number Calculator

- **Heat transfer coefficient h**
- **Thermal conductivity k**
- **Characteristic length from**
- **Characteristic length L_c**
- **Volume**
- **Surface area**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the convection coefficient, the thermal conductivity and either the characteristic length or the volume and surface area.

### 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 enterHeat transfer coefficient hUnits: W/(m²·K), BTU/(h·ft²·°F)Thermal conductivity kUnits: W/(m·K), BTU/(h·ft·°F)Characteristic length fromChoose one: Direct value, Volume and surface areaCharacteristic length L_cUnits: mm, cm, m, in, µmVolumeUnits: cm³, m³, LSurface areaUnits: cm², m²

### Example values

How the main result changes when **Heat transfer coefficient h** changes and everything else stays at the example values above:

Heat transfer coefficient h (W/(m²·K))Biot number12.50.002518.750.0038250.00531.250.006337.50.0075500.01

## Worked example

Inputs — Heat transfer coefficient h: 25 W/(m²·K); Thermal conductivity k: 50 W/(m·K); Characteristic length from: Direct value; Characteristic length L_c: 10 mm.

Results — Characteristic length = 10 mm; **Biot number = 0.005**; Lumped-capacitance model = Valid (Bi < 0.1).

## Key terms

- **Lumped capacitance**: Treating a body as a single temperature.

## FAQ

**What does Bi < 0.1 mean?**
Temperature inside the body is nearly uniform.

**How is it different from the Nusselt number?**
Bi uses the solid's k; Nu uses the fluid's k.

**What is the characteristic length of a sphere?**
V/A = r/3.

**Why does it matter?**
It decides which transient heat model to use.

**What formula does the Biot Number Calculator use?**
Bi = h·L_c / k,  L_c = V/A_s.


## 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/)