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
| Field | What to enter |
|---|---|
| Heat transfer coefficient h | Units: W/(m²·K), BTU/(h·ft²·°F) |
| Thermal conductivity k | Units: W/(m·K), BTU/(h·ft·°F) |
| Characteristic length from | Choose one: Direct value, Volume and surface area |
| Characteristic length L_c | Units: mm, cm, m, in, µm |
| Volume | Units: cm³, m³, L |
| Surface area | Units: 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 number |
|---|---|
| 12.5 | 0.0025 |
| 18.75 | 0.0038 |
| 25 | 0.005 |
| 31.25 | 0.0063 |
| 37.5 | 0.0075 |
| 50 | 0.01 |
Formula
Bi = h·L_c / k, L_c = V/A_sWorked 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.
Frequently asked questions
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.