This Biot number calculator helps you compute the Biot number (Bi) — a dimensionless quantity that tells you how quickly heat transfers from the surface of a body to its interior. Below you will find a definition of the Biot number, an explanation of the physics behind heat transfer, and the Biot number formula.
What is the Biot number?
The Biot number helps us answer the following question: how much will the temperature inside a body vary if we heat up a part of its surface?
- If the Biot number is small (much less than 1), then the temperature on the surface and in the interior will be very similar.
- If the Biot number is large (much larger than 1), there will be a large temperature gradient inside the body.
💡 See our temperature conversion tool for all your temperature conversion needs.
Heat transfer
If we warm the surface of a material, two things happen. First, we warm the surface — the efficiency of this process depends on the heat transfer coefficient (h). Secondly, the heat from the surface starts to flow through the rest of the material, heating the interior. How quickly this happens depends on the thermal conductivity (k) of the material.
The Biot number compares the efficiency of these two processes:
- If the heat transfer is more efficient than the thermal conductivity, the surface will warm up quicker than the rest of the body — the Biot number is larger than 1.
- If the material conducts heat well, then besides warming it up in only one place, its temperature will be pretty uniform — the Biot number is smaller than 1.
🙋 You might also be interested in our specific heat calculator.
Biot number formula
The Biot number formula is given by:
Bi = h · Lc / k
where:
- h — the heat transfer coefficient of the surrounding fluid, in W/(m²·K);
- Lc — the characteristic length of the body, in m; and
- k — the thermal conductivity of the body, in W/(m·K).
The characteristic length is usually defined as the ratio of the body's volume to its surface area, Lc = V / A. For some common shapes this simplifies to:
- Plane wall (slab): Lc = L (the half-thickness for a symmetrically heated wall);
- Long cylinder: Lc = r / 2 (r is the radius);
- Sphere: Lc = r / 3.
How to interpret the Biot number
| Biot number | Meaning |
|---|---|
| Bi < 0.1 | Internal temperature is nearly uniform. The lumped-capacitance (lumped-system) method is valid — you can treat the whole body as a single temperature. |
| 0.1 ≤ Bi ≤ 1 | A moderate temperature gradient exists inside the body. The lumped model becomes inaccurate. |
| Bi > 1 | A large temperature gradient builds up inside the body — the surface heats (or cools) much faster than the core. |
How to use the Biot number calculator: an example
- Enter the heat transfer coefficient h of the fluid in contact with the body — say, 200 W/(m²·K).
- Enter the characteristic length Lc of the body — for example, 0.1 m.
- Enter the thermal conductivity k of the body, or pick a material from the preset list — for example, carbon steel at 40 W/(m·K). (You can also use the preset list for copper, aluminum, ice, brick and more.)
- Read the result: Bi = h · Lc / k = 200 × 0.1 / 40 = 0.5. A value of 0.5 means a moderate temperature gradient — the lumped model is no longer accurate.
Units and measurement systems
The Biot number is dimensionless, so it has the same value in any consistent set of units. This calculator supports both the metric (SI) system — h in W/(m²·K), Lc in m, k in W/(m·K) — and the American/Imperial system — h in BTU/(h·ft²·°F), Lc in ft, k in BTU/(h·ft·°F). Pick the measurement system that fits your data and the units update automatically.
FAQs
What does a small Biot number mean?
A Biot number below 0.1 means the body conducts heat internally much faster than it exchanges heat with its surroundings. The temperature inside the body stays almost uniform, so you can use the simple lumped-capacitance method to model how it heats up or cools down.
What is the characteristic length?
The characteristic length Lc is generally the volume of the body divided by its surface area (Lc = V / A). For a sphere it equals r/3, for a long cylinder r/2, and for a symmetrically heated plane wall it equals the half-thickness.
How is the Biot number different from the Nusselt number?
Both are dimensionless and look similar, but the thermal conductivity in the Biot number is that of the solid body, while in the Nusselt number it is that of the fluid. The Biot number compares internal conduction resistance with surface convection resistance.