Calculate the Biot number to determine if lumped capacitance analysis applies. Compare internal vs external thermal resistance for heat transfer problems.
The **Biot Number Calculator** determines whether a heated or cooled body can be treated as thermally uniform (lumped capacitance) or whether internal temperature gradients must be accounted for (distributed analysis with Heisler charts or numerical methods). The Biot number Bi = hLc/k compares convective resistance at the surface to conductive resistance within the body.
When Bi < 0.1, internal conduction is so fast relative to surface convection that the entire body is at nearly the same temperature at all times — lumped capacitance applies. When Bi ≥ 0.1, significant temperature gradients exist inside the body and a more detailed analysis is required.
Enter the convection coefficient (h), material thermal conductivity (k), and characteristic length (Lc), and the calculator instantly categorises the problem and provides the resistance breakdown. Built-in presets cover common engineering scenarios, and the reference tables show how Biot number changes with h and k.
Use the preset examples to load common values instantly, or type in custom inputs to see results in real time. The output updates as you type, making it practical to compare different scenarios without resetting the page.
Choosing the wrong analysis method — lumped when distributed is needed, or vice versa — leads to large errors in cooling/heating time predictions. This calculator provides instant Biot-number classification so you start with the correct approach.
This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Biot Number: Bi = h Lc / k Characteristic Length: Lc = V / A (general), half-thickness (plate), r/2 (cylinder), r/3 (sphere) where h = convection coefficient, k = thermal conductivity, V = volume, A = surface area.
Result: Bi = 0.01 — lumped capacitance valid
A steel plate (k = 50 W/mK) with Lc = 10 mm and h = 50 W/m²K gives Bi = 0.01. Since Bi < 0.1, the body is nearly isothermal and lumped analysis is appropriate.
Use consistent units throughout your calculation and verify all assumptions before treating the output as final. For professional or academic work, document your input values and any conversion standards used so results can be reproduced. Apply this calculator as part of a broader workflow, especially when the result feeds into a larger model or report.
Most mistakes come from mixed units, rounding too early, or misread labels. Recheck each final value before use. Pay close attention to sign conventions — positive and negative inputs often produce very different results. When working with multiple related calculations, keep intermediate values available so you can trace discrepancies back to their source.
Enter the most precise values available. Use the worked example or presets to confirm the calculator behaves as expected before entering your real data. If a result seems unexpected, compare it against a manual estimate or a known reference case to catch input errors early.
It is the ratio of internal conduction resistance to external convection resistance. Low Bi means heat conducts through the body much faster than it transfers to the surroundings.
When Bi < 0.1 — meaning the body's interior stays within about 5% of its surface temperature.
The surface approaches the fluid temperature quickly while the interior stays at the initial temperature — use Heisler charts or numerical methods. Use this as a practical reminder before finalizing the result.
Lc = Volume / Surface Area in general. For standard shapes: plate half-thickness, cylinder radius/2, sphere radius/3.
If h or k are temperature-dependent, Bi can vary. In most textbook problems, properties are assumed constant.
Both equal hL/k, but Biot uses the solid's conductivity and Nusselt uses the fluid's. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence. conductivity.