What does the Biot number represent?

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 is lumped capacitance valid?

When Bi < 0.1 — meaning the body's interior stays within about 5% of its surface temperature.

What if Bi is very large?

The surface approaches the fluid temperature quickly while the interior stays at the initial temperature — use Heisler charts or numerical methods.

How do I find the characteristic length?

Lc = Volume / Surface Area in general. For standard shapes: plate half-thickness, cylinder radius/2, sphere radius/3.

Does Biot number change over time?

If h or k are temperature-dependent, Bi can vary. In most textbook problems, properties are assumed constant.

Biot vs Nusselt number?

Both equal hL/k, but Biot uses the solid's conductivity and Nusselt uses the fluid's conductivity.

Biot Number Calculator

Calculate the Biot number to determine if lumped capacitance analysis applies. Compare internal vs external thermal resistance for heat transfer problems.

Presets

Geometry

Heat Transfer Coefficient h (W/m²K)

Thermal Conductivity k (W/mK)

Characteristic Length Lc (m)

Surface Area (m²)

Volume (m³)

Biot Number

0.0100

✅ Bi < 0.1 — lumped capacitance valid

Method

Lumped Capacitance

Appropriate analysis method for this Biot number

Internal Resistance

0.000200 K·m²/W

Conduction resistance through the body

External Resistance

0.020000 K·m²/W

Convection resistance at the surface

Resistance Ratio

0.0100

Internal / external — Biot number by another name

Temperature Gradient

Uniform (< 5%)

Expected temperature uniformity inside the body

Biot Number Scale

Green: Bi<0.1 (lumped) · Yellow: 0.1–1 · Red: Bi>1 (distributed)

Biot Number vs h (constant k, Lc)

h (W/m²K)	Bi	Method
5	0.0010	Lumped
10	0.0020	Lumped
25	0.0050	Lumped
50	0.0100	Lumped
100	0.0200	Lumped
500	0.1000	Distributed
1000	0.2000	Distributed

Biot Number vs Material Conductivity

Material	k (W/mK)	Bi	Method
Copper	385	0.0013	Lumped
Aluminum	205	0.0024	Lumped
Steel	50	0.0100	Lumped
Glass	1	0.5000	Distributed
Wood	0.15	3.3333	Distributed
Air	0.026	19.2308	Distributed

Planning notes, formulas, and examples

About the Biot Number Calculator

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 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.

When This Page Helps

Choosing the wrong analysis method — lumped when distributed is needed, or vice versa — leads to large errors in cooling/heating time predictions. It gives Biot-number classification so you start with the correct approach.

How to Use the Inputs

Select a geometry type (plate, cylinder, sphere) to determine characteristic length.
Enter the heat transfer coefficient h in W/m²K.
Enter the material thermal conductivity k in W/mK.
Enter the characteristic length Lc in metres.
Read the Biot number and analysis method recommendation.
Use the reference tables to explore parameter sensitivity.

Formula used

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.

Example Calculation

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.

Tips & Best Practices

Metals in air almost always have Bi < 0.1 — lumped analysis usually works.
Liquids cooling metals often push Bi above 0.1 due to high h values.
For composite bodies, use the effective thermal conductivity.
In quenching (h > 1 000 W/m²K), even small metal parts can have Bi > 0.1.
Always verify your characteristic length matches the geometry.

When To Use This Calculator

Calculate the Biot number to determine if lumped capacitance analysis applies. Compare internal vs external thermal resistance for heat transfer problems. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

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.