# Biot Number Calculator

Created by Miłosz Panfil, PhD
Reviewed by Dominik Czernia, PhD and Steven Wooding
Last updated: Oct 31, 2022

This Biot number calculator helps you compute the Biot number. What is the Biot number? The Biot number determines how quickly heat transfers from the surface of the body to its interior. The text below explains the physics behind the heat transfer and gives 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 interior will be very similar.

On the other hand, 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. 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 of a material. Check the thermal conductivity calculator to learn more about this phenomenon.

The Biot number compares the efficiency of these two processes.

1. 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.

2. On the other hand, if the material conducts heat well, then besides warming it up only in 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:

${\rm Bi} = \frac{h}{k}L_{\rm c},$

where:

• ${\rm Bi}$ – Biot number;
• $L_{\rm c}\ \rm [m]$ – Characteristic length of the material;
• $h\ \rm [W/m^2\! \cdot\! K]$ – Heat transfer coefficient at the material's surface; and
• $k\ \rm [W/m\! \cdot\! K]$ – Thermal conductivity of the material.

We can compute the characteristic length $L_{\rm c}\ \rm [m]$ knowing the volume $V\ \rm [m^3]$ and the area $A\ \rm [m^2]$ of a surface through which the material is heated up (or cooled down):

$L_{\rm c} = \frac{V}{A}$

For example, for a copper pan of water with characteristic length $\small L_{\rm c} = 15\ \rm cm$, the Biot number is $\small \rm Bi = 2.807$. This means that when we heat the pan, there will be a significant difference in temperatures between the water at the bottom and at the top of the pot. If we decrease the amount of water (decrease the characteristic length), the Biot number drops, signaling a more uniform temperature inside the pot.

In the Biot number calculator computations, we took the water thermal conductivity as $\small k = 0.7\ \rm W/m\! \cdot\! K$ and the heat transfer coefficient between copper and water as $\small h = 13.1\ \rm W/m\! \cdot\! K$.

Miłosz Panfil, PhD
Characteristic length
Surface area
Volume
Biot number
Characteristic length
m
Heat transfer coefficient
W/(m²·K)
Thermal conductivity
W/(m·K)
Biot number
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