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Biot Number from Volume, Area & Thermal Properties

Calculate characteristic length V/A and Biot number from convection coefficient and solid conductivity with consistent thermal units.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Volume 1 m³, area 2 m², h = 10 W/(m²·K) and k = 20 W/(m·K) give Lc = 0.5 m and Bi = 0.25.

Lc = V/A; Bi = h Lc / k

Worked example

Enter these known values and leave the other values blank.

Volume
1 m³
Surface area
2 m²
Heat transfer coefficient
10 W/(m²·K)
Thermal conductivity
20 W/(m·K)
Characteristic length
0.5 m
Biot number
0.25

Assumptions and limitations

  • Use the surface area actually exchanging heat for V/A. Geometry-specific definitions of characteristic length must be kept consistent with the chosen analysis.
  • Bi compares internal conduction resistance with boundary convection resistance. A small value supports a lumped-temperature approximation under its other assumptions; it is not a universal accuracy guarantee.
  • Solid volume, exposed area and conductivity must be positive. Zero convection gives Bi = 0. BTU-based choices use the International Table convention.

Common questions

What should I check before using this result?

Use the surface area actually exchanging heat for V/A. Geometry-specific definitions of characteristic length must be kept consistent with the chosen analysis.

References

Bookify accepts zero convection and Biot number and uses exact International Table BTU units for convection. BTU-based thermal units use the International Table BTU and exact mass, time, length and temperature-interval definitions.

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