Fourier Number Calculator
What is a Fourier Number Calculator?
A Fourier Number Calculator computes the Fourier number (Fo), a dimensionless quantity in heat transfer that characterizes the ratio of heat conduction to heat storage in a material. It helps analyze transient (unsteady) heat conduction problems.
The formula is:

Where:
- Fo = Fourier number
- α = Thermal diffusivity (m²/s)
- t = Time (s)
- L = Characteristic length (m)
Why is a Fourier Number Calculator Important?
- Determines how fast heat diffuses through a material
- Helps in cooling and heating analysis of solids
- Used in engineering and physics for thermal modeling
- Essential in food processing, metallurgy, and insulation design
How Does It Work?
- Input values for thermal diffusivity (α), time (t), and characteristic length (L).
- Apply the formula
- Interpret the result:
- Fo << 1 → Heat has not penetrated deeply (early stage of conduction).
- Fo > 1 → Material is reaching thermal equilibrium.
Example:
If a metal with α = 1.2 × 10 −5 m²/s, a thickness of 0.01 m, and heated for 100 s, then:

Since Fo > 1, the material is nearing equilibrium.
When is a Fourier Number Calculator Used?
- Heat treatment of metals (annealing, quenching)
- Thermal insulation design
- Food industry (freezing and cooking time estimation)
- Geothermal and climate studies (heat diffusion in soil and rocks)