Courant Number Calculator
Calculate Courant number from SI inputs (velocity, time step, cell size) for CFD stability estimates.
Governing Formula
Courant Number (C or Co)
Use this as a quick diagnostic / starting point. Verify against your solver setup, mesh, timestep, model assumptions, and operating conditions.
Want to understand the math?
Read the theory behind Courant Number →
Worked Example
Scenario: Transient Aerodynamics
You are setting up a Large Eddy Simulation (LES) over a vehicle where the maximum freestream velocity is 50 m/s and the smallest grid cells in the wake are 0.01 m. You need to determine a stable time step.
- Velocity = 50 m/s
- Cell Size = 0.01 m
- Time Step = 0.0001 s
Interpretation: The Courant (CFL) number is 0.5. For an explicit solver, this is below the stability limit of 1.0, meaning the simulation should be mathematically stable. If you double the time step to 0.0002 s, the CFL becomes 1.0, which is right at the stability limit and may cause divergence.
Assumptions & limitations
Limitations
- Local Velocity: Stability is controlled by the highest local velocity in the smallest local cell, which may not be the freestream velocity.
- Solver Dependent: Acceptable Courant numbers depend heavily on whether your solver uses an explicit scheme (typically requires CFL < 1) or implicit scheme (often stable at CFL > 1, though accuracy degrades).
- Cell Size Definition: In 3D unstructured meshes, "cell size" can refer to distance between cell centers, cube root of volume, or specific dimension in the flow direction.
- Scope: This is a 1D simplified metric. It is a timestep/mesh diagnostic, not a guarantee of convergence, stability, or accuracy.