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Courant Number & CFD Time-Step Calculator

Estimate a transient CFD time step from velocity, local cell size and a target Courant number—or check the Courant number produced by a time step you already use.

FreeTransient CFDRuns in your browserSI units

CALCULATOR

Transient-flow inputs

Calculation mode

Characteristic velocity U m/s Use a representative local or expected maximum transport velocity. Local cell size Δx m Use the relevant small cell length in the direction of transport.

Target Courant numberA planning target—not a universal solver limit.

Include an additional wave / signal speedUseful when the relevant CFL speed is not only the flow velocity. The calculator will use U_eff = U + c.

WHAT COURANT NUMBER TELLS YOU

How far does information travel during one numerical time step?

For the simple one-dimensional convective form, the Courant number compares the distance travelled during one time step, UΔt, with a local mesh length, Δx.

Choose a local speed
U or U + signal speed

Choose a local cell scale
Δx

Set/check Δt
physical time step

Evaluate Co
Co = UΔt/Δx

IMPORTANT

Use the calculator as a pre-simulation estimate.

Local values control the maximum Courant number. Small cells and locally high velocities can dominate even when inlet-based estimates look safe.

Multidimensional finite-volume solvers use more detailed definitions. Solver-reported Courant numbers may be based on face fluxes, cell volumes and summed flux contributions rather than this single UΔt/Δx estimate.

Explicit methods commonly have strict CFL stability limits. Implicit methods may tolerate larger Courant numbers, but a numerically stable time step can still be too large to resolve the physics accurately.

Compressible and wave-dominated problems may require signal speed. When appropriate, include an acoustic or other characteristic propagation speed rather than using flow velocity alone.

Always monitor the solver's own Courant metric. Use this calculator to plan Δt, then verify the actual local/max Courant number after the simulation starts.

ABECATOR CFD TOOLS

Three core CFD planning tools are now live.

Use Reynolds number to characterize the flow, y+ to plan near-wall resolution and Courant number to estimate transient time-step requirements.

See all CFD tools

TIMESTEP → TRANSIENT CREDIBILITY

A stable timestep can still be too coarse for the physics you need to resolve.

Use Courant number as one constraint, then test whether the engineering output is independent of timestep and whether moving interfaces are properly resolved.

Technical Case

Courant Number & CFD Time-Step Calculator

Transient-flow inputs

How far does information travel during one numerical time step?

Use the calculator as a pre-simulation estimate.

Three core CFD planning tools are now live.

A stable timestep can still be too coarse for the physics you need to resolve.

CFD timestep sensitivity

VOF interface unstable or smeared

CFD troubleshooting support