Reynolds Number Calculator
Calculate the Reynolds number of a flow and classify it as laminar, transitional or turbulent.
How it works
Re = ρ · v · L / µ
The Reynolds number is a dimensionless ratio of inertial forces to viscous forces in a flowing fluid. Below about 2,300 the flow is smooth and laminar; above roughly 4,000 it becomes chaotic and turbulent, with a transitional band between. It sets the character of the flow regardless of the specific fluid.
Worked example
Water (ρ = 1,000 kg/m³, µ = 0.001 Pa·s) flowing at 2 m/s through a 0.05 m pipe: Re = 1,000 × 2 × 0.05 ÷ 0.001 = 100,000 — firmly turbulent.
Frequently asked questions
What counts as the characteristic length?
For pipe flow it is the internal diameter; for flow over a surface it is the length along the flow. Choose the dimension most relevant to the geometry you are analysing.
Where are the laminar and turbulent thresholds?
A common convention for pipe flow is laminar below Re ≈ 2,300, turbulent above Re ≈ 4,000, and transitional in between. These are guidelines, not sharp cut-offs.
Why is Reynolds number dimensionless?
The units of density, velocity, length and viscosity cancel out completely, leaving a pure number. That is what lets the same value describe similar flows at very different scales.
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Educational estimate. Check the formula and units for your exact case.