What next?
Reynolds number tells you the flow regime. These give the forces in it.
How to use this calculator
- Enter the fluid density and velocity.
- Enter the characteristic length (e.g. pipe diameter) in metres.
- Enter the dynamic viscosity, or tap the water preset.
What your result means
The Reynolds number is a dimensionless ratio of inertial to viscous forces. Below about 2,300 flow is smooth and laminar; above about 4,000 it is chaotic and turbulent; in between it is transitional.
Why this one is different
The viscosity box wants dynamic viscosity in pascal-seconds; kinematic viscosity in square metres per second is a different quantity and the page says so, because the two are routinely confused and the answer comes out wrong by the density. The regime named beside the number uses the pipe-flow convention — 2,300 and 4,000 — and admits other geometries move those thresholds.
The number that predicts turbulence
Reynolds number lets a model in a wind tunnel stand in for a full-size aircraft: match the number and the flow behaves the same way, whatever the scale. It is one of the most useful dimensionless groups in all of engineering.
How it works
Reynolds number multiplies density, velocity and a characteristic length, then divides by dynamic viscosity. High values mean inertia dominates and flow breaks into turbulence; low values mean viscosity keeps the flow orderly and laminar.
Formula
Worked example
Water at 1.5 m/s through a 50 mm pipe (ρ = 1,000 kg/m³, μ = 0.001 Pa·s):
Re = 1,000 × 1.5 × 0.05 ÷ 0.001
Re = 75,000 → turbulent flow
Below about 2,300 the flow is laminar; above about 4,000 it is turbulent. At 75,000 this pipe is firmly turbulent, so friction losses follow the turbulent correlations.
Frequently asked questions
What counts as laminar or turbulent?＋
As a rule of thumb for pipe flow: below ~2,300 is laminar, above ~4,000 is turbulent, and the range between is transitional. Exact thresholds depend on the geometry.
What is the characteristic length?＋
It is the length scale that matters for the geometry — usually the pipe diameter for internal flow, or the chord length for a wing.
Does pipe roughness change the Reynolds number?＋
No. Reynolds number depends only on density, velocity, diameter and viscosity, so a rough pipe and a smooth one of the same size carrying the same flow give the same figure. Roughness matters for the friction factor and therefore the pressure loss, which is the next step after you know whether the flow is laminar or turbulent.
Why does the transition happen around 2,300 in a pipe?＋
That figure is empirical rather than derived: below it, viscous forces damp disturbances out; above roughly 4,000 they grow into turbulence. The band between is transitional and unpredictable.
What is kinematic versus dynamic viscosity?＋
Dynamic viscosity is the fluid's resistance to shear, in pascal-seconds. Kinematic viscosity is that divided by density, in square metres per second, and it is the form that appears directly in the Reynolds number.
Why does turbulence matter in a design?＋
Turbulent flow mixes far better and transfers heat far better, but it costs much more pressure drop. Heat exchangers want it; long pipelines usually do not.
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Assumptions & limitations
Engineering formulas are exact; the situations they model are not. Read your result with these limits in mind:
- The transition thresholds (roughly 2,300 and 4,000) apply to full, circular pipes. Open channels, flat plates and flow around objects use different critical values.
- Assumes steady, fully developed flow of a Newtonian fluid — oils, slurries and polymer solutions often are not Newtonian.
- Viscosity is strongly temperature-dependent: water at 5 °C is roughly twice as viscous as at 40 °C, which moves the Reynolds number by the same factor.
- For non-circular ducts, substitute the hydraulic diameter for D.