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Reynolds Number Calculator

Find the Reynolds number.

How it is calculated

The Reynolds number compares inertial to viscous forces: Re = ρ × v × L / μ. ρ is fluid density in kg/m³, v is velocity in m/s, L is the characteristic length in metres (the inner diameter for a pipe) and μ is dynamic viscosity in Pa·s. Re is dimensionless and rounded to a whole number. The tool labels the flow Laminar below 2300, Transitional from 2300 to 4000 and Turbulent above 4000. These thresholds are the usual rule of thumb for flow in a pipe; other geometries have other limits. Viscosity must be above zero.

Worked example

Water (998 kg/m³, 0.001 Pa·s) flows at 1.5 m/s in a pipe of 0.05 m inner diameter. Multiply the top: 998 × 1.5 × 0.05 = 74.85. Divide by the viscosity: 74.85 / 0.001 = 74,850. The Reynolds number is 74,850, far above 4000, so the flow is Turbulent.

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Common mistakes

  • Using kinematic viscosity (m²/s) in the dynamic viscosity field; with kinematic viscosity, drop density from the formula.
  • Entering the pipe radius or the outer diameter rather than the inner diameter.
  • Viscosity in centipoise: 1 cP is 0.001 Pa·s, so water is 1 cP, not 1 Pa·s.
  • Entering the flow rate instead of the mean velocity; divide flow by cross-section area first.
  • Applying the 2300 and 4000 limits to flow over a plate or around a sphere, where they differ.

About this calculator

This calculator computes the Reynolds number, Re = ρvL/μ, a dimensionless ratio of inertial to viscous forces in a fluid. Enter the fluid's density, velocity, a characteristic length (like pipe diameter), and viscosity to get Re, plus whether the flow is laminar, transitional, or turbulent.

Mechanical and civil engineers rely on it to design pipelines, HVAC ducts, and aircraft wings, since the flow regime changes drag, heat transfer, and mixing behavior dramatically. It is one of the first numbers checked in any fluid mechanics problem.

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