Reynolds Number Calculator
Calculate Reynolds number from fluid density, velocity, characteristic length, and dynamic viscosity. Identifies laminar, transitional, or turbulent flow for pipe flow, flat plates, and aerodynamics.
kg/m³
m/s
m
Pa·s
Reynolds Number Re
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Flow Regime —
Kinematic Viscosity ν —
Extended More scenarios, charts & detailed breakdown ▾
m/s
m
Reynolds Number
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Flow Regime —
Friction Factor (approx.) —
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kg/m³
m/s
m
Pa·s
Reynolds Number
Reynolds Number —
Kinematic Viscosity ν —
Flow Regime —
Engineering Reference
Critical Re Reference —
Friction Factor (Darcy) —
Wind Tunnel Similitude —
How to Use This Calculator
- Enter fluid density in kg/m³ (water=1000, air=1.225).
- Enter velocity in m/s and characteristic length (pipe diameter, chord, plate length).
- Enter dynamic viscosity in Pa·s.
- Results show Reynolds number and flow regime. Use Extended tabs for preset fluids and geometries.
Formula
Re = ρ × v × L / μ or Re = v × L / ν
ρ = density (kg/m³) | v = velocity (m/s) | L = length (m) | μ = dynamic viscosity (Pa·s) | ν = kinematic viscosity (m²/s)
Example
Example: Water (ρ=998, μ=0.001), v=1 m/s, pipe D=0.05 m → Re = 998×1×0.05/0.001 = 49,900 — turbulent flow.
Frequently Asked Questions
- The Reynolds number (Re) is a dimensionless ratio of inertial to viscous forces: Re = ρvL/μ. It predicts flow behavior — low Re means viscosity dominates (laminar); high Re means inertia dominates (turbulent).
- For pipe flow, Re < 2,300 is laminar, 2,300–4,000 is transitional, and Re > 4,000 is turbulent. For a flat plate, transition typically occurs at Re ≈ 5 × 10⁵. For a sphere, the "drag crisis" occurs at Re ≈ 3.5 × 10⁵.
- Water at 20°C: μ ≈ 0.001 Pa·s (1 mPa·s). Air at 20°C: μ ≈ 1.81 × 10⁻⁵ Pa·s. Engine oil is much more viscous at ~0.1 Pa·s.
- Kinematic viscosity ν = μ/ρ (m²/s). It represents the ratio of viscous force to density. Water: ν ≈ 1 × 10⁻⁶ m²/s. Air: ν ≈ 1.5 × 10⁻⁵ m²/s. Re can also be computed as Re = vL/ν.
- Wind tunnel models must match the Reynolds number of the full-scale object to ensure aerodynamically similar flow patterns. If Re differs, boundary layer behavior, drag coefficients, and stall characteristics will not match reality.
Related Calculators
Sources & References (5) ▾
- NASA Glenn Research Center – Reynolds Number — NASA Glenn Research Center
- OpenStax University Physics Vol. 1 Chapter 14.7 – Viscosity and Turbulence — OpenStax
- White F M — Fluid Mechanics, 8th Edition — McGraw-Hill
- Engineering Toolbox – Reynolds Number — Engineering Toolbox
- Streeter V L, Wylie E B, Bedford K W — Fluid Mechanics — McGraw-Hill