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
Flow Regime
Kinematic Viscosity ν
Extended More scenarios, charts & detailed breakdown
m/s
m
Reynolds Number
Flow Regime
Friction Factor (approx.)
Professional Full parameters & maximum detail
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

  1. Enter fluid density in kg/m³ (water=1000, air=1.225).
  2. Enter velocity in m/s and characteristic length (pipe diameter, chord, plate length).
  3. Enter dynamic viscosity in Pa·s.
  4. 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)
  1. NASA Glenn Research Center – Reynolds Number — NASA Glenn Research Center
  2. OpenStax University Physics Vol. 1 Chapter 14.7 – Viscosity and Turbulence — OpenStax
  3. White F M — Fluid Mechanics, 8th Edition — McGraw-Hill
  4. Engineering Toolbox – Reynolds Number — Engineering Toolbox
  5. Streeter V L, Wylie E B, Bedford K W — Fluid Mechanics — McGraw-Hill