💧 Reynolds Number Calculator
Calculate the Reynolds number using Re = ρvD/μ or Re = vD/ν. Determine whether flow is laminar (Re < 2,300), transitional (2,300 < Re < 4,000), or turbulent (Re > 4,000) in pipes and channels.
What Is the Reynolds Number?
The Reynolds number (Re) is a dimensionless quantity used in fluid mechanics to predict flow patterns in different fluid flow situations. It represents the ratio of inertial forces to viscous forces within a fluid.
The Reynolds number is defined as:
Re = (ρ · v · D) / μ
or Re = (v · D) / ν
where:
- ρ = fluid density (kg/m³)
- v = flow velocity (m/s)
- D = characteristic length (m), e.g., pipe diameter
- μ = dynamic viscosity (Pa·s)
- ν = kinematic viscosity (m²/s) = μ/ρ
Flow Regimes
The Reynolds number determines the flow regime:
- Laminar flow (Re < 2,300): Fluid flows smoothly in parallel layers. Viscous forces dominate.
- Transitional flow (2,300 < Re < 4,000): Flow is unstable and fluctuates between laminar and turbulent.
- Turbulent flow (Re > 4,000): Flow is chaotic with eddies and mixing. Inertial forces dominate.
For pipe flow, the characteristic length is the pipe diameter D. For flow over a flat plate, the characteristic length is the distance from the leading edge. For flow around a sphere, it is the sphere diameter.
Why Use This Calculator?
- Two calculation methods: Use density and dynamic viscosity, or kinematic viscosity directly.
- Instant flow regime: Automatically identifies laminar, transitional, or turbulent flow.
- Flexible units: Supports m/s, cm/s, ft/s, m, cm, mm, ft, in.
- Step-by-step breakdown: See exactly how the Reynolds number is calculated.
- Free & private: No registration, no data storage — all calculations are done in your browser.
❓ Reynolds Number Calculator FAQ
What is the formula for the Reynolds number?
The formula is Re = (ρ · v · D) / μ or equivalently Re = (v · D) / ν, where ρ is density, v is velocity, D is characteristic length, μ is dynamic viscosity, and ν is kinematic viscosity.
What does the Reynolds number tell us?
The Reynolds number indicates the flow regime. A low Reynolds number (< 2,300) means laminar flow (smooth, orderly). A high Reynolds number (> 4,000) means turbulent flow (chaotic, mixing). Between 2,300 and 4,000 is transitional flow.
What is the critical Reynolds number for pipe flow?
The critical Reynolds number for pipe flow is approximately 2,300. Below this value, flow is generally laminar; above 4,000, it is fully turbulent.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity (μ) is a measure of a fluid's resistance to shear flow, measured in Pa·s. Kinematic viscosity (ν) is the ratio of dynamic viscosity to density (ν = μ/ρ), measured in m²/s. Kinematic viscosity is often used because it directly incorporates density effects.
What is the characteristic length for pipe flow?
For flow in a circular pipe, the characteristic length is the pipe diameter D. For non-circular pipes, the hydraulic diameter is used, defined as 4A/P, where A is the cross-sectional area and P is the wetted perimeter.
What are typical viscosity values?
At 20°C: Water has μ ≈ 1.00 mPa·s and ν ≈ 1.00 × 10⁻⁶ m²/s. Air has μ ≈ 18.2 µPa·s and ν ≈ 1.51 × 10⁻⁵ m²/s. Engine oil has μ ≈ 100 mPa·s. Viscosity decreases with increasing temperature for liquids and increases for gases.
Can the Reynolds number be used for gases?
Yes, the Reynolds number is used for both liquids and gases. For gases, density and viscosity depend on temperature and pressure, so these values must be evaluated at the appropriate conditions.
What is the Reynolds number for flow over a flat plate?
For flow over a flat plate, the characteristic length is the distance from the leading edge (x). The critical Reynolds number for transition to turbulence is typically 5 × 10⁵, though this can vary with surface roughness and free-stream turbulence.
How accurate is this calculator?
This calculator uses the standard Reynolds number formula. Accuracy depends on the precision of your input values. You can adjust the decimal precision in the output.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.