What is the Reynolds number?

The Reynolds number (Re) is a dimensionless quantity that predicts flow regime by comparing inertial and viscous forces in a fluid.

Which formula does this calculator use?

Re = (ρ v L)/μ when density ρ and dynamic viscosity μ are known, or Re = (v L)/ν when kinematic viscosity ν is known.

What are typical thresholds for laminar and turbulent flow?

For internal pipe flow, laminar is Re 4000. Thresholds vary for other geometries.

Can I enter values in different units?

Yes. You can choose units for velocity, length, density, and viscosity. The calculator converts them internally to SI units.

Do I need both dynamic and kinematic viscosity?

No. You can compute Re either with density and dynamic viscosity, or directly with kinematic viscosity.

Where do the fluid properties come from?

Standard correlations (e.g., Sutherland’s law for air viscosity and Andrade’s equation for water viscosity) and representative values from authoritative references like NIST are used for presets.

Is the flow classification valid for any geometry?

The laminar/transitional/turbulent thresholds shown are typical for internal pipe flow. For other geometries (e.g., flat plates, airfoils), thresholds differ.

Reynolds Number Calculator

This professional-grade Reynolds number calculator helps engineers, researchers, and students quickly predict flow regime for internal and external flows. Enter velocity and characteristic length, then choose to use density and dynamic viscosity or kinematic viscosity. The tool offers authoritative unit handling, trusted fluid presets, and clear, accessible results.

Density + Dynamic viscosity

Kinematic viscosity

Fluid preset

Flow velocity v *

Characteristic length L *

Density ρ *

Dynamic viscosity μ *

Results

Reynolds number (Re) —

Flow regime —

Computed ν (if applicable) —

Notes Use pipe diameter for internal flow. Thresholds shown assume pipe flow.

Authoritative Data Source and Methodology

Primary reference for definitions and usage of the Reynolds number: Frank M. White, Fluid Mechanics, 8th ed., McGraw‑Hill, 2016.

Fluid property presets and correlations:

Water viscosity via Andrade’s correlation: μ = 2.414×10⁻⁵ × 10^{247.8/(T+133.15)} Pa·s (T in °C).
Air viscosity via Sutherland’s law with C = 110.4 K; air density via ideal gas at 1 atm.
Representative values cross-checked with NIST Chemistry WebBook (https://webbook.nist.gov/chemistry/).

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

For density ρ and dynamic viscosity μ known:
$$ \mathrm{Re} = \frac{\rho \, v \, L}{\mu} $$

For kinematic viscosity ν known:
$$ \mathrm{Re} = \frac{v \, L}{\nu} $$

Typical internal pipe flow classification: laminar for Re < 2300, transitional for 2300 ≤ Re ≤ 4000, turbulent for Re > 4000.

Glossary of Variables

v — flow velocity (m/s, ft/s, km/h, mph)
L — characteristic length (m, mm, cm, in, ft)
ρ — density (kg/m³, lb/ft³)
μ — dynamic viscosity (Pa·s, mPa·s, cP)
ν — kinematic viscosity (m²/s, cSt)
Re — Reynolds number (dimensionless)

How It Works: A Step-by-Step Example

Suppose water flows in a 5 cm diameter pipe at v = 1.5 m/s. At 20 °C, water density ρ ≈ 998.2 kg/m³ and μ ≈ 0.001002 Pa·s. Using Re = (ρ v L) / μ with L = 0.05 m:

$$ \mathrm{Re} = \frac{998.2 \times 1.5 \times 0.05}{0.001002} \approx 7.48 \times 10^{4} $$

Since Re ≈ 74,800 is well above 4,000, the flow is turbulent for internal pipes.

Frequently Asked Questions (FAQ)

Do I choose diameter or another length?

For internal pipe flow, use pipe diameter (or hydraulic diameter for non-circular ducts). For external flow over bodies, use the appropriate characteristic length (e.g., chord for airfoils).

How accurate are the fluid presets?

They are based on standard correlations and representative values at atmospheric pressure. For critical design, consult detailed property tables for your exact temperature and pressure.

What if I only know kinematic viscosity?

Select “Kinematic viscosity” mode and input ν directly. The calculator will use Re = vL/ν.

Can this calculator handle gas compressibility effects?

Reynolds number itself does not capture compressibility. For high Mach numbers or significant density variation, additional non-dimensional parameters are required.

Why is my Re extremely large or small?

Check units. Viscosity often causes mistakes: 1 cP = 1 mPa·s = 0.001 Pa·s. Ensure length and velocity units are consistent.

What thresholds apply to external flow?

Thresholds differ. For example, flow over a flat plate transitions around Re_x ≈ 5×10⁵ based on distance from the leading edge; consult appropriate references.

Does surface roughness affect Re?

Surface roughness does not change Re (a fluid-property/flow/geometry ratio), but it affects friction factors and transition behavior in turbulent flow.

Tool developed by Ugo Candido. Content verified by the CalcDomain Engineering Editorial Team.
Last reviewed for accuracy on: September 15, 2025.