Reynolds Number Calculator

What is the Reynolds number?

The Reynolds number \(Re\) is a dimensionless quantity that compares inertial forces to viscous forces in a fluid flow. It is used to predict whether the flow will be laminar (smooth), transitional, or turbulent (chaotic).

General definition

\[ Re = \frac{\text{inertial forces}}{\text{viscous forces}} \]

Using dynamic viscosity

\[ Re = \frac{\rho \, v \, L}{\mu} \]

\(\rho\) – fluid density (kg/m³)
\(v\) – characteristic velocity (m/s)
\(L\) – characteristic length (m)
\(\mu\) – dynamic viscosity (Pa·s)

Using kinematic viscosity

\[ Re = \frac{v \, L}{\nu} \]

\(\nu\) – kinematic viscosity (m²/s)

Typical flow regime thresholds

For internal flow in circular pipes, engineers commonly use:

Laminar: \(Re < 2{,}300\)
Transitional: \(2{,}300 \le Re \le 4{,}000\)
Turbulent: \(Re > 4{,}000\)

For external flows (e.g., flow over a flat plate or airfoil), the critical Reynolds number depends on geometry and surface roughness, but transition often occurs around \(Re_x \approx 5 \times 10^5\) based on distance from the leading edge.

How to use the Reynolds number calculator

Select the flow type – internal (pipe/duct) or external (over a plate or body). This only affects the descriptive labels and regime hints.
Choose viscosity input – either:
- Dynamic viscosity μ with density ρ, or
- Kinematic viscosity ν directly.
Enter velocity and select the appropriate unit (m/s, ft/s, km/h, mph).
Enter the characteristic length (pipe diameter, hydraulic diameter, plate length, chord length, etc.) and its unit.
Fill in viscosity and density (if needed), then click “Calculate Reynolds Number”.

The tool converts all inputs to SI units, computes \(Re\), and classifies the flow regime. Use the quick presets to see typical values for water, air, and light oil.

Worked examples

Example 1 – Water in a pipe

Water at 20 °C flows through a smooth circular pipe of diameter \(D = 0.05\ \text{m}\) at average velocity \(v = 1.0\ \text{m/s}\). Use \(\rho \approx 998\ \text{kg/m}^3\) and \(\mu \approx 1.0 \times 10^{-3}\ \text{Pa·s}\).

\[ Re = \frac{\rho v D}{\mu} = \frac{998 \times 1.0 \times 0.05}{1.0 \times 10^{-3}} \approx 4.99 \times 10^4 \]

Since \(Re \approx 50{,}000 > 4{,}000\), the flow is turbulent.

Example 2 – Air over a flat plate

Air at 20 °C flows over a flat plate with velocity \(v = 5\ \text{m/s}\). The distance from the leading edge is \(x = 1\ \text{m}\). Take kinematic viscosity \(\nu \approx 1.5 \times 10^{-5}\ \text{m}^2/\text{s}\).

\[ Re_x = \frac{v x}{\nu} = \frac{5 \times 1}{1.5 \times 10^{-5}} \approx 3.3 \times 10^5 \]

This is below the typical transition value \(Re_x \approx 5 \times 10^5\), so the boundary layer is likely still laminar at \(x = 1\ \text{m}\).

Frequently asked questions

What does a high Reynolds number mean?

A high Reynolds number means inertial forces dominate over viscous forces. The flow tends to be turbulent, with eddies, mixing, and fluctuating velocity. This increases momentum and heat transfer but also increases pressure drop and drag.

Is Reynolds number always based on pipe diameter?

No. The characteristic length depends on the problem:

Circular pipe: diameter \(D\)
Non-circular duct: hydraulic diameter \(D_h = 4A/P\)
Flat plate: distance from leading edge \(x\)
Airfoil: chord length \(c\)
Sphere or cylinder: diameter

Can Reynolds number be used for gases and liquids?

Yes. The definition is general and applies to any Newtonian fluid (liquids or gases) as long as you use the appropriate density and viscosity at the operating temperature and pressure.

How accurate are the laminar/turbulent thresholds?

The thresholds (e.g., 2,300 and 4,000 for pipes) are empirical guidelines. Actual transition depends on surface roughness, disturbances, entrance effects, and geometry. For design, engineers often treat flows with \(Re < 2{,}000\) as safely laminar and \(Re > 10{,}000\) as fully turbulent.