🌊 Reynolds Number Calculator (Re=ρvD/μ)

Enter fluid density (ρ), velocity (v), pipe/characteristic diameter (D), and dynamic viscosity (μ) to compute the Reynolds number (Re=ρvD/μ), and this calculator automatically classifies the flow as laminar, transitional, or turbulent.

Fill in all 4 fields. Pick a fluid preset to auto-fill ρ and μ.

Fluid preset (auto-fills density & viscosity)

Fluid Density (ρ) (kg/m³)

Velocity (v) (m/s)

Pipe/Characteristic Diameter (D) (m)

Dynamic Viscosity (μ) (Pa·s)

Reynolds Number (Re)

—

Re < 2,300: laminar · 2,300 ≤ Re ≤ 4,000: transitional · Re > 4,000: turbulent (general empirical thresholds for flow inside a circular pipe.)

Fluid Property Reference Table (at 20°C)

Fluid	ρ (kg/m³)	μ (Pa·s)
Water (20°C)	998	1.003×10⁻³
Air (20°C)	1.204	1.825×10⁻⁵

※ Values below are typical figures commonly used in fluid mechanics references and may vary with actual temperature, pressure, and purity.

GUIDE

Learn more

What is the Reynolds Number? The Re=ρvD/μ Formula

The Reynolds number (Re) is a dimensionless quantity representing the ratio of inertial to viscous forces in a fluid, used to determine whether a flow is laminar or turbulent.

Re = ρ × v × D ÷ μ

ρ is fluid density (kg/m³), v is velocity (m/s), D is the pipe diameter or characteristic length (m), and μ is dynamic viscosity (Pa·s). The concept originates from Osborne Reynolds' 1883 experiments.

Laminar / Transitional / Turbulent Thresholds

For flow inside a circular pipe, Re < 2,300 is generally classified as laminar (fluid flows in smooth parallel layers), Re > 4,000 as turbulent (chaotic, eddying flow), and the range in between (2,300-4,000) as transitional. These are representative empirical thresholds assuming a smooth circular pipe — the actual transition point can shift with pipe shape, surface roughness, and inlet conditions.

Worked Example and Applications

For example, water (ρ=998kg/m³, μ=1.003×10⁻³Pa·s) flowing at 1m/s through a 0.05m-diameter pipe gives Re = 998×1×0.05÷0.001003 ≈ 49,751 — clearly turbulent. The Reynolds number is widely used as a first step in pipe design, heat exchanger performance prediction, and pressure-drop calculations.

Frequently asked questions

Why does the Reynolds number have no units?

Re is a ratio of inertial force (related to ρvD) to viscous force (related to μ), so all units cancel out in the calculation, making it dimensionless. This means it carries the same physical meaning regardless of the unit system used (SI, imperial, etc.).

Are the thresholds (2,300, 4,000) always exact?

No. These are general empirical values assuming a smooth, straight circular pipe. In practice, laminar flow can persist up to Re=10,000 or higher, or transition earlier, depending on pipe surface roughness, curvature, vibration, and other factors.

Can I use values for a different fluid instead of the presets?

Yes. Choose "Custom" and enter the density (ρ) and viscosity (μ) of your fluid directly. Since water and air properties also vary with temperature, consult a property table at the relevant temperature for precise calculations.