Reynolds Number Calculator
The Reynolds number (Re) is a dimensionless ratio of inertial to viscous forces, Re = ρ·v·L / μ. It tells you whether a flow is laminar (smooth, parallel streamlines), transitional (unstable) or turbulent (chaotic eddies). This calculator runs everything in SI internally but accepts common engineering units (kg/m³, g/cm³, lb/ft³, cP, …), classifies the flow against the standard pipe-flow thresholds (Re < 2300 laminar, 2300–4000 transitional, ≥ 4000 turbulent), and also reports the kinematic viscosity ν = μ/ρ as a cross-check.
Enter valid numbers: density, length and viscosity must be > 0 and velocity ≥ 0.
Reynolds number Re
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—
Flow regime (pipe flow)
< 2300 Transitional
2300–4000 Turbulent
≥ 4000
- ρ (kg/m³)
- —
- v (m/s)
- —
- L (m)
- —
- μ (Pa·s)
- —
- Kinematic ν = μ/ρ
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Formula
Re = ρ · v · L / μ = v · L / ν Pipe flow: Re < 2300 laminar, 2300 ≤ Re < 4000 transitional, Re ≥ 4000 turbulent
- · Pick the characteristic length L to match the geometry: for a circular pipe use the inside diameter D; for non-circular ducts or open channels use the hydraulic diameter Dₕ = 4A/P (A = cross-section, P = wetted perimeter); for external flow over a sphere or cylinder use the diameter; for a flat-plate boundary layer use the distance x from the leading edge.
- · Dynamic viscosity units: 1 cP = 1 mPa·s = 10⁻³ Pa·s; 1 poise (P) = 0.1 Pa·s. Kinematic viscosity units: 1 cSt = 1 mm²/s = 10⁻⁶ m²/s.
- · Reference values at 20 °C from CRC Handbook of Chemistry and Physics, 97th ed.: water ρ = 998 kg/m³, μ = 1.002 cP; air ρ = 1.204 kg/m³, μ = 0.01825 cP (18.25 μPa·s); SAE 30 motor oil ρ ≈ 891 kg/m³, μ ≈ 290 cP.
- · The 2300 / 4000 thresholds for pipe flow date back to Reynolds 1883 and are still the values used by modern texts such as Çengel & Cimbala, Fluid Mechanics: Fundamentals and Applications, ch. 8. External flows use completely different thresholds (flat-plate boundary-layer transition is around Re_x ≈ 5 × 10⁵).
- · Real-world behaviour in the transitional band (2300 ≤ Re < 4000) is sensitive to inlet disturbances, wall roughness and vibration; designers generally avoid sizing pipes in that range.
- · Friction pressure drop in turbulent flow needs a Moody chart or the Colebrook equation; laminar flow uses Hagen–Poiseuille, f = 64/Re.
Frequently asked
What value should I use for the "characteristic length" L — the outer diameter or the inner diameter?
It depends on the geometry, but for the most common case — internal flow in a circular pipe (water, oil, gas) — L is always the inside diameter (ID) of the pipe, not the outside diameter. A frequent mistake is to plug in the nominal size or OD of copper or steel pipe, which makes Re too high by 10–30 % and can flip the regime classification. For non-circular ducts (square pipes, elliptical pipes, half-full channels) use the hydraulic diameter Dₕ = 4·A/P, where A is the cross-sectional area of the fluid and P is the wetted perimeter; for a square duct of side a this gives Dₕ = a, for a half-full circular pipe Dₕ equals the full diameter. For external flow (sphere, cylinder, airfoil) use the relevant characteristic length: sphere diameter, airfoil chord, etc.
My handbook only lists kinematic viscosity ν, not dynamic viscosity μ — can I still use this calculator?
Yes. Because Re = v·L / ν, you can recover dynamic viscosity from kinematic viscosity and density via μ = ρ · ν, then enter μ here. Example: water has ν = 1.004 × 10⁻⁶ m²/s (= 1.004 cSt) and ρ = 998 kg/m³, so μ = 998 × 1.004 × 10⁻⁶ ≈ 1.002 × 10⁻³ Pa·s = 1.002 cP. Quick shortcut: 1 cP (mPa·s) = ν (cSt) × ρ (g/cm³), so for water-like fluids with ρ ≈ 1 g/cm³ the numerical values in cSt and cP almost coincide.
Why is pipe flow always laminar below Re ≈ 2300? In my experiment it still looks laminar at Re = 5000.
The 2300 figure is the lower bound of the "natural transition" — with a sufficiently smooth inlet and quiet pipe, laminar flow can in principle be sustained up to Re ≈ 10⁵ (Reynolds himself reported this in his 1883 paper). But in real systems any inlet disturbance, bend, vibration or surface roughness will trigger transition, so engineers use Re ≈ 2300 as a conservative design threshold. If your setup has a bell-mouth inlet, smooth wall and almost no external disturbance, seeing laminar flow at Re = 5000 is plausible — but the system is metastable and will flip to turbulence with the slightest perturbation. Practical designs aim for either firmly turbulent (Re ≫ 4000) or firmly laminar (Re < 1500) flow to avoid the unreliable transitional band.
Beyond laminar vs turbulent classification, what is the Reynolds number actually used for?
Re is the most important similarity parameter in fluid mechanics. Applications include: (1) Model testing — wind-tunnel and water-tunnel studies require the model and full-scale system to have the same Reynolds number to be dynamically similar, so model results scale directly. (2) Pressure-drop calculations — for any pipe Re tells you which curve on the Moody chart (or which form of Colebrook / Haaland / Swamee–Jain) to use to get the Darcy friction factor f, after which Δp = f·(L/D)·(ρv²/2). (3) Drag and lift prediction — drag coefficients for spheres, cylinders and airfoils depend strongly on Re (the dimpled surface of a golf ball deliberately trips the boundary layer to turbulent, reducing the drag jump near Re ≈ 4 × 10⁴). (4) Heat-transfer — Nusselt-number correlations (Dittus-Boelter, Gnielinski) are functions of Re, predicting convective heat-transfer coefficients. In short, Re is the dimensionless ID card of any flow.
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