Reynolds Number Calculator
The Reynolds number (Re) is a dimensionless quantity used in fluid mechanics to predict whether flow will be laminar or turbulent. It is defined as Re = ρvL/μ, where ρ is the fluid density in kg/m³, v is the flow velocity in m/s, L is a characteristic length (pipe diameter or plate length) in metres, and μ is the dynamic viscosity in pascal-seconds (Pa·s). Equivalently, Re = vL/ν where ν is the kinematic viscosity. For internal pipe flow, flow is classified as laminar when Re is below 2,300 (smooth, layered flow), transitional between 2,300 and 4,000, and fully turbulent above 4,000 (chaotic, mixed flow). The thresholds differ for external flows over plates or cylinders. This calculator provides pre-filled viscosity values for common fluids (water at 20°C, air at 20°C, and SAE 30 oil) alongside custom entry, so you can quickly evaluate pipe sizing, heat exchanger design, or aerodynamic modelling scenarios. Understanding whether your flow is laminar or turbulent determines which friction correlations and heat transfer equations apply.
Reynolds number: -- — flow regime: --
Reynolds number formula
The Reynolds number is a ratio of inertial forces to viscous forces in a fluid flow. A higher Re means inertia dominates and turbulence is likely.
Re = (ρ × v × L) / μ = (v × L) / ν
Where:
ρ = fluid density (kg/m³)
v = flow velocity (m/s)
L = characteristic length, e.g. pipe diameter (m)
μ = dynamic viscosity (Pa·s)
ν = kinematic viscosity = μ/ρ (m²/s)
For pipe flow:
Re < 2,300: laminar
2,300 ≤ Re ≤ 4,000: transitional
Re > 4,000: turbulent
Worked example
Water at 20°C (ρ = 998 kg/m³, μ = 0.001002 Pa·s) flowing at 2 m/s through a 50 mm (0.05 m) pipe:
- Re = (998 × 2 × 0.05) / 0.001002 = 99.8 / 0.001002 = 99,601
- Re > 4,000: turbulent flow
Dynamic viscosity of common fluids at 20°C
| Fluid | ρ (kg/m³) | μ (Pa·s) | ν (m²/s) |
|---|---|---|---|
| Water at 20°C | 998 | 0.001002 | 1.004 × 10⁻⁶ |
| Air at 20°C | 1.204 | 1.813 × 10⁻⁵ | 1.506 × 10⁻⁵ |
| SAE 30 oil | 880 | 0.100 | 1.136 × 10⁻⁴ |
| Mercury at 20°C | 13,550 | 0.00153 | 1.13 × 10⁻⁷ |
Source: NIST and NASA. Values are approximate; viscosity varies with temperature.
Reynolds number calculator: frequently asked questions
What does the Reynolds number tell you?
The Reynolds number (Re) is a dimensionless ratio that indicates whether a fluid flow is dominated by viscous (sticky) forces or inertial (momentum) forces. A low Re means viscous forces dominate and the flow is smooth and ordered (laminar). A high Re means inertia dominates and the flow becomes chaotic (turbulent). It was introduced by Osborne Reynolds in 1883 and is one of the most important parameters in fluid mechanics. For pipe flow, Re below 2,300 is laminar, 2,300 to 4,000 is transitional, and above 4,000 is turbulent.
What are the laminar, transitional, and turbulent flow regimes?
In laminar flow (Re below 2,300 for pipes), fluid layers slide past each other in parallel sheets with no mixing between them. Pressure drop is proportional to velocity. In transitional flow (Re 2,300 to 4,000), the flow alternates between laminar and turbulent, and behaviour is unpredictable. In turbulent flow (Re above 4,000), fluid mixes vigorously with eddies and swirls, giving much higher pressure drop but also better heat and mass transfer. The exact transition thresholds vary with pipe roughness, inlet conditions, and disturbances.
Why is Reynolds number important in engineering?
Reynolds number governs pressure drop calculations in piping systems, heat exchanger design, aerodynamics of aircraft and vehicles, mixing in chemical reactors, and filtration. Engineers use it to select appropriate friction factors (Moody chart), to determine whether a flow is suitable for laminar-flow assumptions, and to scale results from model tests to full-size equipment. If you are designing a pipe system and Re is high, you need turbulent-flow friction correlations; if Re is low, laminar formulae apply.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity (mu, Pa·s or N·s/m²) measures a fluid's internal resistance to shear at a given shear rate. Kinematic viscosity (nu, m²/s) is dynamic viscosity divided by density: nu = mu / rho. Both appear in the Reynolds number: Re = rho * v * L / mu = v * L / nu. For water at 20°C, mu is approximately 0.001002 Pa·s and rho is 998 kg/m³, giving nu of about 1.004×10⁻⁶ m²/s. Engineers often use kinematic viscosity because it directly relates flow conditions to Re without needing density separately.
What are common applications of Reynolds number calculations?
Reynolds number is used in pipe flow to size pumps and determine pressure drop, in heat exchangers to calculate Nusselt number and heat transfer coefficients, in aerodynamics to predict boundary layer transition on wings and fuselages, in automotive engineering for drag and cooling analysis, in biomedical engineering for blood flow in arteries, in chemical engineering for mixing and reaction kinetics, and in civil engineering for river flow and sediment transport. It is also essential for wind tunnel and water tunnel testing, where models must match the full-scale Re to ensure flow similarity.
Official sources
- NASA Glenn Research Center: Reynolds Number.
- NIST fluid properties: NIST WebBook Fluid Properties.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.