About the Reynolds Number Calculator
This Reynolds number calculator tells you whether a flow is laminar, transitional or turbulent. Choose a fluid (water at several temperatures, seawater, air or glycerin) or enter your own density and viscosity, then enter the flow velocity and the characteristic length — the inside diameter for pipe flow, or the distance from the leading edge for flow over a flat plate.
Engineers and students use the Reynolds number to pick the right friction-factor or heat-transfer correlation, size pipes and ducts, scale wind-tunnel and water-tunnel models, and sanity-check CFD set-ups. For pipe flow the calculator also gives the Darcy friction factor for a smooth pipe, which feeds directly into pressure-drop calculations.
The regime limits are the usual engineering conventions: in a circular pipe, flow is generally laminar below Re ≈ 2,300 and fully turbulent above about 4,000; on a smooth flat plate the boundary layer typically turns turbulent around Re ≈ 500,000. Real transition depends on surface roughness, inlet conditions and disturbances. For non-circular ducts, enter the hydraulic diameter (4 × area ÷ wetted perimeter).
With the default inputs, the reynolds number is 74,716. Change any value above to recalculate instantly.
How to use the reynolds number calculator
- 1Pick the fluid, or choose custom and enter its density and dynamic viscosity.
- 2Choose pipe flow or flat-plate flow.
- 3Select metric or US units.
- 4Enter the mean velocity and the pipe inside diameter (or distance along the plate).
- 5Read the Reynolds number, the flow regime and, for pipes, the friction factor.
Formula and method
The Reynolds number is the ratio of inertial to viscous forces: density times velocity times a characteristic length, divided by dynamic viscosity (or velocity × length ÷ kinematic viscosity). Inputs are converted to SI units first — metres, metres per second, kg/m³ and Pa·s (1 cP = 0.001 Pa·s) — so Re is dimensionless.
For pipes the calculator labels flow laminar below 2,300, transitional from 2,300 to 4,000 and turbulent above 4,000. The laminar Darcy friction factor is exactly 64/Re; for turbulent flow it uses the Swamee–Jain explicit approximation of the Colebrook equation with zero roughness (a hydraulically smooth pipe). For a flat plate, the boundary layer is taken to transition at Re ≈ 5 × 10⁵ based on distance from the leading edge.
- Re
- Reynolds number (dimensionless)
- ρ
- Fluid density (kg/m³)
- V
- Mean flow velocity (m/s)
- L
- Characteristic length: pipe diameter or distance along a plate (m)
- μ
- Dynamic viscosity (Pa·s)
- ν
- Kinematic viscosity μ/ρ (m²/s)
- f
- Darcy friction factor
Worked examples
Water at 20 °C, 1.5 m/s in a 50 mm pipe
Re = 998.2 × 1.5 × 0.05 ÷ 0.001002 ≈ 74,700, well above 4,000, so the flow is turbulent. The smooth-pipe friction factor from the Swamee–Jain equation is about 0.019.
Glycerin at 0.5 m/s in a 25 mm tube
Glycerin is about 1,400 times more viscous than water: Re = 1,261 × 0.5 × 0.025 ÷ 1.412 ≈ 11. The flow is strongly laminar and the friction factor is 64 ÷ 11.16 ≈ 5.73.
Air at 20 °C over a 1 ft plate at 30 ft/s
Converting to SI, 30 ft/s = 9.144 m/s and 12 in = 0.3048 m. Re = 1.204 × 9.144 × 0.3048 ÷ 0.00001825 ≈ 184,000, below the 500,000 transition value, so the boundary layer is still laminar at the trailing edge.
Frequently asked questions
What is a Reynolds number?+
It is a dimensionless number that compares inertial forces to viscous forces in a moving fluid. Low values mean smooth, layered (laminar) flow dominated by viscosity; high values mean chaotic, mixing (turbulent) flow dominated by inertia.
What Reynolds number is turbulent flow in a pipe?+
In circular pipes, flow is usually laminar below Re ≈ 2,300 and turbulent above about 4,000. Between those values it is transitional and can switch back and forth. Very smooth, disturbance-free set-ups can keep laminar flow to much higher values.
What length should I use for the Reynolds number?+
Use the inside diameter for a round pipe, the hydraulic diameter (4 × cross-section area ÷ wetted perimeter) for non-circular ducts, the distance from the leading edge for a flat plate, and the diameter for flow around a sphere or cylinder.
What is the difference between dynamic and kinematic viscosity?+
Dynamic viscosity μ (Pa·s or centipoise) measures a fluid’s resistance to shear. Kinematic viscosity ν is dynamic viscosity divided by density (m²/s or centistokes). Re can be computed as ρVL/μ or, equivalently, VL/ν.
How does temperature affect the Reynolds number of water?+
Water’s viscosity drops sharply as it warms — from about 1.31 cP at 10 °C to 0.36 cP at 80 °C — so the Reynolds number for the same pipe and velocity is roughly 3.6 times higher in hot water than in cold water.