Reynolds Number Calculator
Find the Reynolds number for flow in a pipe or over a surface. Enter the flow speed (m/s or ft/s), the characteristic length or pipe diameter (m, mm, or inches), and pick a fluid — the tool returns Re and tells you if the flow is laminar or turbulent.
Example: with Flow velocity 2 · Velocity unit m/s · Diameter / length 50 · Length unit mm · Fluid (kinematic viscosity ν) Water, 20 °C → Reynolds number: 99,602.
- Flow regimeTurbulent — chaotic, well mixed
- ThresholdsPipe flow: laminar below 2,300, turbulent above about 4,000.
Computed by the calculator below using its default values. Change any input to see your own numbers.
The Reynolds number is the ratio of inertial forces to viscous forces. Below ~2,300 in a pipe viscosity wins and flow is smooth; above ~4,000 inertia wins and it churns.
What the Reynolds number tells you
Reynolds number, Re = vD/ν, compares the momentum of moving fluid to the viscous drag that tries to keep it in orderly layers. When Re is small, viscosity dominates and the fluid slides in smooth laminae — this is laminar flow. When Re is large, inertia overwhelms viscosity and the flow breaks into eddies and mixing, which is turbulence. Because it is a ratio of forces, Re is dimensionless: the same number predicts the same behavior in a garden hose or an oil pipeline.
For flow inside a round pipe the transition sits near Re = 2,300, with fully turbulent flow above roughly 4,000; the band between is transitional and unpredictable. Turbulence is not always bad — it mixes heat and mass efficiently — but it costs far more pressure to push, which is why the regime matters for pump and duct sizing.
How it’s calculated
Re = v·D/ν, with velocity v in m/s, characteristic length D in m, and kinematic viscosity ν in m²/s. ft/s is converted at 0.3048 m/s, mm at /1000, inches at 0.0254 m. Fluid presets use standard published ν: water 1.004e-6 (20 °C), 1.307e-6 (10 °C), 0.658e-6 (40 °C); air 1.511e-5 (20 °C), 1.338e-5 (0 °C); SAE 30 oil ≈1.0e-4 m²/s.
Uses the vD/ν form, so D must be the correct characteristic length (pipe inner diameter for internal flow). Viscosity is temperature-sensitive; the presets are single-temperature values.
Kinematic viscosity of common fluids
| Fluid | Temperature | ν (m²/s) |
|---|---|---|
| Water | 10 °C | 1.31 × 10⁻⁶ |
| Water | 20 °C | 1.00 × 10⁻⁶ |
| Water | 40 °C | 0.66 × 10⁻⁶ |
| Air | 0 °C | 1.34 × 10⁻⁵ |
| Air | 20 °C | 1.51 × 10⁻⁵ |
| SAE 30 oil | 20 °C | ≈1.0 × 10⁻⁴ |
Standard reference values (Engineering Toolbox / White, Fluid Mechanics); rounded.
Common mistakes
- Using diameter in millimeters without converting to meters — a 1000× error in Re.
- Plugging in dynamic viscosity μ where the vD/ν form expects kinematic viscosity ν (ν = μ/ρ).
- Treating 2,300 as a hard line; the real transition depends on pipe roughness and inlet disturbances.
- Using an outside pipe diameter instead of the inner bore as the characteristic length.
Frequently asked questions
What is the Reynolds number formula?
Re = v·D/ν, where v is velocity, D is the characteristic length (pipe inner diameter), and ν is the fluid's kinematic viscosity. It is dimensionless when all three are in consistent SI units.
What Reynolds number is laminar versus turbulent?
In a round pipe, flow is laminar below Re ≈ 2,300 and turbulent above about 4,000. Between those values it is transitional and can flip between the two.
Why is the Reynolds number dimensionless?
It is a ratio of inertial to viscous forces, so the units cancel. That is what lets a small model and a full-size design behave the same way at matching Re.
Do I use dynamic or kinematic viscosity?
This tool uses kinematic viscosity ν in the vD/ν form. If you only have dynamic viscosity μ and density ρ, compute ν = μ/ρ first, or use the equivalent Re = ρvD/μ.