Reynolds number
Re = ρVD/μ
Density times velocity and characteristic diameter divided by dynamic viscosity.
Reynolds Number Calculator
Calculate Reynolds number for internal flow and classify the result using the workbench thresholds for laminar, transitional, and turbulent pipe flow.
Access: Free to use, no installation, and No account required.
Inputs
The workbench classifies Re < 2300 as laminar, 2300–4000 as transitional, and Re ≥ 4000 as turbulent for internal pipe flow. These thresholds are engineering conventions, not universal boundaries for every geometry.
Results
Reynolds number formula
Re = ρVD/μ = VD/ν. Reynolds number compares inertial effects with viscous effects and is dimensionless.
What it does not tell you
Reynolds number alone does not determine pressure loss. Pipe roughness, fittings, geometry, developing flow, non-Newtonian behavior, and compressibility may also matter. Use the full workbench for Darcy–Weisbach loss, friction factor, sizing, and water hammer.
Engineering reference
Reynolds Number Calculator: background and worked detail
Use the Reynolds Number Calculator to calculate Re = ρVD/μ for internal pipe flow and classify the result as laminar, transitional, or turbulent using the workbench's standard threshold ranges.
Inertial versus viscous forces
Reynolds number compares inertial effects with viscous effects. For internal circular-pipe flow, it is commonly formed from fluid density, mean velocity, hydraulic diameter, and dynamic viscosity.
The regime labels are engineering conventions for fully developed internal flow. Entrance conditions, disturbances, roughness, non-circular passages, non-Newtonian fluids, and other geometries can shift the onset and character of transition.
Equations used by this calculator
Kinematic form
Re = VD/ν
Because ν = μ/ρ, the same dimensionless ratio can be written using kinematic viscosity.
Water in a 50 mm pipe at 1 m/s
Use density 998 kg/m³, velocity 1 m/s, diameter 50 mm, and dynamic viscosity 1.002 mPa·s.
- Convert diameter to 0.050 m and viscosity to 0.001002 Pa·s.
- Re ≈ 49,800.
- The calculator classifies this as turbulent internal pipe flow.
Result: The corresponding kinematic viscosity is about 1.00×10⁻⁶ m²/s.
Transition is a range, not a line
Assumptions
- The entered diameter is the characteristic diameter for internal flow.
- Fluid properties are represented by constant density and viscosity.
- Regime classification uses the engine thresholds Re < 2300 laminar, 2300–4000 transitional, and > 4000 turbulent.
Limitations
- Reynolds number alone does not determine pressure loss or friction factor.
- The regime thresholds are not universal for every geometry, disturbance level, or non-Newtonian fluid.
Validation checks
Textbook transition thresholds anchor these checks.
Velocity scaling
Case: Double velocity with all other inputs unchanged.
Expected: Reynolds number should double.
Viscosity scaling
Case: Double dynamic viscosity with all other inputs unchanged.
Expected: Reynolds number should halve.
Reynolds Number Calculator FAQ
Is Reynolds number dimensionless?
Yes. When units are consistent, the units cancel and Reynolds number is dimensionless.
What Reynolds number is turbulent in a pipe?
This calculator uses Re above 4000 as turbulent, 2300–4000 as transitional, and below 2300 as laminar for internal pipe flow.
Does high Reynolds number always mean high pressure loss?
Not by itself. Pressure loss also depends on geometry, roughness, length, velocity, fittings, and the applicable friction relationship.
Where this calculation comes from
Shared with the Fluid Mechanics Workbench, which carries the full pipe-network and boundary-layer workflow.
Open the source workbench →Read calculation and source methodology →