Reynolds Number Calculator
Calculate the Reynolds number Re = ρvL/μ to determine whether fluid flow is laminar, transitional or turbulent. Enter fluid density, velocity, characteristic length and dynamic viscosity.
How to use this tool
- Enter fluid density ρ, flow velocity v, characteristic length l and dynamic viscosity μ in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your reynolds number re and the full breakdown beneath it.
The Reynolds number Re = ρvL/μ predicts whether flow is laminar (smooth, Re < 2300), transitional (2300–4000), or turbulent (chaotic, Re > 4000). ρ = density (kg/m³), v = velocity (m/s), L = characteristic length (m), μ = dynamic viscosity (Pa·s).
Formula
Reynolds number: Re = ρ v L / μ
Flow regime: Laminar if Re < 2300; Transitional if 2300 ≤ Re < 4000; Turbulent if Re ≥ 4000.
How it works
The Reynolds number is a dimensionless ratio of inertial to viscous forces in a flowing fluid. It uses fluid density ρ (kg/m³), flow velocity v (m/s), a characteristic length L such as pipe diameter (m), and dynamic viscosity μ (Pa·s). The thresholds used here (2300 and 4000) are standard for internal pipe flow; for flow over flat plates or around bodies the critical values differ.
Worked example
- Inputs: ρ = 1000 kg/m³ (water), v = 1.0 m/s, L = 0.05 m (pipe diameter), μ = 0.001 Pa·s.
- Re = 1000 × 1.0 × 0.05 / 0.001 = 50 / 0.001 = 50 000.
- Since Re = 50 000 ≥ 4000, the flow regime is turbulent.
Reynolds number Re = 50 000; flow regime = Turbulent (Re ≥ 4000).
Common mistakes to avoid
- Using dynamic viscosity (Pa*s) when kinematic viscosity (m^2/s) is required, or vice versa. Dynamic viscosity mu and kinematic viscosity nu = mu/rho are different quantities and interchanging them produces a result off by the fluid density.
- Choosing the wrong characteristic length L. For a pipe, L is the inner diameter; for a flat plate, it is the plate length along the flow direction. Using radius instead of diameter halves the Reynolds number.
- Applying the standard laminar/transitional/turbulent thresholds (2300/4000) to non-pipe geometries. Those cutoffs are specific to fully developed pipe flow; flow over a flat plate transitions at Re around 500,000.
Key terms
- Reynolds number (Re)
- A dimensionless number expressing the ratio of inertial forces to viscous forces in a fluid; higher Re indicates a greater tendency for turbulence.
- Laminar flow
- Smooth, orderly fluid motion in parallel layers with no mixing between them; occurs at low Re (below ~2300 in pipes).
- Turbulent flow
- Chaotic, irregular fluid motion with significant mixing and eddies; occurs at high Re (above ~4000 in pipes).
- Dynamic viscosity (μ)
- A measure of a fluid's resistance to flow or shear deformation, in Pa·s. Water at 20°C has μ ≈ 0.001 Pa·s.
- Characteristic length (L)
- A representative geometric dimension of the flow geometry, such as pipe inner diameter or plate length, used to non-dimensionalise the flow.
Frequently asked questions
- What fluid properties should I use for water and air?
- Water at 20°C: ρ = 998 kg/m³, μ = 0.001002 Pa·s. Air at 20°C: ρ = 1.204 kg/m³, μ = 1.81×10⁻⁵ Pa·s.
- What is the characteristic length for a pipe?
- For flow inside a pipe, use the internal diameter as the characteristic length. For flow over a flat plate, use the plate length.