Calculation
Re = ρ · v · D / μ
Low Re suggests laminar and high Re turbulent flow; thresholds depend on geometry and disturbances.
Re = ρvD/μ
Reynolds Number Calculator
Low Re suggests laminar and high Re turbulent flow; thresholds depend on geometry and disturbances.
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Result
Select a target and calculate.
Understand the inputs
- Reynolds number Re — The Reynolds number – a dimensionless quantity for the ratio of inertial to viscous forces in the flow. Low Re (roughly below 2300 in pipes) suggests laminar flow, high Re suggests turbulent flow; the exact threshold depends on roughness and disturbances.
- Density ρ — The fluid density at operating temperature. Source: a material table (water at 20 °C ≈ 998 kg/m³) or a datasheet.
- Mean velocity v — The mean flow velocity in the pipe. Source: computed from Q/A, or measured (see the flow-velocity calculator).
- Internal diameter D — The inner or hydraulic diameter of the line at the location considered. Source: pipe datasheet or calliper.
- Dynamic viscosity μ — The dynamic viscosity of the fluid at operating temperature – a measure of its stickiness. Source: a material table (water at 20 °C ≈ 1 mPa·s); for oils it rises sharply as temperature falls.
Example
Water, 1 m/s and 35.7 mm at 1 mPa·s gives Re ≈ 35,700.
Assumptions and limits
Round, fully developed pipe flow.
Understand Reynolds Number Calculator
This calculator finds a pipe flow's Reynolds number from density, velocity, internal diameter and dynamic viscosity. It explains why a water stream from a tap stays smooth and clear at low flow but suddenly turns rough and milky-white when opened further — the same transition the Reynolds number quantifies.
What does this quantity describe?
The Reynolds number is a dimensionless figure describing the ratio of inertial to viscous forces in a flow: Re = ρ·v·D/μ. It helps determine whether pipe flow is laminar (orderly) or turbulent (chaotic).
You can watch this transition directly at a kitchen tap: at low flow, the stream stays smooth, clear and nearly silent — laminar flow. Open the tap further and velocity rises, and with it the Reynolds number, until the stream turns rough, milky-white and louder — a visible sign of the transition to turbulent flow.
Formula and variables
Re = ρ · v · D / μ
Re = ρ · v · D / μv = Re · μ / (ρ·D)D = Re · μ / (ρ·v)
| Symbol / input | Meaning |
|---|---|
| Reynolds number Re | The Reynolds number – a dimensionless quantity for the ratio of inertial to viscous forces in the flow. Low Re (roughly below 2300 in pipes) suggests laminar flow, high Re suggests turbulent flow; the exact threshold depends on roughness and disturbances. |
| Density ρ | The fluid density at operating temperature. Source: a material table (water at 20 °C ≈ 998 kg/m³) or a datasheet. |
| Mean velocity v | The mean flow velocity in the pipe. Source: computed from Q/A, or measured (see the flow-velocity calculator). |
| Internal diameter D | The inner or hydraulic diameter of the line at the location considered. Source: pipe datasheet or calliper. |
| Dynamic viscosity μ | The dynamic viscosity of the fluid at operating temperature – a measure of its stickiness. Source: a material table (water at 20 °C ≈ 1 mPa·s); for oils it rises sharply as temperature falls. |
Choose the inputs correctly
Enter three of the four quantities to find the Reynolds number, or solve for another quantity. Use density and viscosity at the fluid's actual operating temperature, since both properties are temperature-dependent.
How to use the calculator
Select the target quantity and enter the other known values with units. Compare the result against the reference thresholds for laminar, unstable and turbulent flow afterward.
Worked example
Given water (ρ = 1,000 kg/m³, μ = 1 mPa·s) at v = 1 m/s and D = 35.7 mm, substitution gives Re ≈ 35,700 — well into the turbulent range.
Understand the result and units
A Reynolds number of about 35,700 sits well above the usual transition threshold, indicating clearly turbulent pipe flow. Turbulent flow causes higher pressure losses than laminar flow, but mixes a fluid more effectively.
The Reynolds number is dimensionless. Density is given in kg/m³, velocity in m/s, diameter in m or mm, and dynamic viscosity in mPa·s or Pa·s.
Typical applications
The Reynolds number is used to classify flow regimes in pipework, select pressure-loss models (laminar: Hagen-Poiseuille; turbulent: Darcy-Weisbach with roughness dependence), in heat transfer, and to design measurement and control sections.
Assumptions, limits and common mistakes
The classic thresholds (Re < 2,000 laminar, Re > 3,000 turbulent, unstable in between) apply to fully developed flow in smooth, circular pipes. Rough pipe walls, fittings, bends or pipe entrances can trigger turbulent behaviour at lower Reynolds numbers.
Common mistake: Do not apply the fixed 2,000/3,000 thresholds uncritically to other geometries (e.g. flow around bodies, open channels) — these specific values apply to fully developed pipe flow. Also, do not use room-temperature density and viscosity if the fluid actually flows at a noticeably different operating temperature.
Frequently asked questions
At what Reynolds number does pipe flow become turbulent?
By common classification, Re < 2,000 counts as laminar, Re > 3,000 as turbulent, with an unstable transition range in between — depending on pipe roughness and disturbances, transition can start earlier.
Why does a water stream turn milky-white at higher flow?
Because the flow becomes turbulent, trapping air bubbles through eddies or scattering light diffusely, instead of passing through clearly as in laminar flow.
Why is the Reynolds number dimensionless?
Because in ρ·v·D/μ, all base units (kg, m, s) cancel out exactly. That makes it directly comparable regardless of the unit system used.