Reynolds Number Calculator – Free Calculator

Q: What is a good characteristic length for a non-circular duct?

Use the hydraulic diameter D_h = 4A ÷ P, where A is the flow area and P the wetted perimeter.

Q: What is the Reynolds number of air flow?

Use ρ ≈ 1.2 kg/m³ and μ ≈ 0.018 mPa·s at room temperature; air at 5 m/s in a 0.2 m duct gives Re ≈ 67,000.

Q: Is 1 mPa·s the same as 1 cP?

Yes. One centipoise equals one millipascal-second.

Understanding the Reynolds number calculator — concept and principle

The Reynolds number Re is a dimensionless number that tells you whether a flow is likely to be smooth and orderly (laminar) or chaotic and mixing (turbulent). Enter a velocity, a characteristic length (the inner diameter for a pipe), the density and the dynamic viscosity, and the calculator returns Re and a pipe-flow regime. It is the first number to check before choosing a friction formula, a heat-transfer correlation or a scale for a model test.

Re 74,850 is well past 4,000, so this pipe flow is turbulent (scale is logarithmic).

How it is calculated

Re = ρvD ÷ μ, with ρ in kg/m³, v in m/s, D in m and μ in Pa·s (the entered mPa·s is divided by 1000).
Equivalent form: Re = vD ÷ ν, where ν = μ/ρ is kinematic viscosity (water at 20 °C ≈ 1.0 × 10⁻⁶ m²/s).
Pipe regime used here: Re < 2300 laminar, 2300–4000 transitional, above 4000 turbulent.

The principle

Re compares inertial forces, which carry disturbances along and amplify them, with viscous forces, which damp them out. Inertia scales with ρv², viscous stress with μv/D, and their ratio is ρvD/μ. When viscosity dominates (small Re), small disturbances die away and fluid moves in layers. When inertia dominates (large Re), eddies grow and the flow becomes turbulent. Osborne Reynolds showed this with dye experiments in glass pipes in 1883. Because Re is dimensionless, two flows with the same geometry and the same Re behave alike, which is why scale models work.

Worked example

Inputs: v = 1.5 m/s, D = 0.05 m, ρ = 998 kg/m³, μ = 1.0 mPa·s = 0.001 Pa·s.
ρvD = 998 × 1.5 × 0.05 = 74.85 kg/(m·s).
Re = 74.85 ÷ 0.001 = 74,850.
74,850 is above 4000, so the regime is turbulent.

Each point is the calculator re-run with only “Dynamic viscosity (mPa·s)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Dynamic viscosity (mPa·s)	Re
0.25	299,400
0.5	149,700
0.75	99,800
1	74,850
1.25	59,880
1.5	49,900
2	37,425

How to read the result

Where does your result fall?

Ordinary water pipes are almost always turbulent: even 0.1 m/s in a 50 mm pipe gives Re ≈ 5,000. Laminar pipe flow is typical of oils, syrups, blood in small vessels and microchannels. The 2300 limit is not sharp: in very smooth, disturbance-free pipes laminar flow has been kept to much higher Re, while rough or vibrating systems can turn turbulent sooner. For other geometries the thresholds differ; a flat plate boundary layer, for example, usually becomes turbulent around Re ≈ 5 × 10⁵ based on distance from the leading edge.

Common mistakes

Entering viscosity in Pa·s when the field expects mPa·s (centipoise), giving Re 1000 times too large.
Using the pipe radius instead of the diameter.
Applying the pipe thresholds to flow around spheres, plates or open channels.
Forgetting that viscosity changes strongly with temperature; water at 60 °C has about half the viscosity of water at 20 °C.

Keep in mind: The regime label is a guide based on pipe-flow conventions. Transition depends on inlet conditions, roughness and vibration, so treat values near 2300–4000 with caution in design work.

Frequently asked questions

What is a good characteristic length for a non-circular duct?