Reynolds Number Calculator
The Reynolds number Re = ρvD/μ compares inertial and viscous forces: water at 20 °C flowing at 1 m/s in a 50 mm pipe has Re ≈ 49800, which is turbulent.
49810
Turbulent (Re > 4000): mixing flow; friction depends on Re and pipe roughness (Colebrook).
- v = 1 m/s, D = 0.05 m
- Re = ρ v D / μ = 998.2 × 1 × 0.05 ÷ 0.001002 = 49810.4
Reynolds Number Formula
Re = ρ v D / μ = v D / ν
ρ density, v mean velocity, D diameter (characteristic length), μ dynamic viscosity, ν kinematic viscosity
The Reynolds number is the ratio of inertial to viscous forces. Low values mean viscosity damps disturbances and the flow stays laminar; high values mean inertia dominates and the flow becomes turbulent, which raises friction and heat transfer.
Worked Examples
- Water at 20 °C, 1 m/s, 50 mm pipe: Re = 998.2 × 1 × 0.05 ÷ 0.001002 = 49810 (turbulent).
- Air at 20 °C, 5 m/s, 300 mm duct: Re = 1.204 × 5 × 0.3 ÷ 0.0000181 = 99779 (turbulent).
- ISO VG 46 oil at 40 °C, 0.5 m/s, 25 mm line: Re = 870 × 0.5 × 0.025 ÷ 0.040 = 271.9 (laminar).
Flow Regimes in Pipes
| Re | Regime | Friction factor |
|---|---|---|
| < 2300 | Laminar | f = 64 / Re |
| 2300 – 4000 | Transitional | Uncertain; avoid for design |
| > 4000 | Turbulent | Colebrook–White (depends on roughness) |
Frequently asked questions
What Reynolds number is turbulent?
In pipes, flow is usually laminar below about 2300 and turbulent above about 4000; between them it is transitional. Other geometries (plates, spheres, stirred tanks) use different thresholds.
Which length goes into the Reynolds number?
For a full circular pipe, the inside diameter. For ducts that are not round, use the hydraulic diameter D_h = 4A/P (area over wetted perimeter).
Can I use kinematic viscosity?
Yes: Re = vD/ν. Kinematic viscosity already includes density (ν = μ/ρ). With ν in cSt, convert to m²/s by multiplying by 10⁻⁶.
Is the Reynolds number dimensionless?
Yes. Any consistent units give the same result; this calculator converts every input to SI first.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Reynolds Number Calculator. Retrieved October 17, 2026, from https://scientificconverters.com/calculators/reynolds-number/
IEEE
Scientific Converters, "Reynolds Number Calculator," scientificconverters.com. Accessed: Oct. 17, 2026. [Online]. Available: https://scientificconverters.com/calculators/reynolds-number/