Reynolds Number Calculator
Find the Reynolds number Re = ρvL/μ and see whether a flow is laminar, transitional or turbulent. Choose a pipe, rectangular duct, open channel, flat plate or sphere, pick water, air, oil or another fluid preset, or enter your own density and viscosity.
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Pipe inside diameter, sphere diameter, plate distance or hydraulic radius
How to use the Reynolds Number Calculator
- Choose the flow situation: pipe, duct, channel, flat plate, sphere or other.
- Enter the characteristic length (pipe inside diameter, sphere diameter, etc.) or the duct width and height.
- Enter the velocity and its unit.
- Select the fluid, or enter its density and viscosity under Custom.
- Read Re and the regime, and check the velocity at which the flow would change regime.
Reynolds number formulas
- Reynolds number: Re = ρ v L ÷ μ = v L ÷ ν
- Kinematic viscosity: ν = μ ÷ ρ (1 cSt = 10⁻⁶ m²/s; 1 cP = 0.001 Pa·s)
- Hydraulic diameter: D_h = 4 A ÷ P; for a rectangle w × h, D_h = 2wh ÷ (w + h)
- Hydraulic radius: R_h = A ÷ P (for a full round pipe R_h = D ÷ 4)
- Critical velocity: v = Re_crit × ν ÷ L
Typical regime limits
| Situation | Length used | Laminar | Turbulent |
|---|---|---|---|
| Round pipe | Inside diameter | Re < 2,300 | Re > 4,000 |
| Non-circular duct | Hydraulic diameter | Re < ~2,300 | Re > ~4,000 |
| Open channel | Hydraulic radius | Re < ~500 | Re > ~2,000 |
| Flat plate boundary layer | Distance from leading edge | Re_x < ~5 × 10⁵ | Re_x > ~10⁶ (depends on roughness) |
| Sphere | Diameter | Stokes flow Re < 1 | Turbulent wake above ~1,000; drag crisis near 2–4 × 10⁵ |
Fluid properties used
| Fluid | Density (kg/m³) | Dynamic viscosity (cP) | Kinematic viscosity (cSt) |
|---|---|---|---|
| Water, 0 °C | 999.8 | 1.792 | 1.792 |
| Water, 20 °C | 998.2 | 1.002 | 1.004 |
| Water, 60 °C | 983.2 | 0.467 | 0.475 |
| Water, 100 °C | 958.4 | 0.282 | 0.294 |
| Air, 20 °C, 1 atm | 1.204 | 0.01825 | 15.16 |
| Hydraulic oil ISO VG 46, 40 °C | 870 | 40 | 46 |
| Glycerin, 20 °C | 1261 | 1,410 | 1,118 |
Air is about 15 times more viscous than water in kinematic terms, so at the same speed and size an air flow has a Reynolds number about 15 times lower.
Frequently asked questions
What is the Reynolds number formula?
Re = ρ × v × L ÷ μ = v × L ÷ ν, where ρ is the density (kg/m³), v the velocity (m/s), L the characteristic length (m), μ the dynamic viscosity (Pa·s) and ν = μ/ρ the kinematic viscosity (m²/s). Re has no units; it is the ratio of inertial to viscous forces.
What Reynolds number is laminar or turbulent in a pipe?
For flow in round pipes, Re below about 2,300 is laminar, above about 4,000 is turbulent, and between them the flow is transitional and can switch back and forth. Very smooth, disturbance-free pipes can stay laminar to higher values, so these are engineering guidelines.
What length should I use?
Use the dimension that controls the flow: the inside diameter for a pipe, the hydraulic diameter 4A/P for a non-circular duct, the diameter for a sphere or particle, the distance from the leading edge for a flat plate, and the hydraulic radius (area ÷ wetted perimeter) for an open channel. Regime limits only apply to the length they were defined with.
What is the Reynolds number of water in a pipe?
Water at 20 °C has ν ≈ 1.004 × 10⁻⁶ m²/s. At 1.5 m/s in a 50 mm pipe, Re = 1.5 × 0.05 ÷ 1.004e-6 ≈ 74,700, well into turbulent flow. Almost all water flow in household and industrial piping is turbulent.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity μ (Pa·s or centipoise) measures internal friction. Kinematic viscosity ν = μ ÷ ρ (m²/s or centistokes) divides that by density. Water at 20 °C is about 1.0 cP and 1.0 cSt; oils are usually specified in cSt, for example ISO VG 46 is 46 cSt at 40 °C.
Why does temperature matter so much?
Viscosity changes strongly with temperature. Water’s viscosity drops from 1.79 cP at 0 °C to 0.28 cP at 100 °C, so the same flow has a Reynolds number over six times higher when hot. Oils change even more. Gases behave oppositely: their viscosity rises with temperature.
Why is Re important?
It decides which equations apply. Friction factors and pressure drop in pipes, drag coefficients, heat-transfer rates and mixing all depend on Re. Two geometrically similar flows with the same Reynolds number behave the same way, which is why scale-model tests match Re.
Are all the tools on FreeToolCabin tested for quality and accuracy?
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