Case 1
- Density ρ
- 998kg/m³
- Velocity v
- 1m/s
- Characteristic length L
- 0.05m
- Dynamic viscosity μ
- 0.001002Pa·s
49,800.399
Open with these valuesReynolds Number Calculator
49,800.399
Result: 49,800.399Re = ρ × v × L ÷ μ, with the dynamic viscosity in pascal-seconds. Water at 1 m/s in a 5 cm pipe gives about 49 800 — firmly turbulent. Inside a pipe, below roughly 2300 the flow is laminar, above roughly 4000 turbulent, and in between transitional.
Worked examples
Case 2
- Density ρ
- 1.225kg/m³
- Velocity v
- 10m/s
- Characteristic length L
- 0.5m
- Dynamic viscosity μ
- 0.0000181Pa·s
338,397.790
Open with these valuesCase 3
- Density ρ
- 850kg/m³
- Velocity v
- 0.8m/s
- Characteristic length L
- 0.08m
- Dynamic viscosity μ
- 0.03Pa·s
1,813.333
Open with these valuesHow it's calculated
Re = (ρ × v × L) ÷ μ
- StepEnter the density and the flow speed of the fluid.
- StepEnter the length scale — for a pipe, its inside diameter.
- StepEnter the dynamic viscosity in Pa·s, not the kinematic one in m²/s.
- ResultRead the dimensionless number and compare it with 2300 and 4000.
Reference table
| ρ, v, L, μ | Regime in a pipe | Re |
|---|---|---|
| 998, 1, 0.05, 0.001002 | Turbulent | 49800.399 |
| 1000, 2, 0.1, 0.001 | Turbulent | 200000 |
| 1.225, 10, 0.5, 0.0000181 | Turbulent | 338397.790 |
| 1260, 0.5, 0.02, 1.49 | Laminar | 8.456 |
| 850, 0.8, 0.08, 0.03 | Laminar | 1813.333 |
Questions
How do I calculate the Reynolds number?
Multiply density by velocity and by the characteristic length, then divide by the dynamic viscosity: Re = (ρ × v × L) ÷ μ. With SI units the result is dimensionless — water at 1 m/s in a 0.05 m pipe gives about 49 800.
What is the Reynolds number?
It is a dimensionless ratio of the inertial forces in a moving fluid to the viscous forces resisting that motion. It predicts whether a flow will be smooth or chaotic and is used across engineering, aerodynamics and biology.
Which Reynolds numbers are laminar and which turbulent?
For flow inside a pipe, Re below about 2300 is laminar, above about 4000 turbulent, and the range between is transitional. Those thresholds belong to pipe flow; wings, plates and spheres have their own critical values.
Dynamic or kinematic viscosity?
This calculator takes the dynamic viscosity μ in pascal-seconds, which is why density appears in the numerator. If you only have the kinematic viscosity ν in m²/s, multiply it by the density to get μ, or use the shorter form Re = v × L ÷ ν instead.
What is the characteristic length?
It is the length scale that defines the flow geometry. For flow inside a circular pipe it is the pipe diameter, for flow over a flat plate the distance along the plate, for flow around a sphere its diameter.
Sources and last check
Information, not professional advice.