Reynolds Number Calculator
Reynolds number, flow regime, and per length value for air and water.
What it does
Reynolds number sorts every flow into smooth or chaotic with one division. Low values mean viscosity rules and layers slide; high values mean inertia wins and eddies take over.
The tool above takes fluid, speed, and a length scale in metric or imperial. It returns Re, the regime word, and the per length figure that scales with size.
The default air case at 10 m/s over 0.2 m gives Re near 130,000, firmly turbulent, with 660,000 per m. The imperial mirror at 32.81 ft/s over 0.66 ft lands on the same 130,000.
NASA Glenn derives Re as density times speed times length over dynamic viscosity, then rewrites it with kinematic viscosity. OpenStax University Physics walks the same viscosity and turbulence chapter with the same bands.
Engineers match Re between model and full size so tunnel tests predict flight. Below 2,300 pipes run laminar, above 4,000 turbulent, and flat plates hold laminar far longer, toward 500,000.
How to use
- Pick metric or imperial units.
- Pick air or water.
- Type the flow speed.
- Type the length scale.
- Read Re first, regime beside it.
- Read the per length value last.
Formula
- V
- Flow speed in m/s or ft/s.
- L
- Length scale in m or ft: chord, diameter, or depth.
- nu
- Kinematic viscosity: air 0.0000151, water 0.000001004 m2/s.
NASA Glenn derives Re = rho V L / mu from the momentum equation and simplifies with nu = mu / rho. Kinematic values near 20 C are 0.0000151 m2/s for air and 0.000001004 m2/s for water. Display rounds to 2 significant figures, the engineering custom for this estimate.
Worked example
Example: air at 10 m/s over 0.2 m
Metric defaults: air, 10 m/s, 0.2 m length.
- Flow: air at 10 m/s past a 0.2 m chord.
- Air kinematic viscosity: 0.0000151 m2/s at room conditions.
- Re: 10 x 0.2 / 0.0000151 = 132,450, shown as 130,000.
- Band: far above 4,000, so turbulent.
- Per meter: 10 / 0.0000151 = 660,000 per m.
- Tool shows 130,000, Turbulent, 660,000 per m.
Reference table
| Setup | Re | Regime |
|---|---|---|
| Air 10 m/s, 0.2 m | 130,000 | Turbulent |
| Water 2 m/s, 0.05 m | 100,000 | Turbulent |
| Air 0.01 m/s, 0.02 m | 13 | Laminar |
| Air 1 m/s, 0.03 m | 2,000 | Laminar |
Limits
- Pipe bands shown; plates and channels differ.
- Room condition viscosities, not hot or cold extremes.
- One length scale; complex shapes need judgment.
- Estimate for learning, not certification testing.
Common mistakes
- Mixing diameter with radius as the length.
- Using dynamic instead of kinematic viscosity.
- Reading pipe bands onto wing surfaces.
- Forgetting temperature moves viscosity.
- Expecting exact transition at 2,300.
Try it yourself
Quick checks. Answers sit tucked under each question.
Water at 2 m/s over 0.05 m?
Re near 100,000, turbulent, 2,000,000 per m.
Air at 0.01 m/s over 0.02 m?
Slow and small: order 10, laminar.
32.81 ft/s over 0.66 ft in air?
Same 130,000 and turbulent in ft/s and ft.
Questions
What is the Reynolds formula?
Density times speed times length over dynamic viscosity, or speed times length over kinematic viscosity. Both give the same dimensionless number.
Where are the laminar lines?
Under about 2,300 laminar, 2,300 to 4,000 transitional, above 4,000 turbulent for pipe flow. Plates transition near 500,000.
What units does Re carry?
No units at all. All lengths and times cancel, which is why tunnels can test small models.
What lowers Re?
Thicker fluids and slower, smaller setups lower Re toward smooth laminar flow.
Which viscosities are built in?
Air uses 0.0000151 and water 0.000001004 m2/s near 20 C. Temperature shifts both, so treat results as estimates.
Do the bands fit every flow?
Yes for pipe style internal flow. External and open flows use higher transition bands, noted on the page.