A Reynolds number calculator for pipes and plates
The Reynolds number compares inertial and viscous forces in a flowing fluid and tells you whether the flow is smooth (laminar) or chaotic (turbulent). This Reynolds number calculator computes it for flow in a round pipe, entered as a velocity or a flow rate, and for the boundary layer on a flat plate, using water or air properties taken from the temperature you enter, or a fluid of your own.
It reports the density, dynamic and kinematic viscosity it used, the Reynolds number, the regime, the velocity or distance at which the flow changes regime, and a table showing how the same flow behaves at other temperatures. That table makes the effect clear: cold water is more than four times as viscous as boiling water, so the same pipe at the same velocity has a very different Re.
Use it for a quick regime check before choosing a friction model. For the pressure drop that follows, use the pipe flow calculator, which applies Darcy–Weisbach and the Colebrook friction factor.
How to use the Reynolds Number Calculator
- Choose pipe, flat plate or another length scale, and the fluid: water, air or custom.
- Enter the temperature (and the air pressure), or your own density and viscosity for a custom fluid.
- Enter the pipe inner diameter or plate length, and the velocity, or for a pipe the flow rate.
- Read the Reynolds number and regime, then check the temperature table.
Reynolds Number Calculator features
Pipe and plate
Pipe regimes at 2,300 and 4,000, plate transition near 5 × 10⁵.
Water and air properties
Density and viscosity computed from the temperature.
Flow rate input
Enter litres per second, cubic metres per hour or gallons per minute for a pipe.
Temperature table
See the same flow at other temperatures at a glance.
The Reynolds number formula
The Reynolds number is Re = ρ v L ÷ μ = v L ÷ ν, where ρ is the density, v the velocity, L the characteristic length (the inner diameter of a pipe, or the distance from the leading edge of a plate), μ the dynamic viscosity and ν = μ ÷ ρ the kinematic viscosity. For a pipe given a flow rate the velocity is v = Q ÷ (π D² ÷ 4).
Example: water at 20 °C (ρ = 998.2 kg/m³, μ = 1.002 mPa·s) flowing at 1 m/s in a 50 mm pipe gives Re = 998.2 × 1 × 0.05 ÷ 0.001002 = 49,800, which is turbulent. The same water at 0.03 m/s would give Re of about 1,500, which is laminar. For air at 20 °C (ρ = 1.204 kg/m³, μ = 18.1 µPa·s) at 10 m/s along a 1 m plate, Re is about 665,000.
| Case | Laminar | Transitional | Turbulent |
|---|---|---|---|
| Full pipe | Re < 2,300 | 2,300 to 4,000 | Re > 4,000 |
| Flat plate boundary layer | Re < about 5 × 10⁵ | depends on roughness and disturbances | beyond transition |
Where the properties come from
- Water density uses the Tanaka et al. (2001) equation, accurate to a few parts in ten thousand from 0 to 100 °C.
- Water viscosity uses the Vogel equation with constants of 2.414 × 10⁻⁵ Pa·s, 247.8 K and 140 K, good to about 2.5% over 0 to 100 °C.
- Air density comes from the ideal gas law with a specific gas constant of 287.05 J/(kg·K), and viscosity from Sutherland’s law (1.716 × 10⁻⁵ Pa·s at 273.15 K, S = 110.4 K).
- Dissolved salts, steam, ice and high pressure are outside these fits; use the custom fluid with your own values.
Reynolds Number Calculator FAQ
How do I calculate the Reynolds number in a pipe?
Re = velocity × inner diameter ÷ kinematic viscosity. If you know the flow rate, first find the velocity as flow rate divided by the pipe cross-section.
What Reynolds number is laminar?
In a round pipe, below about 2,300. Above 4,000 the flow is turbulent and in between it is transitional.
What is the Reynolds number of water?
It depends on the size and speed. Water at 20 °C at 1 m/s in a 50 mm pipe has Re of about 49,800. Its kinematic viscosity is 1.004 mm²/s at 20 °C.
How do I find the Reynolds number for air?
Choose air, enter the temperature and pressure, then the length and speed. At 20 °C and 1 atm air has a kinematic viscosity of about 15.06 mm²/s.
Does the pipe roughness change the Reynolds number?
No. Roughness affects the friction factor and can trigger turbulence earlier, but Re itself uses only the fluid, the speed and the length.
Which length do I use for a non-circular duct?
Use the hydraulic diameter, 4 × area ÷ wetted perimeter, in the pipe diameter box.