Reynolds Number Calculator
The Reynolds number is the ratio of inertial to viscous forces in a moving fluid, and it predicts whether flow is smooth or chaotic. Enter a flow velocity, a characteristic length such as pipe diameter, and the fluid viscosity, and the calculator returns the dimensionless Reynolds number plus the flow regime. You can supply kinematic viscosity on its own, or density with dynamic viscosity.
How to find the Reynolds number
- Pick the viscosity input from the dropdown: 'Density + dynamic viscosity' or 'Kinematic viscosity'.
- Enter the flow velocity in meters per second.
- Enter the characteristic length, usually the inside pipe diameter, in meters.
- Type the kinematic viscosity in m2/s, or the density in kg/m3 and dynamic viscosity in Pa s.
- Read the Reynolds number and the regime label, then copy the summary if you need it.
Examples
Water in a 50 mm pipe (density and viscosity)
v = 2 m/s, D = 0.05 m, density 1000 kg/m3, viscosity 0.001 Pa s
Re = 100000, turbulent
Slow trickle, same pipe (kinematic viscosity)
v = 0.01 m/s, D = 0.05 m, kinematic viscosity 1e-6 m2/s
Re = 500, laminar
On the edge of transition (kinematic viscosity)
v = 0.06 m/s, D = 0.05 m, kinematic viscosity 1e-6 m2/s
Re = 3000, transitional
Frequently asked questions
What is the Reynolds number formula?
With density it is Re = density times velocity times length divided by dynamic viscosity. With kinematic viscosity it simplifies to Re = velocity times length divided by kinematic viscosity, since kinematic viscosity already equals dynamic viscosity divided by density.
Which thresholds decide laminar versus turbulent?
This tool uses the standard pipe-flow bands: below 2300 is laminar, 2300 to 4000 inclusive is transitional, and above 4000 is turbulent. These are conventional cutoffs, and real transition depends on pipe roughness and disturbances.
What counts as the characteristic length?
It is the length scale that governs the flow. For a full round pipe it is the inside diameter. For non-circular ducts or partially filled pipes, use the hydraulic diameter, which is four times the flow area divided by the wetted perimeter.
Do I supply one viscosity or two numbers?
Either path works. Choose 'Kinematic viscosity' to enter a single m2/s value, or choose 'Density + dynamic viscosity' and the tool divides density into the dynamic viscosity for you. Both give the same Reynolds number.
Why is the Reynolds number dimensionless?
The units of density, velocity, length and viscosity cancel exactly, leaving a pure ratio. That is what lets engineers compare a model in a wind tunnel with a full-size design, since matching Reynolds numbers means matching flow behavior.
What viscosity values should I use for water and air?
At about 20 C, water is roughly 998 kg/m3 with dynamic viscosity near 0.001 Pa s, giving a kinematic viscosity around 1e-6 m2/s. Air is about 1.2 kg/m3 with dynamic viscosity near 1.8e-5 Pa s, so a kinematic viscosity around 1.5e-5 m2/s.
What are the input rules and error messages?
Every field must be a number greater than zero. Blank or non-numeric entries show 'Enter all values as numbers', and any zero or negative value shows 'All values must be greater than zero', so no result appears until inputs are valid.
Is my data uploaded anywhere?
No. The calculation runs in your browser, so the velocities, lengths and viscosities you enter stay on your device and are never sent to a server.
Can I call this from a script?
Yes. The JSON API accepts velocity and characteristicLength plus either kinematicViscosity or both density and dynamicViscosity, and returns the reynoldsNumber and regime, which is useful for sweeping many operating points.
Learn more
- Laminar vs turbulent flow: what the Reynolds number tells you
How the Reynolds number separates smooth laminar flow from chaotic turbulent flow, why the transition band is fuzzy, and how to use the result.
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