Reynolds Number Calculator
Free Reynolds number calculator: enter the fluid, speed and size in any units to get Re, whether the flow is laminar or turbulent, pipe friction and pressure drop, drag and vortex-shedding frequency. Or solve for the speed or size that gives a target Re.
More results for this situation
| Quantity | Value | How |
|---|
These use standard textbook correlations and are good to roughly 10 to 20%, not to the last digit.
Typical Reynolds numbers
| Flow | Re (about) |
|---|
What the Reynolds number is
The Reynolds number is the single number that tells you what kind of flow you have. It is the ratio of inertial forces (the fluid wanting to keep moving) to viscous forces (the internal friction that smooths things out):
ρ is the density, v the speed, L a size that matters for the flow (a pipe's diameter, a wing's chord, a ball's diameter), μ the dynamic viscosity and ν = μ/ρ the kinematic viscosity. Re has no units, so a small wind tunnel model and a full-size aircraft with the same Reynolds number flow in the same way: the idea behind scale-model testing.
How to use the calculator
- Pick the fluid. Water and air change with temperature (the page uses accepted formulas for both); other fluids use values at about 20 °C. Choose Custom to enter your own density and viscosity.
- Pick the situation so you get the right regime limits. Flow in a pipe turns turbulent near Re 2,300 to 4,000; along a flat plate near 500,000; behind a cylinder a regular vortex street starts at about 47.
- Enter speed and size in any units, or choose Find the speed or Find the size to work backwards from a target Reynolds number, for example to see how fast water can flow in a hose and stay laminar.
Common questions
- What Reynolds number is turbulent? It depends on the geometry. For pipe flow, below about 2,300 is laminar and above about 4,000 is turbulent. Between them it is unpredictable.
- Which length do I use? The one conventional for the shape: inside diameter for a pipe, diameter for a sphere or cylinder, chord for a wing, distance from the leading edge for a plate. For a non-circular duct use the hydraulic diameter, 4 × area ÷ wetted perimeter.
- Does a high Reynolds number mean fast? Not only. A huge, slow ship has a far higher Re than a fast but tiny insect, because Re grows with size as well as speed and falls with viscosity.
- Why do small organisms live at low Re? A bacterium swimming in water has Re around 0.00001: viscosity dominates and it stops the moment it stops pushing, like swimming through honey.
Related: Fluid Simulator (watch the flow change as you slide the Reynolds number) · Unit Conversion · More calculators