Reynolds Number Calculator
Determine whether flow is laminar or turbulent from the Reynolds number.
Please note: These are idealised textbook models using representative material data. They are for study, sizing and sanity-checking only — never for final design. Real engineering requires code-compliant analysis, verified material certificates and a qualified engineer’s sign-off.
What the Reynolds Number Calculator does
The Reynolds number compares inertial forces against viscous ones. Below about 2,300 viscosity dominates and flow stays in orderly layers; above 4,000 inertia wins and the flow becomes turbulent, which changes pressure drop and heat transfer completely.
Formula
Re = ρ v D ÷ μRe = v D ÷ νν = μ ÷ ρLaminar below 2,300; turbulent above 4,000
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Fluid | one of 7 options | Yes | — |
| Custom density | kg/m³ | Optional | Overrides the fluid if set. Accepts 0 or more. |
| Custom dynamic viscosity | Pa·s | Optional | Accepts 0 or more. |
| Flow given as | one of 2 options | Yes | — |
| Flow velocity | m/s | In some modes | Accepts more than 0. Shown Flow given as is Velocity. |
| Flow rate | number | In some modes | Per second. Shown Flow given as is Volumetric flow rate. |
| Flow rate unit | one of 6 options | In some modes | Shown Flow given as is Volumetric flow rate. |
| Pipe inside diameter | number | Yes | — |
| Pipe inside diameter unit | one of 9 options | Yes | — |
How to use it
- Choose Fluid and Flow given as.
- Enter Pipe inside diameter.
- Fill in the remaining inputs the form shows for your choice.
- Optionally add Custom density and Custom dynamic viscosity.
- Select Calculate.
Worked example
Water at 20 °C flowing at 2 m/s through a 50 mm pipe.
- Fluid
- Water at 20 °C
- Velocity
- 2 m/s
- Diameter
- 50 mm
Re = 998.2 × 2 × 0.05 ÷ 0.001002 = 99,621 — firmly turbulent.
Frequently asked questions
Why does the Reynolds number have no units?
Because the units cancel exactly. That is the point: flows with equal Reynolds numbers behave identically regardless of scale, which is why wind tunnel models predict full-size behaviour.
Why avoid the transitional range?
Flow there switches unpredictably between laminar and turbulent, and pressure drop can change by a factor of two or more with no change in conditions.
Method and sources
Method. The Reynolds number as the ratio of inertial to viscous forces, Re = ρvD/μ, with the conventional flow-regime bands for pipe flow.
Assumptions
- Steady, fully developed flow of a Newtonian fluid in a straight circular pipe, far enough from the entrance for the velocity profile to have settled.
- Fluid properties are uniform and taken at a single temperature.
Limitations
- The laminar and turbulent bands are conventions from pipe-flow experiments, and the transition between them is a range rather than a line — real transition depends on surface roughness, vibration and inlet disturbance.
- The pipe-flow bands do not carry over to flow over a plate, around a body, or in an open channel, each of which has its own critical values.
Sources
- An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels — Philosophical Transactions of the Royal Society 174:935–982 (Osborne Reynolds), 1883. The dimensionless group and the existence of a laminar-to-turbulent transition.