Reynolds Number Calculator
The Reynolds number of a flow from the fluid, its speed and the pipe diameter — and whether that makes the flow laminar, transitional or turbulent.
The Reynolds number compares inertial forces with viscous ones: Re = ρvD ÷ μ.
How the reynolds number calculator works
The Reynolds number compares inertial forces with viscous ones: Re = ρvD ÷ μ. Below about 2,300 in a pipe the flow is laminar and orderly; above about 4,000 it is turbulent, with far higher friction and mixing; between the two it flips unpredictably. Water in ordinary plumbing is nearly always turbulent; syrup in a tube, blood in a capillary, are laminar.
Formula: Re = ρ v D ÷ μ = v D ÷ ν
Worked examples
| Inputs | Reynolds number | Note |
|---|---|---|
| Water at 1 m/s in a 50 mm pipe | 49,810 | 49,810 — turbulent |
| Oil at 0.5 m/s in a 25 mm pipe | 38 | 38 — laminar |
| Air at 5 m/s in a 200 mm duct | 65,973 | 65,973 — turbulent |
FAQFrequently asked questions
Why does the regime matter?
Turbulent flow needs several times the pumping pressure of laminar flow for the same rate, but mixes and transfers heat far better. Pipe sizing, heat exchangers and chemical reactors are all designed around which side of the line they sit.
What length do I use for something other than a pipe?
The characteristic length changes with the geometry: hydraulic diameter for ducts, chord for a wing, sphere diameter for a falling particle. The critical values change with it — a sphere’s wake becomes turbulent near Re 2 × 10⁵.
Why is oil laminar when water is turbulent?
Viscosity: SAE 30 oil is about 300 times more viscous than water at room temperature, so the same speed and pipe give a Reynolds number 300 times smaller.
Does temperature matter?
Very much for liquids — water’s viscosity halves between 20 °C and 50 °C, and oil’s falls tenfold. Use the custom fluid with the viscosity at your operating temperature.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.