formula.expertYour record

Reynolds Number

Also known as Re · laminar or turbulent

Re=ρvDμRe = \frac{\rho v D}{\mu}

or type the values yourself

sig figs

Worked example: Water, 1 m/s, D = 5 cm, mu = 1 mPa*s → Re = 50000. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Reynolds Number fits

Missing an input?
Your answer feeds
Laminar Friction Factor (f = 64/Re)Swamee–Jain Friction FactorColebrook–White Friction FactorDittus-Boelter Correlation
In this toolkit

See also

Air Viscosity by Sutherland's Law: The viscosity μ of air at any temperature, for a Reynolds number in wind or a duct.Graetz Number: Both use Reynolds number and characteristic length.Colebrook–White Friction Factor: Both use Reynolds number.Dittus-Boelter Correlation: Both use Reynolds number.Laminar Friction Factor (f = 64/Re): Both use Reynolds number.Swamee–Jain Friction Factor: Both use Reynolds number.
Here the solver did the work. Could you?

Reynolds and the regime →

UniversityFluid Mechanics, HVAC & Refrigeration

Test your skills in the Exam Room: new numbers every attempt. Free lessons for students, no sign-up, just pure learning. Find 2 more lessons on this formula.

See your Report Card
Learning zone

Reynolds Number explained

vρμDRe

Osborne Reynolds injected dye into pipe flow in 1883 and watched it either glide in a smooth filament or erupt into eddies, and found one dimensionless group predicted which. Below about Re = 2300 pipe flow is laminar; above roughly 4000 it is turbulent. Water at 1 m/s in a 5 cm pipe gives Re = 1000 × 1 × 0.05 / 0.001 = 50 000: solidly turbulent, like nearly all industrial water flow.

Because only the combination ρvD/μ matters, a small model in a wind tunnel can faithfully stand in for a full-size aircraft as long as the Reynolds numbers match: the principle that makes scale testing legitimate.

Reynolds Number formula

Re=ρvDμRe = \frac{\rho v D}{\mu}
Where
  • ReRe= Reynolds number
  • ρ\rho= Fluid density (kg/m³)
  • vv= Flow velocity (m/s)
  • DD= Characteristic length (mm)
  • μ\mu= Dynamic viscosity (Pa·s)
In this toolkit

Pipe friction losses

9 formulasDarcy–Weisbach, Hazen–Williams, friction factors, minor losses and equivalent length — every way the trade computes head loss in pipe.

Revised 31 October 2026
Cite this page

formula.expert. (2026, October 31). Reynolds Number Formula & Calculator. https://formula.expert/solvers/reynolds-number

formula.experthttps://formula.expert/solvers/reynolds-number