Math
Reynolds Number Calculator
Compute the Reynolds number for pipe or flat-plate flow from velocity, characteristic length, density, and viscosity. Classifies laminar, transitional, or turbulent.
Flow inputs
Reynolds number
99,600.8
Flow regime: turbulent
Re = (rho * v * L) / mu
Darcy friction factor: 0.02
Frequently Asked Questions about the Reynolds Number Calculator
What is the Reynolds number?
The Reynolds number (Re) is a dimensionless ratio of inertial forces to viscous forces in a fluid flow. It predicts whether flow is smooth (laminar) or chaotic (turbulent). Re = (density x velocity x characteristic length) / dynamic viscosity, or equivalently (velocity x length) / kinematic viscosity.
What counts as laminar, transitional, or turbulent flow?
For pipe flow, Re below 2300 is laminar, 2300 to 4000 is transitional, and above 4000 is turbulent. For flow over a flat plate, the transition is much higher: Re below 5 x 10^5 is laminar, 5 x 10^5 to 3 x 10^6 is transitional, and above is turbulent.
What is the characteristic length?
It depends on the geometry. For flow inside a pipe, use the inner diameter. For flow around a sphere, use the diameter. For flow over a flat plate, use the distance from the leading edge. Picking the wrong length scale by a factor of 10 changes Re by a factor of 10.
Why does dynamic viscosity divide and kinematic viscosity not need density?
Dynamic viscosity (mu) measures resistance to deformation per unit shear rate. Kinematic viscosity (nu = mu / rho) bakes in the density divide, so the Reynolds formula simplifies to v x L / nu. Use whichever value you have from a fluid table.
What is the Darcy friction factor for laminar flow?
For laminar pipe flow (Re less than 2300), the Darcy friction factor f equals 64 / Re. The calculator returns this exact value when Re is in the laminar range and switches to a Swamee-Jain approximation for smooth pipes when Re is turbulent.