Reynolds Number Calculator

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.

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.

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.

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.

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.