Reynolds Number Calculator

The Reynolds number is a dimensionless ratio of inertial to viscous forces that predicts whether a flow will be laminar and smooth or turbulent and mixing.

For pipe flow, values below 2300 are laminar, values between 2300 and 4000 are transitional, and values above 4000 are turbulent.

Density times velocity times length divided by dynamic viscosity has units that cancel completely, leaving a pure number. That is why the same threshold values apply to any fluid and any scale, from blood vessels to oil pipelines.

No. The 2300 and 4000 values are conventional transition thresholds for flow inside a circular pipe, using the pipe diameter as the characteristic length. Other geometries transition at very different Reynolds numbers - a flat-plate boundary layer, for example, typically stays laminar up to a critical value near 5 × 10⁵. Choose the threshold that matches your geometry rather than applying the pipe-flow values everywhere.

Replace the pipe diameter with the hydraulic diameter, D_h = 4A ÷ P, where A is the cross-sectional area of the flow and P is the wetted perimeter. For a full circular pipe this reduces to the ordinary diameter. For a rectangular duct of sides a and b it gives D_h = 2ab ÷ (a + b), and for a thin slot it approaches twice the gap width. Use D_h as the characteristic length L in Re = ρvL ÷ μ, and the usual pipe-flow transition thresholds then apply as a reasonable approximation.

They span an enormous range. Blood flowing in a small artery is around a few hundred to about 1000 (mostly laminar). Flow in a household water pipe is often tens of thousands (turbulent). Air over a commercial airliner wing reaches roughly 10⁷, and a large crude-oil or gas pipeline runs from about 10⁵ to well over 10⁶. At the other extreme, a swimming bacterium lives at Re far below 1, where viscosity completely dominates and inertia is negligible.