Reynolds Number Calculator
Enter a fluid’s density, speed, a characteristic length, and its dynamic viscosity to get the dimensionless Reynolds number — and see whether the flow is laminar or turbulent.
Flow regime at a glance
The Reynolds number calculator returns Re = ρvL/μ and tells you whether the flow is laminar (Re < 2300), transitional, or turbulent (Re > 4000).
Use SI units
Density in kg/m³, velocity in m/s, length in metres, and viscosity in Pa·s keep the result dimensionless — mix units and the number is meaningless.
What is the Reynolds number?
The ratio of inertial to viscous forces
The Reynolds number is a dimensionless quantity that predicts whether a fluid flow will be smooth and orderly or chaotic and mixing. It compares the inertial forces pushing a fluid along to the viscous forces that resist motion. This Reynolds number calculator turns four measurements — the fluid density, the flow velocity, a characteristic length such as a pipe diameter, and the dynamic viscosity — into a single number that engineers use everywhere from designing pipelines and aircraft wings to modelling blood flow.
Enter density, velocity, length, and viscosity in SI units to get the Reynolds number and its flow regime instantly.
The Reynolds number is the density times the velocity times the characteristic length, all divided by the dynamic viscosity.
Re = (ρ × v × L) / μBecause the result is a ratio of forces with matching units, it has no dimensions — the same number means the same thing for water, air, or oil. A large Reynolds number means inertia dominates and the flow tends to be turbulent; a small one means viscosity dominates and the flow stays laminar.
Suppose water (density 998 kg/m³, viscosity 0.001002 Pa·s) flows at 1 m/s through a pipe 0.05 m across.
Multiply the top line
998 × 1 × 0.05 = 49.9 — density times velocity times length.
Divide by the viscosity
49.9 / 0.001002 ≈ 49,800 — the dimensionless Reynolds number.
Read the regime
49,800 is far above 4000, so the flow is firmly turbulent.
The Reynolds number tells you which physics dominates. For flow in a pipe, a value below about 2300 means laminar flow: the fluid moves in smooth, parallel layers with little mixing, and friction losses are predictable. Above roughly 4000 the flow is turbulent: it swirls and mixes, friction rises sharply, and pressure drops grow faster than speed. Between 2300 and 4000 lies the transitional range, where the flow can switch unpredictably between the two. The example above (≈ 49,800) sits well into the turbulent zone, which is typical for everyday water flow in household plumbing. These thresholds are specific to internal pipe flow; flow over a flat plate, around a sphere, or through a channel uses different critical values, so always match the threshold to the geometry described by your characteristic length.
The formula is exact, but a couple of practical points are worth keeping in mind.
Geometry-dependent thresholds and consistent units
The 2300 and 4000 cut-offs apply to flow inside a circular pipe, where the characteristic length is the pipe diameter. Other geometries — wings, spheres, open channels — have their own critical Reynolds numbers and their own definition of the characteristic length. Keep every input in SI units (kg/m³, m/s, m, Pa·s) so the result stays dimensionless and comparable.