Aviation Calcs

Reynolds number

Reynolds Number Calculator

Compute the Reynolds number Re = ρ V L / μ = V L / ν for a speed and a characteristic length — a wing chord, a fuselage length, a pipe diameter. Air properties can come from the U.S. Standard Atmosphere 1976 at a geopotential altitude, or from a density, viscosity, or pressure and temperature you type.

Air properties from

Optional: override the ISA temperature (K) to hold pressure at the ISA value for that altitude but recompute μ and ρ.

Use a chord for an airfoil (Rec), a diameter for a pipe or a cylinder (ReD), or a length along a plate (Rex).

Reynolds number

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What Reynolds number measures

The Reynolds number is the ratio of inertial to viscous forces in a flow:

Re = ρ V L / μ = V L / ν

Two geometrically similar bodies at the same Reynolds number have the same relative balance of those forces, which is why a wind-tunnel model is tested at a Reynolds number as close as possible to the full-size airplane. Laminar-to-turbulent transition, skin friction, and the behavior of a high-lift system all depend on Re.

Air properties

For atmospheric flight the density ρ and the dynamic viscosity μ come from the ambient air. This page can take them from the U.S. Standard Atmosphere 1976 at a geopotential altitude (Sutherland’s law for μ), or from a pressure and temperature, or from values you type. At sea-level ISA, ρ = 1.225 kg/m³ and μ ≈ 1.7894×10−5 Pa·s, so a 1 m chord at 50 m/s has Re ≈ 3.42×106.

A rough sea-level rule of thumb is Re ≈ 10,735 × Vkt × Lft. Use the calculator, not the thumb rule, when altitude or temperature matters.

Sources

NASA Glenn Beginner’s Guide to Aeronautics (Reynolds number); U.S. Standard Atmosphere 1976 (Sutherland constants); Anderson, Fundamentals of Aerodynamics.

Frequently asked questions

What length should I use for a wing Reynolds number?

The reference chord — typically the mean aerodynamic chord for a whole wing, or the local chord at a span station. For a fuselage or a boom, use a length; for a circular cylinder or a landing-gear leg, use the diameter.

Does Reynolds number change with altitude?

Yes. Density falls faster than viscosity, so Re at a given true airspeed and length is lower at altitude than at sea level. That is one reason high-altitude cruise and low-Reynolds-number UAV work need care with transition and flap effectiveness.

What viscosity law is used with the ISA option?

Sutherland’s law as in the U.S. Standard Atmosphere 1976, μ = β T3/2/(T+S), with the same constants as the standard-atmosphere calculator on this site.