Compute the two dimensionless numbers that define an aerodynamic flow: the Reynolds number, which sets the balance of inertial to viscous forces, and the Mach number, which sets the importance of compressibility. The calculator also returns the local speed of sound and classifies the flow regime from subsonic to hypersonic.
Two dimensionless numbers govern almost every aerodynamic flow. The Reynolds number tells you whether viscous or inertial forces dominate — and therefore whether the boundary layer is laminar or turbulent. The Mach number tells you whether the air can be treated as incompressible or whether shock waves and compressibility effects come into play. Together they place a flow on the map and set which physics matter.
Re = ρ·V·L / μ, the ratio of inertial forces (ρV²) to viscous forces (μV/L).
Here ρ is density, V the velocity, L a characteristic length (chord, diameter, or body length), and μ the dynamic viscosity. Low Re means viscosity dominates and flow is smooth and laminar; high Re means inertia dominates and the boundary layer transitions to turbulence. Because two flows with the same Re and shape are dynamically similar, Re is the key to scaling wind-tunnel tests up to full size.
The speed of sound in an ideal gas is a = √(γ·R·T), where γ = 1.4 and R = 287 J/(kg·K) for air. It depends only on temperature, so it falls with altitude as the air gets colder. The Mach number M = V/a compares the flight speed to that signal speed. At low M, pressure disturbances outrun the body and the flow adjusts smoothly; as M approaches 1, disturbances pile up into shock waves.
By Mach number: subsonic (M < 0.8) where compressibility is mild and lift/drag theory is largely incompressible; transonic (0.8–1.2) where mixed sub- and supersonic regions and shock-induced drag rise make this the hardest regime to design for; supersonic (1.2–5) dominated by oblique and bow shocks and wave drag; and hypersonic (M > 5) where shock layers grow thin, aerodynamic heating becomes severe, and the air may dissociate. This calculator color-codes which regime your input falls in.
Aerodynamic forces depend on both Re and M, so faithful testing must match (or correct for) each. Re controls skin-friction drag, boundary-layer transition, and stall behaviour; M controls wave drag, shock location, and the onset of buffet. A model that matches lift at the right Mach but the wrong Reynolds can still mispredict drag and separation — which is why facilities chase high-Reynolds, variable-Mach capability and why CFD must resolve both effects.
Use the length that defines the flow over the body of interest: the mean aerodynamic chord for a wing or airfoil, the diameter for a cylinder or pipe, and the body length for a fuselage or missile. Reynolds number is only meaningful alongside the length scale it was computed with, so always state it (e.g., "Re based on chord").
There is no single value — it depends on geometry and surface roughness. For flow over a flat plate, transition typically begins around Re ≈ 5×10⁵ based on distance from the leading edge. In pipes, flow is generally laminar below Re ≈ 2300 and turbulent above ≈ 4000. Disturbances, roughness, and pressure gradients can move these thresholds substantially.
Because a = √(γRT) depends only on temperature. In the troposphere the air cools with altitude, so the speed of sound drops — from about 340 m/s at sea level to roughly 295 m/s in the stratosphere. That means a constant true airspeed corresponds to a higher Mach number as you climb, which matters for transonic airliners cruising near their drag-divergence Mach.
Transonic flow (roughly Mach 0.8–1.2) contains both subsonic and supersonic pockets at the same time. Local supersonic flow over the wing terminates in shock waves that cause a sharp rise in drag (drag divergence) and can trigger shock-induced separation and buffet. Designing for this regime requires supercritical airfoils and careful area ruling, making it the most demanding speed range.
The Mach definition M = V/a is general, but the speed of sound formula here uses γ = 1.4 and R = 287 J/(kg·K), which are the values for dry air. For other gases, substitute the appropriate ratio of specific heats and gas constant. At very high temperatures even air departs from γ = 1.4 as vibrational modes and dissociation activate, which matters in hypersonic flows.