How to Use Mach Number Calculator
The Mach Number Calculator converts a flow speed or vehicle speed into a Mach number and classifies the result into the appropriate compressibility regime, making it straightforward to apply shock-wave theory and isentropic flow tables.
- Enter freestream velocity V — the vehicle airspeed or pipe flow velocity in m/s; use the unit selector to input in km/h or ft/s if preferred.
- Enter local speed of sound a — supply the known value, or enable temperature mode to compute a automatically from T.
- Enter temperature T (optional) — if a is unknown, input the local static temperature in Kelvin; the calculator derives a = √(γ·R·T).
- Adjust γ and R — defaults are 1.4 and 287 J/(kg·K) for dry air; set γ = 1.3 for CO₂, or γ = 1.67 for He or Ar.
- Read M and the flow regime — the result panel identifies subsonic, transonic, supersonic or hypersonic, with brief implications for design.
Formula & Theory — Mach Number Calculator
The Mach Number Calculator uses the definition of Mach number as the ratio of bulk flow velocity to the local thermodynamic speed of sound:
M = V / a
a = √( γ · R · T ) (ideal gas)
a ≈ 20.05 · √T (dry air, m/s)| Symbol | Meaning | SI Unit |
|---|---|---|
| M | Mach number (dimensionless) | — |
| V | Flow or vehicle velocity | m/s |
| a | Local speed of sound | m/s |
| γ | Specific-heat ratio | — |
| R | Specific gas constant (dry air: 287) | J/(kg·K) |
| T | Absolute static temperature | K |
Regime thresholds: subsonic M < 0.8 — incompressible approximation often valid below M ≈ 0.3; transonic 0.8–1.2 — local shock waves appear on lifting surfaces, mixed flow, wave drag rises sharply; supersonic 1.2–5 — oblique shocks, expansion fans, Mach cone clearly formed, wave drag dominant; hypersonic M > 5 — aerodynamic heating, real-gas dissociation, viscous interaction effects.
Use Cases for Mach Number Calculator
- Aircraft and missile aerodynamics — define the compressibility regime to select the correct drag model and decide whether linearised or nonlinear theory applies.
- Wind-tunnel similarity scaling — match M between a sub-scale model and full-scale vehicle to preserve shock patterns, boundary-layer transition and wave-drag coefficients.
- Gas turbine and jet engine inlets — verify that diffuser inlet Mach numbers remain below critical values to avoid choking, normal shocks and compressor surge.
- Supersonic nozzle design — check throat conditions (M = 1) and design area ratios from isentropic tables for the target exit Mach number.
- Re-entry vehicle thermal management — estimate stagnation enthalpy and aerodynamic heating rates at critical locations as M climbs during descent.
- Sonic boom prediction — quantify the overpressure signature of supersonic aircraft at ground level as a function of cruise M and flight altitude.