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Formula & Calculator

Mach Number

Ratio of flow velocity to the local speed of sound, defining subsonic, transonic, supersonic, and hypersonic regimes.

Written by the Vorzep Team

AerodynamicsCompressible FlowFundamental

Mach Number Calculator

M = V / a
Select the variable to solve for, then enter the other two values
MVa
Solve for:
Speed of Sound Presets
Select condition: a:m/s
Mach Presets
Select Mach: M:
Speed Units
Speed unit: Speed of sound unit:
Temperature (optional, for a)
°C
Enter temperature to compute a = 20.05·√T (T in K) for air
Enter the other two values
—
m/s
m/s
a = speed of sound M ≥ 0

Variables

SymbolQuantityUnit
MMach number
VFlow velocitym/s
aLocal speed of soundm/s

What it means

The Mach number is a dimensionless parameter that defines the speed of a flow relative to the local speed of sound. It is named after Ernst Mach and is central to compressible aerodynamics. The speed of sound a = √(γRT) in an ideal gas. Mach number determines the flow regime: incompressible (M<0.3), subsonic (0.35). It influences shock waves, drag divergence, and stability. In aircraft design, M is used to determine critical Mach number, wave drag, and performance boundaries. It also appears in many compressible flow relations (isentropic, normal shock, etc.). Understanding Mach number is essential for high‑speed aerodynamics and for interpreting flight envelopes.

Worked example

Mach Number – Two Examples

Real‑World
Scenario: An aircraft cruises at 250 m/s at 11,000 m where speed of sound is 295 m/s. Find Mach number.
ParameterValue
V250 m/s
a295 m/s
1M = V/a = 250/295 = 0.847
Result M = 0.847 ✓ Subsonic
Scenario: An F‑16 flies at 680 m/s at sea level (a = 340 m/s). Find Mach number.
ParameterValue
V680 m/s
a340 m/s
1M = 680/340 = 2.0
Result M = 2.0 ✓ Supersonic
Key insight: M < 1 subsonic, M = 1 sonic, M > 1 supersonic – Mach number determines compressibility effects.

Common mistakes

  • Mach number M: Ratio of flow speed V to local speed of sound a.
  • Speed of sound a: Depends on temperature and gas properties (a = √(γRT)) – not constant.
  • Subsonic vs. supersonic: M<1 (subsonic), M=1 (sonic), M>1 (supersonic) – different flow physics.
  • Units: V and a must be in the same units (m/s).
  • Compressibility effects: Significant for M>0.3; use compressible flow equations.

Applications

Mach number, M = V/a, is the ratio of the speed of an aircraft or flow to the local speed of sound. It is the fundamental parameter governing compressible flow behaviour. Below Mach 0.3, flow is incompressible; between 0.3 and 0.8, compressibility effects become important (transonic); above 1.0, shock waves form. Engineers use Mach number to design aerodynamic shapes, to size wings and intakes, and to predict drag rise and control effectiveness. It is essential for designing commercial aircraft (cruising at M≈0.8) and military fighters (supersonic). Mach number also determines the design of supersonic inlets, nozzles, and afterburners. By understanding Mach effects, aerospace engineers can avoid the adverse consequences of shock‑induced separation and ensure stable and efficient flight.

  • Aircraft cruise speed definition and performance planning
  • Design of transonic and supersonic airfoils
  • Inlet and nozzle design for gas turbines and ramjets
  • Compressibility drag and wave drag estimation
  • Flight envelope definition and dynamic stability analysis