Mach Number Calculator
Calculate Mach number from speed and air temperature.
Covers subsonic, transonic, supersonic, and hypersonic regimes with speed-of-sound formula.
Mach Number
The Mach number (M) is a dimensionless ratio of an object’s speed to the local speed of sound. It was named after the Austrian physicist Ernst Mach who studied shock waves in the 1880s.
Formula:
M = v / c
Where:
- v = object speed (m/s, km/h, mph, or ft/s)
- c = local speed of sound (depends on air temperature)
Speed of sound in air:
c = 331.3 * sqrt(1 + T_C / 273.15) m/s
Or equivalently: c = 20.05 * sqrt(T_K) m/s
where T_C is temperature in Celsius and T_K is temperature in Kelvin.
At standard sea-level conditions (15°C), c ≈ 340 m/s ≈ 1,225 km/h ≈ 761 mph. At high altitude where T = -56°C, c ≈ 295 m/s (18% slower — why jets flying at altitude reach lower Mach numbers for the same airspeed).
Mach regimes:
| Regime | Mach Range | Notes |
|---|---|---|
| Subsonic | M < 0.8 | No shock waves |
| High Subsonic | 0.8 – 1.0 | Local shocks may form |
| Transonic | 1.0 – 1.2 | Mixed subsonic/supersonic flow |
| Supersonic | 1.2 – 5.0 | Bow shock wave forms |
| Hypersonic | M > 5.0 | Extreme heating, plasma effects |
Notable Mach numbers:
- Commercial airliners cruise at approximately Mach 0.85
- The SR-71 Blackbird held the record for fastest air-breathing aircraft at Mach 3.3
- The X-15 rocket plane reached Mach 6.7 in 1967
- Space Shuttle re-entry reached approximately Mach 25
Practical note: Because the speed of sound changes with temperature (and altitude), two aircraft flying at the same indicated airspeed can have different Mach numbers depending on where they are in the atmosphere.