Mach Number Calculator
Use this Mach converter to convert any speed to Mach number at sea level or any altitude. Includes temperature-corrected speed of sound, shock cone angle, and flight regime classification.
Speed & Conditions
Result
Mach Regime Reference
| Regime | Mach Range | Speed at 15°C | Examples |
|---|---|---|---|
| Subsonic | M < 0.8 | < 272 m/s (978 km/h) | Commercial aircraft cruise (M 0.85 is high subsonic) |
| Transonic | 0.8 – 1.2 | 272–408 m/s | Sound barrier region, shock waves form |
| Supersonic | 1.2 – 5.0 | 408–1700 m/s | Concorde (M 2.04), SR-71 Blackbird (M 3.3) |
| Hypersonic | 5.0 – 10.0 | 1700–3400 m/s | Space Shuttle reentry (M 25), X-43 (M 9.6) |
| High hypersonic | > 10.0 | > 3400 m/s | ICBM reentry, orbital velocity (M ~25) |
Why Mach Number Depends on Temperature
The Mach number is a dimensionless ratio of an object’s speed to the local speed of sound, not an absolute speed. Because the speed of sound in air rises with temperature — approximately c = 331.4 + 0.6 × T(°C) m/s — the same aircraft traveling at 900 km/h is at a higher Mach number on a cold winter day than on a hot summer one. At cruising altitude (around −56°C in the stratosphere), Mach 1 is only about 295 m/s (1062 km/h), which is why airliners flying at M 0.85 are actually traveling slower in absolute speed than they would at sea level at the same Mach number.
This temperature sensitivity is why aviation uses Mach number — not km/h or knots alone — to define aerodynamic regimes. The behavior of airflow over a wing, the onset of wave drag, and the formation of shock waves all depend on how close the airflow is to the local speed of sound, regardless of what that speed is in absolute terms. To explore how sound itself travels through the air, see the speed of sound calculator, which covers temperature, humidity, and medium effects in detail.
Shock Waves and the Sound Barrier
When an object moves at or above Mach 1, the pressure waves it generates can no longer outrun it. They pile up into a Mach cone — a conical shock wave that trails the object at the angle μ = arcsin(1/M). This is the source of the sonic boom heard on the ground: not a single event at the moment of breaking the sound barrier, but a continuous cone of compressed air that sweeps across the ground as the aircraft flies overhead. A narrower cone (higher Mach) means the boom reaches a smaller ground track per second but at higher intensity. The calculator shows the half-angle of this cone in real time as you adjust speed.
In the transonic regime (roughly M 0.8–1.2) shock waves form locally on the wings before the whole aircraft reaches Mach 1, causing wave drag that demanded special swept-wing and area-ruling designs — hence the distinctive shape of aircraft like the F-86 Sabre. True supersonic speed — above Mach 1.2 — is where wave drag stabilizes and aircraft like the Concorde and SR-71 Blackbird operated efficiently. At hypersonic speeds above Mach 5, aerodynamic heating from shock-layer compression becomes the dominant engineering challenge, which is why spacecraft reentry vehicles require thermal-protection systems. For the Doppler frequency shift associated with a moving sound source — distinct from shock waves — see the Doppler effect calculator.
How to Calculate Mach Number: Worked Example
The formula the tool uses is M = v / c, where v is the object's speed in m/s and c is the local speed of sound calculated as c = 331.4 + 0.6 × T(°C). Both steps are shown in the formula box below the result while you type.
Example: a fighter jet at 700 m/s on a 20°C day.
- Find the speed of sound: c = 331.4 + 0.6 × 20 = 343.4 m/s
- Divide: M = 700 / 343.4 = Mach 2.039 (supersonic)
- Cone half-angle: μ = arcsin(1 / 2.039) = 29.3°
Two common reference values (sea level, 15°C standard atmosphere): Mach 1 = 340.3 m/s (1225 km/h / 761 mph); Mach 2 = 680.6 m/s (2450 km/h / 1522 mph). At cruising altitude (around −56°C), both values are roughly 12% lower because the speed of sound drops with temperature — see the speed of sound calculator for a full breakdown by altitude and medium. For context on the wavelengths associated with these pressure waves, the wavelength calculator can convert any frequency to its corresponding wavelength at a given wave speed.