Mach Number
$$\text{Mach} = \frac{v}{c_s}$$
What is Mach Number?
A Mach number is the ratio of an object's speed to the local speed of sound in the surrounding medium. Mach 1 means the object is travelling at the speed of sound. Mach 0.5 is half the speed of sound; Mach 2 is twice the speed of sound.
The speed of sound varies with temperature and the medium it travels through. At sea level and 15°C in air, Mach 1 is approximately 340.3 m/s (1,225 km/h or 761 mph). At cruising altitude (~10,000 m), where temperatures reach around -50°C, Mach 1 drops to about 295 m/s (1,062 km/h). This is why airliner cruise speeds are quoted in Mach - the aircraft's aerodynamic behaviour depends on Mach number, not absolute speed.
When to use Mach Number
Use Mach numbers when describing aircraft performance, particularly for jet aircraft, supersonic vehicles, and anything where compressibility effects in air matter (above approximately Mach 0.3). For subsonic vehicles like cars, trains, and ships, use km/h, mph, or knots instead.
Worked examples
| Mach | km/h (sea level, 15°C) | mph | Category |
|---|---|---|---|
| Mach 0.5 | 612.5 km/h | 380.5 mph | Subsonic |
| Mach 0.85 | 1,041 km/h | 647 mph | Commercial airliner cruise |
| Mach 1 | 1,225 km/h | 761 mph | Speed of sound |
| Mach 2 | 2,450 km/h | 1,522 mph | Supersonic (Concorde cruise) |
| Mach 5 | 6,125 km/h | 3,806 mph | Hypersonic (X-51A) |
Common pitfalls
Mach 1 is not a fixed speed - it changes with air temperature. At 10,000 m altitude, Mach 1 is about 295 m/s (1,062 km/h), significantly slower than the 340 m/s at sea level. Never convert a Mach number to km/h without specifying the altitude and temperature conditions.
Frequently asked questions
What is the difference between subsonic, transonic, supersonic, and hypersonic?
Subsonic: Mach below 0.8. Transonic: Mach 0.8–1.2 (shock waves begin forming). Supersonic: Mach 1.2–5. Hypersonic: Mach 5 and above. The Concorde cruised at Mach 2; the Space Shuttle re-entered at around Mach 25.
Who is Mach named after?
Ernst Mach, an Austrian physicist (1838–1916) who studied the shock waves formed by projectiles moving faster than sound. The unit was named in his honour by the aeronautical engineer Jakob Ackeret in 1929.