How this instrument works
Mach number M is the ratio of an object's speed v to the local speed of sound a: M = v ⁄ a. Because both quantities carry the same units, the result is a pure number with no unit of its own — an aircraft at Mach 0.8 is moving at eighty percent of the speed sound travels through the air around it at that instant, wherever that happens to be.
The formula is a ratio rather than a raw speed because air behaves very differently on either side of it. Below about Mach 0.8, air moves out of an object's way smoothly and can be treated as incompressible; past Mach 1, it cannot get out of the way fast enough, pressure waves pile up into shocks, and drag rises sharply. Ernst Mach's 1887 photographs of bullets in flight first captured that pile-up as a visible cone, and the number named after him is what aerospace engineers still use to say how close a design sits to that boundary.
The local speed of sound a is not a fixed constant — it depends on the temperature of the medium the object moves through, roughly a = √(γRT) for air, where γ and R are properties of the gas and T is absolute temperature. Colder air carries sound more slowly, so the same physical velocity converts to a higher Mach number at altitude than at sea level, and a figure calculated with the wrong local speed of sound describes the wrong airplane entirely.
- Enter the object's speed in Object velocity — m/s, km/h, or mph, whichever your source data already uses.
- Enter Local speed of sound for the air at that exact altitude and temperature, not a generic textbook constant.
- Read Mach number: below 1 is subsonic, exactly 1 is sonic, above 1 is supersonic.
- Recompute Local speed of sound before comparing two altitudes — colder air lowers a and raises the Mach number even at an unchanged velocity.
Worked example — an airliner near Mach 1
Cruise radar clocks an airliner's speed at 340 m/s, and the outside air temperature at that altitude puts the local speed of sound at 343 m/s. Enter Object velocity = 340 and Local speed of sound = 343, and the instrument returns M = 340 ⁄ 343 = 0.991254 — Mach 0.991, a hair under the speed of sound itself.
That 0.009 of headroom matters more than it looks. Most transport aircraft cruise nearer Mach 0.85; pushing to 0.99 drives the accelerated airflow over the wing's curved upper surface past Mach 1 even while the aircraft itself has not, which is exactly the transonic buffet and shock-induced drag rise that keeps airliners from routinely cruising this close to the boundary.
Questions
What does a Mach number greater than 1 mean?
It means the object is moving faster than sound travels through the surrounding air — supersonic. Doubling the velocity in this instrument's own check vector, 686 m/s against a = 343 m/s, returns exactly M = 2.0, twice the local speed of sound. Below Mach 1 is subsonic, passing through 1 is transonic, and past roughly Mach 5 is hypersonic.
Why does the same velocity give a different Mach number at altitude?
Because the local speed of sound a changes with air temperature, not with the object's velocity. Colder high-altitude air carries sound more slowly than warm sea-level air, so 340 m/s reads Mach 0.991 at a = 343 m/s near sea level but Mach 1.153 at a = 295 m/s, roughly −50°C — the object did not speed up, the air around it changed.
Is Mach number the same thing as airspeed?
No. Airspeed is a velocity with units — knots, m/s, mph — while Mach number is a dimensionless ratio of that velocity to the local speed of sound. Two aircraft can share an airspeed and still have different Mach numbers if the air around them sits at different temperatures, which is why pilots track both instruments separately.
Why is Mach 1 treated as such a significant threshold?
Because compressibility effects change sharply there. Below about Mach 0.8, airflow behaves close to incompressible and drag rises gently with speed; near Mach 1, air can no longer get out of an object's way fast enough, pressure waves compress into shocks, and drag climbs steeply — the 'sound barrier' the Bell X-1 first flew through in 1947 was really this drag barrier, not a physical wall.
Does Mach number apply to anything besides aircraft?
Yes — any object moving through a compressible fluid. Bullets, rocket exhaust, wind-tunnel flows, and even the tip of a cracking bullwhip, which briefly exceeds Mach 1 in air and produces the crack as a tiny sonic boom, are all described the same way: object speed divided by the local speed of sound in whatever gas surrounds them.
What speed of sound should I use if I don't know the exact air temperature?
343 m/s is a reasonable default for air near 20°C, a common room-temperature reference; 340.3 m/s is the ISA sea-level standard at 15°C. For real flight or ballistics work, source the local speed of sound from the actual air temperature at altitude instead of assuming a constant — it can drop to around 295 m/s in the cold air near typical cruise altitude.