What this calculator does
Mach number is speed divided by the local speed of sound. It matters because the behaviour of air changes fundamentally as an object approaches and passes that speed, with shock waves forming and drag rising sharply.
The catch is that the speed of sound is not a fixed number. It depends on air temperature, which falls with altitude, so the same true airspeed corresponds to a higher Mach number high up than at sea level.
The formula
Divide the object's speed by the local speed of sound, which for air is calculated from temperature as 331.3 times the square root of one plus temperature over 273.15.
| Term | Meaning |
|---|---|
| Mach 1 | The local speed of sound, about 343 m/s in air at 20°C. |
| Transonic | Roughly Mach 0.8 to 1.2, where some airflow over the object is supersonic and some is not. The most difficult regime aerodynamically. |
| Supersonic | Above Mach 1, where shock waves form and the aerodynamics change character entirely. |
The inputs explained
| Field | What to enter |
|---|---|
| Object speed (m/s) | The object's speed in metres per second. |
| Air temperature (°C) | Air temperature in degrees celsius. It falls with altitude, so use the temperature at the relevant height rather than at ground level. |
When to use it
Converting an airspeed to a Mach number
Aircraft performance limits are often stated in Mach rather than in airspeed, because it is the aerodynamic behaviour that matters.
Understanding why altitude matters
Colder air at altitude means a lower speed of sound, so the same true airspeed is a higher Mach number.
Identifying the flow regime
Whether a flow is subsonic, transonic or supersonic determines which aerodynamic models apply.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What Mach numbers do common speeds correspond to?
A range of speeds at a fixed air temperature.
| Speed | Mach number | Flow regime |
|---|---|---|
| 100 m/s | 0.291 | Subsonic |
| 300 m/s | 0.874 | Transonic |
| 343 m/s | 0.999 | Transonic |
| 600 m/s | 1.748 | Supersonic |
Questions
Why does the speed of sound change with temperature?
Because sound travels by molecular collisions, and molecules in warmer air move faster. Pressure has almost no effect, which is why altitude matters only through the temperature change that comes with it.
Why is the transonic region so difficult?
Because parts of the airflow go supersonic while others remain subsonic, producing shock waves that move unpredictably with small changes in speed or attitude. Drag rises sharply and control behaviour can change.
What causes a sonic boom?
At supersonic speed the object outruns the pressure waves it creates, which pile up into a shock front. That front sweeps across the ground as a continuous boom for as long as the object stays supersonic.
Is Mach 1 the same everywhere?
No, and that is the point of using Mach at all. At sea level on a warm day it is around 343 m/s; at cruising altitude in much colder air it drops to roughly 295 m/s.
For the speed of sound on its own, see the speed of sound calculator. For the drag that rises so sharply near Mach 1, see the drag force calculator.