Mach Number Calculator
Speed Relative to Sound, Not Relative to the Ground
Mach number expresses velocity as a ratio against the local speed of sound rather than as an absolute figure, which matters because the speed of sound itself changes with air temperature — and therefore with altitude. An aircraft holding a constant true airspeed climbs through a steadily rising Mach number as it ascends into colder air, even though nothing about its actual speed has changed.
The Formula
Temperature mode: Speed of Sound = √(γ × R × T)
Mach = Velocity / Speed of Sound
In the temperature-based formula, γ (1.4) is the ratio of specific heats for air, R (287 J/(kg·K)) is the specific gas constant for air, and T is absolute air temperature in Kelvin.
Where This Calculation Matters
- Transonic and supersonic flight envelopes — aircraft performance and handling change fundamentally as Mach number crosses roughly 0.8 to 1.2, the transonic region where shock waves begin forming.
- High-altitude performance — because air temperature drops with altitude, the same true airspeed corresponds to a higher Mach number at altitude than at sea level.
- Engine inlet design — jet engine inlets are designed around specific Mach ranges, since supersonic and subsonic airflow require very different inlet geometry.
- Reentry and hypersonic vehicles — Mach 5 and above defines the hypersonic regime, where aerodynamic heating becomes a dominant design constraint.
Common Speeds in Mach Number (Sea Level)
| Velocity | Mach number |
|---|---|
| 100 m/s (360 km/h) | Mach 0.29 |
| 171.5 m/s | Mach 0.50 |
| 343 m/s | Mach 1.00 (sonic) |
| 686 m/s | Mach 2.00 |
| 1,029 m/s | Mach 3.00 |
| 2,058 m/s | Mach 6.00 |
At altitude, the speed of sound drops (air is colder), so the same true airspeed yields a higher Mach number than at sea level — use the Custom Temperature mode for accurate high-altitude results.
How to Use This Calculator
- Choose Standard (sea level, 15°C) or Custom Temperature.
- Enter the velocity in meters per second.
- For Custom Temperature mode, also enter the local air temperature in Kelvin.
- Select Calculate to get the Mach number.
Related Calculations
For vehicles operating at hypersonic reentry speeds, see the Reentry Heating Calculator, or check orbital speed with the Orbital Insertion Velocity Calculator.