Mach Number Calculator
Enter an object speed and the local air temperature (or altitude) to instantly calculate the Mach number and flow regime. Switch between four solve modes to find velocity, speed of sound, or temperature instead. The calculator uses the standard isentropic speed-of-sound formula with an International Standard Atmosphere altitude model and supports metric and imperial units throughout.
Formula
Worked example
An aircraft flies at 680 m/s at sea level where T = 15 C. The speed of sound is sqrt(1.4 x 287.058 x 288.15) = 340.3 m/s. Mach number = 680 / 340.3 = 2.00, so the aircraft is in the supersonic regime.
What is Mach number?
Mach number (symbol M) is a dimensionless ratio of an object's speed to the local speed of sound in the surrounding medium. Named after Austrian physicist Ernst Mach, it is the fundamental similarity parameter in compressible flow: two flows with the same Mach number are aerodynamically similar regardless of their absolute speeds or altitudes. At M = 1 the object moves at exactly the speed of sound, below M = 1 it is subsonic, and above M = 1 it is supersonic.
Why does the speed of sound vary with temperature?
Sound travels through air by pressure waves that propagate at a = sqrt(gamma x R x T), where gamma (1.4 for dry air) is the ratio of specific heats, R (287.058 J/kg/K) is the specific gas constant for air, and T is the absolute temperature in Kelvin. Because temperature falls with altitude in the troposphere (about 6.5 C per 1 000 m by the International Standard Atmosphere), the speed of sound also falls. At 15 C it is about 340 m/s; at -56.5 C (the tropopause near 11 000 m) it drops to about 295 m/s. A jet flying at a fixed 900 km/h therefore has a higher Mach number at cruise altitude than at sea level.
Flow regimes and their engineering significance
The Mach number determines which physical effects dominate the flow. In the subsonic regime (M < 0.8), compressibility is a minor correction and incompressible equations work well. The transonic regime (0.8 to 1.2) is the most complex: regions of subsonic and supersonic flow coexist on the same vehicle, shock waves form on the upper wing surface, and wave drag rises sharply. The supersonic regime (1.2 to 5.0) is dominated by oblique shocks, expansion fans, and sonic booms. In the hypersonic regime (M > 5) aerodynamic heating is severe enough to ionise air, and the thin shock layer merges with the vehicle boundary layer, creating unique design challenges solved with ablative heat shields or reinforced carbon-carbon panels.
How to use this calculator
Select what you want to solve for from the "Solve for" drop-down: Mach number (given velocity and sound speed), velocity (given M and sound speed), speed of sound (given velocity and M), or temperature (given velocity and M). Choose how to determine the local speed of sound: from a temperature entry, from altitude using the ISA lapse model, or by entering the speed of sound directly. Select your unit system and velocity unit, then fill in the remaining fields. Results update instantly. The "Show your work" panel below the result card traces every conversion and calculation step.
Mach number speed regimes
| Mach range | Regime | Typical examples |
|---|---|---|
| < 0.8 | Subsonic | Commercial jets, propeller aircraft, helicopters |
| 0.8 - 1.2 | Transonic | Military trainers, T-tail jets at cruise |
| 1.2 - 5.0 | Supersonic | Fighter jets (F-22, MiG-29), Concorde at cruise |
| 5.0 - 10.0 | Hypersonic | Ballistic missile re-entry vehicles, scramjet test articles |
| > 10.0 | High-hypersonic | Orbital re-entry vehicles, Space Shuttle at entry interface |
Standard aerodynamic classification used by NASA, the USAF, and most textbooks. Boundaries are approximate; the exact subsonic/transonic transition depends on vehicle geometry.
Frequently asked questions
What is Mach 1 in km/h and mph?
Mach 1 is not a fixed speed in km/h or mph because the speed of sound changes with air temperature. At 15 C (standard sea-level ISA conditions) the speed of sound is about 340.3 m/s, which equals 1 225 km/h or 761 mph. At -56.5 C (tropopause, about 11 000 m altitude) it drops to about 295 m/s, or 1 062 km/h / 660 mph.
What Mach number do commercial airliners fly at?
Most narrow-body and wide-body jets cruise between Mach 0.78 and Mach 0.85. The Boeing 787 and Airbus A350 cruise near Mach 0.85, while the Boeing 737 and Airbus A320 family cruise around Mach 0.78 to 0.82. The Concorde, retired in 2003, cruised at about Mach 2.04 at 18 000 m.
What is the Mach number of the International Space Station?
The ISS orbits Earth at roughly 7.66 km/s (about 27 580 km/h). At that altitude, there is effectively no atmosphere, so a conventional Mach number is not well-defined. However, if measured against the sea-level speed of sound (340 m/s), the ISS would correspond to approximately Mach 22.5. During re-entry vehicles descend through the upper atmosphere at similar speeds, producing the intense plasma sheath visible from the ground.
Why does the calculator use the ISA lapse rate?
The International Standard Atmosphere defines how temperature, pressure, and density vary with altitude in a standardised way used globally in aviation, ballistics, and aerospace engineering. In the troposphere (sea level to about 11 000 m / 36 089 ft) temperature decreases at a lapse rate of 6.5 K per 1 000 m. Above that the stratosphere is isothermal at about -56.5 C. The ISA model gives a reproducible reference point even though real atmospheric conditions vary with location and season.
What happens to an aircraft when it exceeds its critical Mach number?
The critical Mach number (Mcr) is the lowest speed at which local airflow anywhere on the vehicle first reaches Mach 1, even though the vehicle itself is still subsonic. Above Mcr, shock waves form on the wing, boundary layers separate behind them, and wave drag rises sharply. This produces "Mach tuck," a nose-down pitching moment, and buffeting. Modern swept-wing transonic jets are designed so that Mcr lies well above their cruise speed, and their aircraft operating manuals define a maximum operating Mach number (Mmo) below the Mach at which these effects become dangerous.
How does Mach number differ from true airspeed?
True airspeed (TAS) is the actual speed of the aircraft relative to the undisturbed air mass, measured in knots or km/h. Mach number is TAS divided by the local speed of sound. At constant TAS, Mach number increases as altitude increases because the speed of sound decreases in the colder air. A pilot at 11 000 m flying 295 m/s TAS is at exactly Mach 1.0, whereas the same 295 m/s TAS at sea level (15 C) is only about Mach 0.87.