Mach Number Converter (Mach to km/h, mph, ft/s)

Understanding the Mach number converter — concept and principle

The Mach number is a speed expressed as a multiple of the local speed of sound: Mach 1 is exactly the speed of sound, Mach 2 twice that. It is used in aviation because shock waves and drag rise depend on this ratio, not on km/h. This converter turns a Mach number and an air temperature into m/s, km/h, mph, knots and ft/s.

The same Mach number means a lower ground speed high up, where the air is colder.

How it is calculated

First the speed of sound in dry air is found from the temperature: a = √(γ × R × T), with γ = 1.4 (ratio of specific heats of air), R = 287.05287 J/(kg·K) (specific gas constant of dry air in the ICAO standard atmosphere) and T the absolute temperature in kelvin (°C + 273.15). The speed is then v = M × a. Unit conversions: km/h = m/s × 3.6; mph = m/s ÷ 0.44704; knots = m/s × 3,600 ÷ 1,852; ft/s = m/s ÷ 0.3048.

The principle

Sound is a pressure wave, and it travels as fast as air molecules can pass on a disturbance. That depends on how fast the molecules themselves move, which is set by temperature. For an ideal gas, pressure and density cancel out of the formula, so the speed of sound depends on temperature alone. This is why Mach 1 is lower at cruising altitude: in the standard atmosphere the air at 11 km is about −56.5 °C and sound travels at only about 295 m/s (1,062 km/h), compared with about 340 m/s at sea level at 15 °C.

Worked example

Inputs: Mach number M = 1, air temperature 15 °C (the ISA sea-level standard).
T = 15 + 273.15 = 288.15 K.
a = √(1.4 × 287.05287 × 288.15) = 340.293988 m/s.
v = 1 × 340.293988 = 340.293988 m/s; × 3.6 = 1,225.058357 km/h.
Other units: 761.2159718 mph, 661.4785944 knots, 1,116.450092 ft/s.

How to read the result

Speed regimes are usually described by Mach number: below about 0.8 is subsonic, roughly 0.8 to 1.2 is transonic (where shock waves start to form on parts of the aircraft), above 1 is supersonic and above about 5 is often called hypersonic. Many airliners cruise near Mach 0.78–0.85. Because Mach depends on temperature, the same ground speed in km/h can mean different Mach numbers on a warm day and a cold day, or at different altitudes.

Common mistakes

Using a fixed 1,225 km/h for Mach 1 at every altitude. Enter the actual air temperature at that height instead.
Entering the temperature in Fahrenheit. The field expects degrees Celsius.
Confusing Mach (relative to air) with ground speed.

Keep in mind: The formula assumes dry air behaving as an ideal gas with γ = 1.4. Humidity raises the speed of sound slightly, and very high temperatures or hypersonic flows need more advanced models.

Frequently asked questions

Does Mach 1 depend on air pressure or altitude itself?

Not directly. In the ideal-gas model only temperature matters; altitude affects Mach 1 because temperature usually falls with height in the lower atmosphere.

What temperature should I use for an aircraft at altitude?

Use the static outside air temperature. Without a measurement, the standard atmosphere gives 15 °C at sea level falling by 6.5 °C per kilometre up to 11 km, then −56.5 °C up to 20 km.

How fast is Mach 2 at sea level?

About 2 × 340.29 = 680.6 m/s, or about 2,450 km/h at 15 °C.

Sources: ICAO Doc 7488, Manual of the ICAO Standard Atmosphere · ISO 2533:1975, Standard Atmosphere · J. D. Anderson, Fundamentals of Aerodynamics, McGraw-Hill

Checked 8 Nov 2026. ICAO Standard Atmosphere (Doc 7488); ISO 2533.