About the Mach Number Converter
Mach number is speed divided by the local speed of sound, so “Mach 1” is not a fixed speed — it depends on the air temperature. This Mach converter works that out for you: give it a Mach number and an altitude (or an air temperature) and it returns the true airspeed in miles per hour, kilometres per hour, knots, metres per second and feet per second. Switch modes to turn a known speed into a Mach number.
It is handy for aviation enthusiasts comparing airliner cruise speeds, students working physics problems, flight-sim pilots, and anyone wondering how fast a supersonic jet really goes. At sea level on a standard day Mach 1 is about 761 mph (1,225 km/h); at 35,000 ft, where the air is around −55 °C, it drops to about 663 mph.
Altitude mode uses the International Standard Atmosphere temperature profile (geopotential altitude, valid to about 85 km). Real temperatures differ from the standard day, so use temperature mode if you know the actual outside air temperature.
How to use the mach number converter
- 1Choose Mach → speed or speed → Mach.
- 2Enter the Mach number, or the speed and its unit.
- 3Choose whether to use an altitude (standard atmosphere) or a known air temperature.
- 4Enter the altitude in feet or metres, or the outside air temperature.
- 5Read the speed in every unit, the Mach number and the local speed of sound.
Formula and method
The speed of sound in air depends only on temperature for an ideal gas: a = √(γRT), with γ = 1.4 for air and R = 287.05287 J/(kg·K), the specific gas constant used in the International Standard Atmosphere. At 15 °C (288.15 K) this gives 340.29 m/s. Mach number M is true airspeed divided by a, so speed = M × a.
In altitude mode the temperature comes from the ISA profile: it falls 6.5 °C per kilometre from 15 °C at sea level to −56.5 °C at 11 km, stays constant to 20 km, then warms slowly in the stratosphere. Pressure and density do not affect the speed of sound directly, which is why it is the same at all altitudes from 11 to 20 km.
- a
- Local speed of sound (m/s)
- γ
- Ratio of specific heats for air, 1.4
- R
- Specific gas constant for air, 287.05287 J/(kg·K)
- T
- Absolute air temperature (K)
- M
- Mach number
Worked examples
Mach 1 at sea level
At sea level the standard air temperature is 15 °C (288.15 K). √(1.4 × 287.053 × 288.15) = 340.29 m/s, which is 761.2 mph, 1,225 km/h or 661.5 knots.
Airliner cruising at Mach 0.85 and 35,000 ft
35,000 ft is 10,668 m, where the standard temperature is 288.15 − 0.0065 × 10,668 = 218.81 K (−54.3 °C). The speed of sound there is 296.5 m/s, so Mach 0.85 is 252.1 m/s — about 564 mph or 490 knots true airspeed.
1,500 mph at 50,000 ft as a Mach number
At 50,000 ft (15,240 m) the ISA temperature is a constant 216.65 K, so the speed of sound is 295.07 m/s. 1,500 mph is 670.56 m/s, and 670.56 ÷ 295.07 = Mach 2.27.
Speed of sound on a 20 °C day
At 293.15 K the speed of sound is √(1.4 × 287.053 × 293.15) = 343.2 m/s, or 767.8 mph — the value often quoted in physics textbooks.
Frequently asked questions
How fast is Mach 1 in mph?+
At sea level on a standard 15 °C day, Mach 1 is about 761 mph (1,225 km/h or 340 m/s). At typical airliner cruise altitudes it is lower, around 660–663 mph, because the air is much colder.
Why does the speed of sound change with altitude?+
Sound travels faster in warmer air. Temperature generally falls with height up to about 11 km (36,000 ft), so the speed of sound falls too. Between 11 and 20 km the standard temperature is constant, so Mach 1 stays the same.
How fast is Mach 2 or Mach 5?+
At sea level Mach 2 is about 1,522 mph and Mach 5 about 3,806 mph. At 50,000 ft, where Mach 1 is about 660 mph, Mach 2 is about 1,320 mph and Mach 5 about 3,300 mph.
Is Mach number based on ground speed?+
No. Mach number uses true airspeed — speed relative to the surrounding air — divided by the local speed of sound. Wind changes ground speed but not Mach number.
What speed of sound value should I use for homework?+
Many textbooks use 343 m/s, which is the speed of sound in dry air at 20 °C. At 0 °C it is about 331 m/s. Use temperature mode with your problem’s temperature for an exact value.