Pilot tools
Mach to knots converter
Turn a Mach number into true airspeed in knots at your altitude, or true airspeed into Mach. The speed of sound changes with the air temperature, so the same Mach is a different speed at different altitudes.
For example 0.78 in a jet airliner
Pressure altitude: feet, or a flight level like FL350
Degrees warmer (+) or colder (-) than standard. Leave at 0 if unsure
True airspeed
450kt
knots true airspeed at 35,000 ft.
- Speed of sound
- 576kt
- Air temperature
- -54.3°C
- TAS in km/h
- 833
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Flying with Stratos? Its tracking screen shows your indicated airspeed in knots alongside your altitude and groundspeed for the whole flight.
For flight simulation only. Don't use it for real-world flight planning or navigation.
How it works
Mach number is your speed divided by the speed of sound in the air you are flying through. Sound travels faster in warm air, so the speed of sound falls as you climb and the air cools. This page works out the air temperature at your altitude from the International Standard Atmosphere (ISA), adds any deviation you enter, finds the speed of sound from that temperature, and multiplies by the Mach number.
temperature (°C) = 15 − 0.0019812 × altitude (ft), then −56.5 °C above 36,089 ft
speed of sound (kt) = 38.9679 × √(temperature in kelvin)
true airspeed (kt) = Mach × speed of sound
Mach 0.78 at FL350 on a standard day is about 450 kt true airspeed. The same Mach at 10,000 ft is about 498 kt, because the air is warmer.
The answer is true airspeed (TAS): your speed through the air. It is not the number on your airspeed indicator. Indicated airspeed (IAS) comes from air pressure, and it is much lower than TAS at altitude, where the air is thin: at Mach 0.78 and FL350 an airliner indicates about 265 kt. Turning Mach into IAS takes a pressure-based conversion that also accounts for the air compressing at speed, which this page does not do. And groundspeed is TAS plus the wind: a 50 kt tailwind adds 50 kt. Our descent calculator takes groundspeed.
Questions
How do you convert Mach to knots?
Multiply the Mach number by the speed of sound where you are flying. The speed of sound depends only on the air temperature: about 661 kt at sea level on a standard day and about 576 kt at FL350. So Mach 0.78 at FL350 is 0.78 × 576 kt, or about 450 kt. That is a true airspeed, not the speed on your airspeed indicator.
Is Mach 1 always the same speed in knots?
No. Mach 1 is the speed of sound, and the speed of sound falls as the air gets colder. It is about 661 kt at sea level on a standard day, 576 kt at FL350 and 573.6 kt from 36,089 ft up, where a standard atmosphere stops getting colder. Air warmer than standard raises it.
Is this true airspeed, indicated airspeed or groundspeed?
True airspeed (TAS): your speed through the air around you. Indicated airspeed (IAS) is what the airspeed indicator reads, which comes from air pressure and is much lower at altitude. Groundspeed is your speed over the ground, which is TAS with the wind added or subtracted. A 450 kt TAS with a 50 kt tailwind is a 500 kt groundspeed.
Can I convert Mach to indicated airspeed here?
No. Indicated airspeed depends on the air pressure and on how much the air compresses at speed, not on temperature alone, so it needs a different calculation that this page doesn't do. Your aircraft shows the answer for you: most airliners display both Mach and IAS (or calibrated airspeed) on the primary flight display.
What is ISA deviation?
The difference between the actual air temperature and the temperature a standard atmosphere (ISA) has at that altitude. If ISA at FL350 is -54 °C and the outside air is -44 °C, ISA deviation is +10. Many airliner FMS pages show it as ISA DEV. Leave it at 0 if you are not sure, but each 10 °C moves true airspeed by about 10 kt at Mach 0.78.
Why does the speed of sound depend on temperature?
Sound travels through air at a speed set by how fast the air's molecules move, and that is a matter of temperature. The speed of sound is proportional to the square root of the temperature in kelvin, which is why it drops as you climb through the lower atmosphere, where the air gets colder, and stays level in a standard atmosphere above 36,089 ft, where the temperature stops falling.
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