Educational calculators only. Not for operational flight planning.

Mach Number Calculator

Mach number is a ratio: true airspeed divided by the speed of sound in the air the aircraft is flying through. Because the speed of sound depends on temperature alone, the same true airspeed is a higher Mach number in the cold air of the upper atmosphere than near a warm surface. This calculator computes the local speed of sound from the temperature you enter and divides your true airspeed by it.

The ratio is what governs how air behaves around a wing or fuselage. Compressibility effects, shock waves and the associated changes in drag and handling track Mach number rather than knots, which is why fast aircraft are flown by Mach at altitude.

Inputs

Results

Enter your values and select Calculate.

Educational use only. Results are not certified for operational flight planning or aircraft performance decisions. Always use approved aircraft documentation and official aviation information before flight.

How to use this calculator

  1. Type the True airspeed and set its unit to kt, km/h, mph or m/s.
  2. Type the Outside air temperature at the flight level and set its unit to °C, °F or K.
  3. Read the Mach number, the local speed of sound and the speed regime.

Two details matter. The speed must be true airspeed, not indicated or calibrated; the true airspeed calculator makes that conversion. The temperature must be the static temperature of the air at flight level, in the range −100 °C to 60 °C. If you do not have a measured value, the standard atmosphere calculator gives the standard temperature for an altitude, which is a reasonable stand-in for study purposes but not the temperature of any actual day.

Formula

a = √(γ × R × T)

M = TAS ÷ a

What the variables mean

M
Mach number (no units)
TAS
true airspeed
a
local speed of sound
T
outside air temperature in kelvin
γ, R
1.4 and 287.05287 J/(kg·K) for dry air

Worked example

These example values are illustrative round numbers, not data for any particular aircraft. Select "Fill in the example" in the calculator to load them.

Inputs

  • True airspeed: 450 kt
  • Outside air temperature: −50 °C

Working

  1. T = 223.15 K.
  2. a = √(1.4 × 287.05287 × 223.15) = 299.5 m/s = 582.1 kt.
  3. M = TAS ÷ a = 450.0 ÷ 582.1 = 0.773.

Result

  • Mach number: 0.773
  • Local speed of sound: 582.1 kt (299.5 m/s)
  • Speed regime: Subsonic (Conventional bands: below 0.8, 0.8 to 1.2, 1.2 to 5, above 5)

Reading the result

Mach number is given to three decimal places and has no unit; 0.773 means 77.3% of the speed of sound. Local speed of sound is shown in knots with m/s beside it, and is the figure your true airspeed was divided by. Speed regime places the result in one of four conventional bands: subsonic below 0.8, transonic from 0.8 to 1.2, supersonic from 1.2 to 5 and hypersonic above 5. The band edges are textbook conventions for describing airflow, not properties of any particular aircraft, and say nothing about what a given design can do.

Assumptions and limitations

  • Air is treated as an ideal gas with a constant ratio of specific heats of 1.4 and the dry-air gas constant.
  • Humidity is ignored; moist air has a very slightly higher speed of sound.
  • The temperature entered is assumed to be the static temperature of the undisturbed air, not a reading warmed by compression at a probe.
  • The result is the flight Mach number of the aircraft as a whole; local airflow over parts of the airframe can be faster.
  • The regime boundaries are fixed conventional values and are not adjusted for aircraft shape.
  • At very high Mach numbers real-gas effects change the ratio of specific heats, which this simple formula does not capture.

Common mistakes

  • Dividing indicated airspeed by the speed of sound instead of true airspeed.
  • Using the sea-level standard speed of sound of about 661 kt for a calculation at cruise altitude.
  • Assuming altitude itself changes the speed of sound, when only temperature does.
  • Forgetting to convert temperature to kelvin when working the formula by hand.
  • Reading the transonic band as beginning exactly where shock waves first form on every aircraft.

References

  1. NASA Glenn Research Center, Role of the Mach Number.
  2. NASA Glenn Research Center, Speed of Sound Interactive.
  3. Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25).

These public sources explain the formulas and definitions used here. Citing them does not mean they have reviewed, endorsed or certified AviationCalc.

Speed of Sound Calculator

Speed of sound in air from temperature, in knots, m/s, km/h, mph and ft/s.

Atmosphere and Altitude

True Airspeed Calculator

Convert calibrated airspeed to true airspeed from pressure altitude and outside air temperature.

Flight Speed and Distance

Flight Speed and Distance

Understanding Mach Number

Mach number is true airspeed divided by the local speed of sound. See why temperature alone sets that speed and how one airspeed gives two Mach numbers.

Atmosphere and Altitude

Understanding the Speed of Sound

The speed of sound in air depends on temperature, not pressure or density. See the formula, a table of values and how it sets Mach number.

Flight Speed and Distance

How Airspeed Changes With Altitude

Hold one calibrated airspeed in a climb and true airspeed and Mach number both rise. A table for 200 kt in the standard atmosphere shows by how much.