Mach Number Calculator
Convert between Mach number, true airspeed and calibrated airspeed from the outside air temperature, and add a pressure altitude for the calibrated airspeed.
Free · runs in your browser · nothing is uploaded
How to use the Mach number calculator
- Open Convert and pick the direction: True airspeed to Mach, Mach to true airspeed, Calibrated airspeed to Mach or Mach to calibrated airspeed.
- Enter the speed the mode asks for: True airspeed (TAS), Mach number or Calibrated airspeed (CAS). Pick its unit in Speed unit: knots, mph or km/h.
- Enter the Outside air temperature and choose the Temperature unit, °C or °F. Enter the static air temperature, not the total air temperature a probe reads.
- For the two CAS conversions, enter the Pressure altitude and choose the Altitude unit, feet or meters. For the other two modes it is optional; when you give it, the table gains a CAS column.
- Read the headline Mach number and True airspeed, then the Speed of sound and Density ratio below them. A calibrated airspeed at or above 661.5 kt is refused, and a true airspeed at Mach 1 or above is still shown with a note.
- Open How it was calculated to see the speed of sound and the relations used with your numbers.
The presets load Mach 0.80 at FL360, 450 kt at -56.5 °C, 250 kt CAS at 25,000 ft and Mach 1 at sea level. Print / save result prints or saves the result, Copy link keeps your inputs in the address, and Reset starts over.
How do I calculate the Mach number?
The Mach number is the true airspeed divided by the speed of sound at your air temperature: M = TAS / a, with a = sqrt(gamma x R x T), gamma 1.4 and R 287.053 J/(kg K), where T is the static air temperature in kelvin.
Mach 1 at 15 °C in the standard atmosphere is 340.29 m/s, which is 661.48 kt or 1,225 km/h. At -56.5 °C (216.65 K, the standard temperature from 36,089 ft up) the speed of sound is 295.07 m/s, or 573.6 kt. There Mach 0.80 is 458.9 kt TAS, and 450 kt TAS is Mach 0.7846.
How fast is Mach 1?
Mach 1 is the speed of sound, which is 340.29 m/s, 661.48 kt or 1,225 km/h at 15 °C in the standard atmosphere. It falls as the air gets colder, to 573.6 kt at -56.5 °C.
At 30 °C it is 349.0 m/s (678.5 kt, 1,257 km/h), and at -20 °C it is 319.0 m/s (620.0 kt).
How do you convert Mach to calibrated airspeed?
Calibrated airspeed comes from the subsonic pitot relation. The calculator first finds the impact pressure qc = p x [(1 + 0.2 M^2)^3.5 - 1], where p is the standard static pressure at your pressure altitude, then solves the sea-level relation for CAS using P0 = 1013.25 hPa and a0 = 661.48 kt.
Mach 0.80 at 36,000 ft and -56.5 °C gives a CAS of 265.8 kt and a density ratio of 0.298. The tool’s table for that place lists each Mach number with its TAS and CAS:
| Mach | TAS (kt) | CAS (kt) |
|---|---|---|
| 0.30 | 172.1 | 94.8 |
| 0.50 | 286.8 | 160.4 |
| 0.60 | 344.1 | 194.4 |
| 0.70 | 401.5 | 229.5 |
| 0.75 | 430.2 | 247.5 |
| 0.80 | 458.9 | 265.8 |
| 0.85 | 487.5 | 284.4 |
| 0.90 | 516.2 | 303.3 |
| 0.95 | 544.9 | 322.6 |
| 1.00 | 573.6 | - |
The CAS shows as a dash at Mach 1.00 because the subsonic relation ends there. Above Mach 1 a shock wave forms ahead of the probe and the pitot relation changes, so the calculator refuses a CAS result.
Does Mach 1 change with altitude?
The speed of sound, and so Mach 1, changes with temperature and not with altitude itself. Standard temperature reaches -56.5 °C at 36,089 ft, which lowers Mach 1 from 661.48 kt to 573.6 kt.
Temperature changes the TAS at a given Mach number. Mach 0.80 is 458.9 kt at -56.5 °C, but 0.80 x 661.5 = 529.2 kt at 15 °C. A 250 kt CAS at 25,000 ft and -35 °C gives Mach 0.604, a TAS of 363.0 kt and a speed of sound of 601.4 kt.
Sources
U.S. Standard Atmosphere 1976 (NASA-TM-X-74335), Tables 2 and 10; isentropic pitot-static relations of compressible flow (subsonic); NIST SP 811 for the knot (1,852 m per hour) and unit conversions. Checked October 2026.
Questions from readers
What is the speed of sound at a given temperature?
Use a = sqrt(gamma x R x T) with T in kelvin, or read the table. At 0 °C the speed of sound is 331.3 m/s (644.0 kt), and at 40 °C it is 354.7 m/s (689.6 kt, 1,277 km/h).
How do I convert TAS to Mach?
Select True airspeed to Mach, enter the True airspeed (TAS) with its Speed unit, and enter the Outside air temperature. The tool divides TAS by the speed of sound at that temperature. For example, 450 kt TAS at -56.5 °C is Mach 0.7846.
What temperature do I enter?
Enter the static air temperature, not the total air temperature a probe reads. Set the Temperature unit to match the value you type.
Why does a fixed Mach number have a lower CAS at altitude?
Impact pressure falls as static pressure falls, so the same Mach number produces a lower pitot reading higher up and the CAS comes out lower. Mach 0.80 at 36,000 ft and -56.5 °C is 265.8 kt CAS.
Is Mach the same in km/h and knots?
Yes. Mach is a ratio, so it does not depend on the speed unit. 450 kt is 833.4 km/h or 517.8 mph, and the Mach number for that speed is the same in every unit.
Why no CAS above Mach 1?
Above Mach 1 a shock wave forms ahead of the pitot probe and the subsonic relation no longer applies, so the calculator refuses a calibrated airspeed result at Mach 1 or above. A true airspeed at Mach 1 or above is still shown, with a note.
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