Calculate true airspeed, Mach number, or speed of sound from any two values, with unit conversion between m/s, km/h, mph, and knots.
Mach To Airspeed (True Airspeed) Formula
The following formula is used to calculate the speed of an object relative to the surrounding air (true airspeed) for a given Mach number and local speed of sound. In still air (no wind), this speed is also equal to ground speed.
V = M \times a
Variables:
- V is the speed relative to the surrounding air (true airspeed); in still air it equals ground speed
- M is the Mach number
- a is the local speed of sound (in the same speed units as V; commonly m/s)
To calculate true airspeed, multiply the Mach number by the local speed of sound.
| Mach (M) | m/s | km/h | mph | knots |
|---|---|---|---|---|
| 0.1 | 34.029 | 122.504 | 76.121 | 66.148 |
| 0.2 | 68.058 | 245.009 | 152.241 | 132.296 |
| 0.3 | 102.087 | 367.513 | 228.362 | 198.443 |
| 0.4 | 136.116 | 490.018 | 304.483 | 264.591 |
| 0.5 | 170.145 | 612.522 | 380.604 | 330.739 |
| 0.6 | 204.174 | 735.026 | 456.724 | 396.887 |
| 0.7 | 238.203 | 857.531 | 532.845 | 463.035 |
| 0.8 | 272.232 | 980.035 | 608.966 | 529.182 |
| 0.9 | 306.261 | 1102.540 | 685.086 | 595.330 |
| 1.0 | 340.290 | 1225.044 | 761.207 | 661.478 |
| 1.1 | 374.319 | 1347.548 | 837.328 | 727.626 |
| 1.2 | 408.348 | 1470.053 | 913.448 | 793.774 |
| 1.3 | 442.377 | 1592.557 | 989.569 | 859.921 |
| 1.4 | 476.406 | 1715.062 | 1065.690 | 926.069 |
| 1.5 | 510.435 | 1837.566 | 1141.811 | 992.217 |
| 1.6 | 544.464 | 1960.070 | 1217.931 | 1058.365 |
| 1.7 | 578.493 | 2082.575 | 1294.052 | 1124.513 |
| 1.8 | 612.522 | 2205.079 | 1370.173 | 1190.660 |
| 1.9 | 646.551 | 2327.584 | 1446.293 | 1256.808 |
| 2.0 | 680.580 | 2450.088 | 1522.414 | 1322.956 |
| Assumes ISA sea level conditions (T = 15°C). Speed of sound a ≈ 340.29 m/s ≈ 1225.04 km/h ≈ 761.21 mph ≈ 661.48 knots. True airspeed V = M × a. In still air, true airspeed equals ground speed; with wind, ground speed differs by the wind component along the track. | ||||
What is Mach Number?
Mach number is a dimensionless quantity representing the ratio of the speed of an object moving through a fluid to the local speed of sound in that fluid. It is named after the Austrian physicist Ernst Mach. When the Mach number is less than one, the object is moving at subsonic speeds. When the Mach number is equal to one, the object is moving at the speed of sound, and when it is greater than one, the object is moving at supersonic speeds. Mach numbers are commonly used in aerodynamics and fluid dynamics to describe the speed of aircraft, rockets, and other objects moving through air or other gases.
How to Calculate Airspeed from Mach Number?
The following steps outline how to calculate true airspeed from the Mach number and local speed of sound. (In still air, this is also the ground speed.)
- First, determine the Mach number (M).
- Next, determine the local speed of sound (a) in the medium through which the object is moving.
- Finally, calculate the true airspeed using the formula V = M × a.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Mach number (M) = 2
Speed of sound (a) = 343 m/s
True airspeed (V) = M × a = 2 × 343 = 686 m/s