OneTaskBy Tim King · Updated
Mach Number Calculator
Speed to Mach and Mach to Speed at Any Altitude
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How the Mach Number Calculator works
This Mach number calculator converts an airspeed into a Mach number, or a Mach number back into km/h, mph, m/s, knots and ft/s. The speed of sound depends on air temperature, so choose an altitude in the standard atmosphere or enter the temperature directly. It also names the flight regime, from subsonic to hypersonic.
Mach 1 is not a fixed speed. Sound travels faster in warm air and slower in cold air, so Mach 1 is about 1,225 km/h at sea level on a standard day but only about 1,062 km/h at the 11 km cruising height of an airliner. That is why a jet at the same ground speed can be well below Mach 1 on the runway and close to it in the cold upper air.
How the mach number calculator works
The formula for the speed of sound in dry air is a = √(γ × R × T), where γ = 1.4, R = 287.05 J/(kg·K) and T is the temperature in kelvin. The Mach number is the speed divided by a. With an altitude, the temperature comes from the International Standard Atmosphere: 15 °C at sea level, falling 6.5 °C per kilometre up to 11 km, then a steady −56.5 °C up to 20 km. Humidity and pressure barely change the answer and are ignored.
First example. An airliner flies at 900 km/h at 11,000 m. The air there is −56.5 °C, or 216.65 K, so a = √(1.4 × 287.05 × 216.65) = 295.1 m/s, which is 1,062 km/h. The Mach number is 900 ÷ 1,062 = 0.847, in the transonic band.
Second example. Mach 2 at sea level, where a = 340.3 m/s, is 680.6 m/s. That is 2,450 km/h, 1,522.4 mph or 1,323 knots.
Third example. In a 20 °C room sound travels at 343 m/s, so a speed of 343 m/s is Mach 0.999.
How many mph is Mach 1? About 761 mph at sea level in standard conditions, falling to about 660 mph above 11 km.
Speed of sound, Mach 1, by altitude in the International Standard Atmosphere
| Altitude | Temperature | m/s | km/h | mph | knots |
|---|---|---|---|---|---|
| 0 m (0 ft) | 15 °C | 340.3 | 1,225 | 761 | 661 |
| 1,000 m (3,281 ft) | 8.5 °C | 336.4 | 1,211 | 753 | 654 |
| 2,000 m (6,562 ft) | 2 °C | 332.5 | 1,197 | 744 | 646 |
| 3,000 m (9,843 ft) | -4.5 °C | 328.6 | 1,183 | 735 | 639 |
| 4,000 m (13,123 ft) | -11 °C | 324.6 | 1,168 | 726 | 631 |
| 5,000 m (16,404 ft) | -17.5 °C | 320.5 | 1,154 | 717 | 623 |
| 6,000 m (19,685 ft) | -24 °C | 316.4 | 1,139 | 708 | 615 |
| 7,000 m (22,966 ft) | -30.5 °C | 312.3 | 1,124 | 699 | 607 |
| 8,000 m (26,247 ft) | -37 °C | 308.1 | 1,109 | 689 | 599 |
| 9,000 m (29,528 ft) | -43.5 °C | 303.8 | 1,094 | 680 | 591 |
| 10,000 m (32,808 ft) | -50 °C | 299.5 | 1,078 | 670 | 582 |
| 11,000 m (36,089 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 12,000 m (39,370 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 13,000 m (42,651 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 14,000 m (45,932 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 15,000 m (49,213 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 16,000 m (52,493 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 17,000 m (55,774 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 18,000 m (59,055 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 19,000 m (62,336 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
| 20,000 m (65,617 ft) | -56.5 °C | 295.1 | 1,062 | 660 | 574 |
How to read the result
- Mach number is the speed as a multiple of the local speed of sound.
- Speed of sound here is Mach 1 for the conditions you set, in m/s and km/h.
- Air temperature used shows the standard atmosphere temperature for your altitude, or the temperature you entered.
- Flight regime follows the usual bands: below Mach 0.8 subsonic, 0.8 to 1.2 transonic, 1.2 to 5 supersonic, above 5 hypersonic.
Tips and pitfalls
- Use true airspeed. The indicated airspeed in a cockpit reads low at altitude; Mach needs the true speed through the air.
- Ground speed is not airspeed. A tailwind raises ground speed without changing the Mach number.
- Real air differs from the standard. On a hot day the speed of sound is higher; switch to the temperature option when you know the actual air temperature.
FAQ
How fast is Mach 1?
At sea level on a standard 15 °C day, Mach 1 is 340.3 m/s, about 1,225 km/h, 761 mph or 661 knots. It falls with temperature, to about 1,062 km/h at 11 km where the air is −56.5 °C.
Why does the speed of sound change with altitude?
It depends on air temperature, not pressure or height as such. The air gets colder as you climb through the lower atmosphere, so the speed of sound drops until the temperature levels off at about 11 km.
What Mach number do airliners fly at?
Most jet airliners cruise between Mach 0.78 and Mach 0.85. Concorde cruised at about Mach 2.0 at around 18 km, and business jets reach Mach 0.9 or a little more.
What is hypersonic speed?
Speeds above about Mach 5 are called hypersonic. At these speeds air heating and chemistry become major design problems, which is why re-entry vehicles and hypersonic missiles need special heat shielding.
Is the speed of sound the same in water?
No. Sound travels about 1,480 m/s in water, more than four times faster than in air. The Mach number here is for air only, which is how it is used in aviation.
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