High and fast, a pilot stops thinking in knots and starts thinking in Mach, and the reason is the same physics that makes the standard atmosphere so useful: the speed of sound is set by temperature alone.
This is general educational information, not operational, legal, or regulatory advice. Rules differ by authority and change over time. Always verify against current official sources and follow your operator's approved procedures.
The speed of sound follows temperature
In the standard atmosphere, the speed of sound depends only on the temperature of the air, not on its pressure or density on their own. Colder air carries sound more slowly. As the NASA Glenn Research Center sets out, it varies with the square root of the absolute temperature, which gives a handy approximation: the local speed of sound in knots is roughly 39 times the square root of the temperature in kelvin.
Run that down the standard atmosphere:
- At ISA sea level, 15 degrees Celsius (288 K), the speed of sound is about 661 knots.
- At the standard tropopause, about minus 56.5 degrees Celsius (217 K), it has fallen to about 573 knots.
So a wing climbing into the cold upper air meets a steadily falling speed of sound, and that is what makes Mach matter up high.
What Mach number actually is
Mach number is true airspeed divided by the local speed of sound. It is a ratio, so it has no units: Mach 0.80 means flying at 80 per cent of the speed of sound in the air you are actually in. Because the speed of sound changes with temperature, the same true airspeed is a different Mach number at a different level, as SKYbrary describes.
A worked example, using the rounded standard temperatures:
- At FL350 on a standard day, the temperature is about minus 54 degrees Celsius (219 K).
- The speed of sound is about 39 times the square root of 219, which is about 577 knots.
- A true airspeed of 480 knots is then 480 divided by 577, or about Mach 0.83.
Climb higher into colder air, hold 480 knots true, and that Mach number creeps up, which is exactly why a jet transitions from holding a constant indicated speed lower down to holding a constant Mach higher up.
The speed chain: IAS, CAS, TAS, Mach
These are four different things, and mixing them up is a classic trap. In order, as the FAA Pilot's Handbook lays them out:
- Indicated airspeed (IAS): what the airspeed indicator reads.
- Calibrated airspeed (CAS): IAS corrected for instrument and position error.
- True airspeed (TAS): CAS corrected for air density. Because density falls with altitude, TAS is higher than CAS up high, by very roughly 2 per cent per 1000 feet as a rule of thumb.
- Mach number: TAS as a fraction of the local speed of sound, which depends on temperature.
The instrument measures dynamic pressure, so the indicator reads close to true at sea level on a standard day, and increasingly under-reads your true speed as you climb.
Common pitfalls
- Speed of sound is about temperature, not pressure. Two levels at the same temperature have the same speed of sound, whatever their pressure.
- Mach rises in the climb at constant TAS. It is the falling speed of sound, not a change in your speed, that does it.
- TAS is not what the dial shows. At altitude your true speed is well above the indicated figure, so use TAS for navigation and flight planning, not IAS.
In Pilot EFB
Pilot EFB includes true airspeed and Mach among its built-in flight calculators, with the working shown so you can follow how temperature and altitude feed the answer. The figures are for your own planning and reference; Pilot EFB is offline-first and is not a certified Electronic Flight Bag, so check them against your aircraft's approved data and instruments before you act on them.