Mach number calculator.
Convert between true airspeed and Mach for any temperature, and see the local speed of sound that links them.
Mach number & speed of sound
Convert between true airspeed and Mach for a given outside air temperature. Leave OAT blank and enter a pressure altitude to assume ISA. The local speed of sound depends only on temperature.
Enter a speed and a temperature (or a pressure altitude for ISA) to convert.
In the EASA ATPL exam
The TAS-to-Mach relationship is examined head-on in ATPL Principles of Flight (subject 081), where it underpins critical Mach number, buffet margins and coffin corner, and again in Instrumentation (022) through the machmeter and the IAS/Mach crossover in the climb. The questions are rarely hard arithmetic; they test whether you know that the local speed of sound follows temperature alone, then make you use that fact in one of the two conversion directions.
Exam-style example
You are cruising at Mach 0.78 where the static air temperature is −52 °C. What is your true airspeed?
- Convert the temperature to kelvin: −52 + 273 = 221 K.
- Local speed of sound = 38.97 × √221 ≈ 38.97 × 14.87 ≈ 579 kt.
- TAS = Mach × LSS = 0.78 × 579.
True airspeed ≈ 452 kt.
Common trap: Reaching for the altitude instead of the temperature. Two aircraft at the same flight level but in different air masses have different speeds of sound, and in an isothermal layer the speed of sound does not change as you climb. Any answer chain that computes the speed of sound from pressure or density is wrong by construction.
How to calculate Mach number
The definition, the formula, a worked example and how it shows up in the ATPL exams.
How to calculate Mach number
The definition, the formula, a worked example and how it shows up in the ATPL exams.Mach number and the speed of sound
Mach number is simply your true airspeed expressed as a fraction of the local speed of sound: M = TAS ÷ LSS. Mach 0.80 means you are travelling at 80% of the speed of sound around you.
The crucial point for the ATPL is that the local speed of sound depends only on air temperature, not on pressure or density. In knots it is about 38.97 × √(T in kelvin). At sea-level ISA (15 °C, 288 K) that is roughly 661.5 kt; in the cold of high cruise it drops well below 600 kt.
Worked example
Cruising at FL350 with an outside air temperature of −54 °C. Convert to kelvin: −54 + 273 = 219 K. Local speed of sound = 38.97 × √219 ≈ 38.97 × 14.8 ≈ 577 kt.
If your true airspeed is 480 kt, then Mach = 480 ÷ 577 ≈ 0.83. The same 480 kt TAS down at sea level, where the speed of sound is about 661 kt, would only be Mach 0.73, which is why high-altitude cruise is flown to a Mach limit.
The climb and the crossover altitude
Climb at a constant indicated airspeed and two things happen at once: your true airspeed increases (thinner air) while the speed of sound decreases (colder air). Both push the Mach number up. Eventually you reach the Mach number you want to hold, the IAS/Mach crossover altitude, and from there you climb and cruise at a constant Mach instead.
Why it matters for Principles of Flight
Critical Mach number, the onset of shock waves and buffet, high-speed handling and 'coffin corner' all hang off this TAS-to-Mach relationship. Being fluent with the speed-of-sound dependence on temperature is essential for ATPL Principles of Flight and high-speed flight questions.
Good to know
Background and tips for getting the most out of this calculator.
Good to know
Background and tips for getting the most out of this calculator.Speed of sound
It depends only on temperature, about 38.97 × √(T in Kelvin) knots. Roughly 661.5 kt at sea-level ISA.
Crossover
Climbing at a fixed IAS, TAS rises and the speed of sound falls, so Mach increases, the classic climb to the Mach/IAS crossover altitude.
POF link
Critical Mach, buffet, and high-speed handling all hang off this relationship. Get fluent with it for ATPL Principles of Flight.
Frequently asked questions
Tap to read the full background and answers.
Frequently asked questions
Tap to read the full background and answers.- How is Mach number calculated?
- Mach number is true airspeed divided by the local speed of sound. The speed of sound depends only on temperature: about 661.5 kt at 15 °C, falling as the air gets colder.
- What is the formula for the speed of sound?
- The local speed of sound in knots is about 38.97 × √(T) where T is the temperature in kelvin (°C + 273; 273 is the exam shorthand, the calculator uses the precise 273.15). At 15 °C (288 K) that gives roughly 661.5 kt.
- Can I go from Mach to TAS?
- Yes. Switch the conversion direction, enter a Mach number and the temperature (or a pressure altitude to assume ISA), and SkyStudy returns the true airspeed.
- Why does Mach rise as I climb at constant TAS?
- Colder air higher up has a lower speed of sound, so the same true airspeed becomes a higher fraction of it, a higher Mach number.
- Does the speed of sound change with altitude?
- Only through temperature. Pressure and density on their own do not change it. In the ISA troposphere the temperature falls as you climb, so the speed of sound falls with it, but above the tropopause, where the standard temperature is constant, the speed of sound stops changing too.
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