How is Mach number calculated?

Mach number is true airspeed divided by the local speed of sound. The speed of sound is the square root of gamma times R times T, where gamma is 1.4 for air, R is 287 joules per kilogram kelvin, and T is the static air temperature in kelvin.

Why does altitude affect Mach number?

Altitude affects Mach only through temperature. The speed of sound depends solely on temperature, and air gets colder with altitude up to the tropopause. Colder air lowers the speed of sound, so the same true airspeed becomes a higher Mach number up high.

What is the speed of sound at cruise?

At a typical jet cruise temperature near minus 50 degrees Celsius, the speed of sound is about 575 kt, compared to roughly 661 kt at sea level standard temperature. That is why a 480 kt cruise can be Mach 0.83 high up but only Mach 0.73 lower down.

What are Mmo and critical Mach number?

Mmo is the maximum operating Mach number, a structural and handling limit shown as a barber-pole on the airspeed indicator. Critical Mach is where airflow over the wing first reaches Mach 1 locally, causing shock-induced drag and buffet. Both are why high cruise is flown by Mach, not airspeed.

Does pressure or humidity matter?

For the standard dry-air formula used here, only temperature matters. Humidity slightly raises the speed of sound and pressure has almost no direct effect on it, so they are ignored. The result is accurate to a fraction of a percent for normal flight conditions.

Mach Number Calculator

High and fast, pilots manage speed by Mach number rather than airspeed, because the limits that matter — buffet, shock-induced drag, and Mmo — are tied to the speed of sound, not the airspeed indicator. This calculator converts between true airspeed and Mach number at any temperature and shows the local speed of sound.

How it works

Mach number is true airspeed divided by the local speed of sound. The speed of sound a follows the standard relation a = sqrt(gamma x R x T), which for dry air simplifies to a = 20.0468 x sqrt(T) metres per second, with T the static air temperature in kelvin. Crucially the speed of sound depends only on temperature — not pressure or altitude directly.

The tool converts your temperature to kelvin, computes the speed of sound in knots and metres per second, then divides TAS by it to get Mach, or multiplies Mach by it to get TAS.

Worked example

At minus 50 degrees Celsius the speed of sound is about 575 kt. A true airspeed of 450 kt is therefore about Mach 0.78. The same 450 kt down at plus 15 degrees Celsius, where the speed of sound is about 661 kt, is only Mach 0.68 — the same airspeed, a very different Mach number.

Notes

The dry-air formula ignores humidity and pressure, which is accurate to a fraction of a percent for flight. Always respect the published Mmo and the barber-pole on the airspeed indicator; this tool is for speed management, not for exceeding limits.