Mach Number At Altitude Calculator

Work out mach number at altitude instantly with clear inputs, formula shown and shareable results.

About Mach Number At Altitude Calculator

Mach number is true airspeed divided by the local speed of sound, and the speed of sound depends only on absolute temperature: a = sqrt(gamma x R x T). Because air gets colder with altitude, the same true airspeed gives a higher Mach number the higher you fly, which is why high-level cruise is Mach limited rather than airspeed limited.

Formula

Mach number

M = TAS / a, a = sqrt(1.4 x 287.053 x T) with T in kelvin

Worked example

With the default values below, Mach Number At Altitude Calculator returns Mach number of 0.7645. Change any input above and every figure here is recalculated in your browser.

Inputs used

True airspeed: 450 kt
Static air temperature: -45 °C
Maximum operating Mach: 0.82 M

Results

Mach number: 0.7645 M
Local speed of sound: 588.60 kt
Margin to Mmo: 0.0555 M
Speed of sound: 302.80 m/s

Step by step

1Values used
2Mach number
3Mach number= 0.7645 M
4Local speed of sound= 588.60 kt
5Margin to Mmo= 0.0555 M
6Speed of sound= 302.80 m/s

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
Aviation results are planning estimates only. Always verify take-off, landing, fuel, weight and balance figures against the certified Aircraft Flight Manual, current performance charts and applicable aviation regulations before flight.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Aviation results are planning estimates only. Always verify take-off, landing, fuel, weight and balance figures against the certified Aircraft Flight Manual, current performance charts and applicable aviation regulations before flight.

Frequently Asked Questions

Why does Mach rise in a climb at constant TAS?

The speed of sound falls with temperature, and temperature falls about 2 degrees per 1,000 ft in the troposphere, so the same TAS becomes a larger fraction of the local speed of sound.

What is the crossover altitude?

The level where the climb speed schedule changes from a constant indicated airspeed to a constant Mach number, because Mach becomes the limiting factor above it.