Mach Number Converter Calculator

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

About Mach Number Converter Calculator

Mach number is a ratio, not a fixed speed: it is the true airspeed divided by the local speed of sound. The speed of sound in dry air depends only on temperature, following a = √(γRT) with γ = 1.4 and R = 287.05 J/(kg·K). That is why Mach 1 is about 1,225 km/h at sea level but roughly 1,062 km/h in the cold air at cruising altitude — the same Mach number is a slower true airspeed when the air is colder.

Formulas

Speed of sound

a = √(1.4 × 287.05 × T) where T is in kelvin

Mach number

M = true airspeed ÷ a

Worked example

With the default values below, Mach Number Converter Calculator returns Mach Number of 1.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Convertone of Mach number → speed, Speed → Mach number: Mach number → speed
Mach numberminimum 0: 1
True airspeedminimum 0 km/h: 1,000 km/h
Air temperature: 15 °C

Results

Mach Number: 1.0000
Local Speed of Sound: 340.29 m/s
True Airspeed: 1,225.05 km/h
Flight Regime: Transonic

Step by step

1Values used
2Speed of sound
3Mach number
4Mach Number= 1.0000
5Local Speed of Sound= 340.29 m/s
6True Airspeed= 1,225.05 km/h
7Flight Regime= Transonic

Assumptions and limits

The result is derived only from the 4 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.

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

Frequently Asked Questions

Why does Mach 1 change with altitude?

Because the speed of sound falls as air gets colder. Mach 1 is 340.3 m/s at 15 °C but only about 295 m/s at −50 °C, so the same Mach number means a lower true airspeed high up.

Does air pressure affect the speed of sound?

Not on its own. For an ideal gas the speed of sound depends on temperature alone — pressure and density changes cancel out — which is why only temperature is needed here.