Speed of Sound and Mach Calculator

The calculator

The top field is the air temperature in Celsius. From it the tool works out the speed of sound and shows it in meters per second, miles per hour, kilometers per hour, and knots. The lower pair of fields takes a speed in mph and divides it by that same speed of sound to give the Mach number. Change either input and every result updates live. The defaults model warm sea-level air at 20 degrees Celsius, where the speed of sound is about 343.2 m/s, and a 600 mph aircraft, which works out to roughly Mach 0.78.

Why temperature changes the speed of sound

Sound is a pressure wave passed along by air molecules bumping into one another. The hotter the air, the faster those molecules already move, so they hand the wave along sooner and sound travels quicker. Cold air does the opposite: slower molecules, slower sound. Pressure and altitude barely matter on their own, because thinner air has both fewer molecules and the room for them to move further, and those two effects cancel. What is left is temperature.

This is the reason Mach 1 is slower high in the atmosphere. Cruising altitude air can sit near minus 50 degrees Celsius, where the speed of sound falls to about 670 mph, far below the roughly 768 mph of warm ground-level air. An aircraft holds the same Mach number with a lower true airspeed up there, simply because the sound barrier itself has moved down to meet it.

What Mach numbers mean

Subsonic covers everything below Mach 1, the range where almost all flight happens. Transonic, roughly Mach 0.8 to 1.2, is the awkward zone where part of the airflow goes supersonic while the rest stays below the speed of sound, which is why airliners cruise just under it. Supersonic means faster than Mach 1, where the aircraft outruns its own pressure waves and produces a sonic boom. Hypersonic begins around Mach 5 and brings intense heating, the regime of reentry vehicles and advanced missiles.

FAQ

What is the speed of sound in mph?

At 20 degrees Celsius the speed of sound is about 343 m/s, which is roughly 768 mph or 1,236 km/h. The value rises with warmer air and falls with colder air, so there is no single fixed figure. At freezing it drops to about 741 mph.

Does the speed of sound change with altitude?

Yes, but the cause is temperature, not altitude itself. Air gets colder as you climb through the troposphere, and colder air carries sound more slowly. At a typical cruising altitude near minus 50 degrees Celsius the speed of sound is around 670 mph, well below the 768 mph you get at warm ground level.

What is Mach 1?

Mach 1 is the speed of sound in the surrounding air. Mach number is a ratio, not a fixed speed: an object travels at Mach 1 when it moves at exactly the local speed of sound. Because that speed depends on temperature, Mach 1 is a different number of mph at sea level than it is high in the atmosphere.

Why is Mach 1 slower at high altitude?

Sound travels by collisions between air molecules, and warmer molecules move faster, so they pass the pressure wave along more quickly. High in the atmosphere the air is very cold, the molecules are slower, and the speed of sound drops. Since Mach 1 just means the local speed of sound, Mach 1 itself is slower up there.

How do you calculate Mach number?

Divide the speed of the object by the local speed of sound, using the same units for both. First find the speed of sound from the air temperature, then convert the object speed to m/s and divide. For example, 600 mph is 268 m/s, and at 20 degrees Celsius that gives Mach 0.78.