# Mach Number Calculator

Created by Davide Borchia
Last updated: Aug 16, 2022

If you want to know how fast your plane is going in terms of the speed of sound, our Mach number calculator comes in handy. With few inputs and straightforward outputs, you will easily find your answers. And if you are curious, read our article to learn:

• What is Mach number;
• How to calculate your speed in terms of speed of sound;
• What does it mean to go supersonic?
• The Mach number equation: convert from Mach to mph and km/h, and vice-versa;
• Some plane facts!

## Bang! What is Mach number, or velocity in term of the speed of sound

Mach number is a fundamental quantity in fluid dynamics. This dimensionless quantity indicates the speed of an object as a multiple of the speed of sound it travels in.

The speed of sound is a complex quantity (not in the mathematical sense), which highly depends on the local property of the medium. As the name tells us, the speed of sound is the velocity at which sound waves propagate: sound moves at different speeds according to the medium. It is generally faster in solids (since they are more "compact") and lower in gases; that is — coincidentally — where we care more for Mach number.

You can also use the speed of sound to calculate the distance of lightning! We hope you won't need our calculator to determine that the distance is too small. ⚡

In the early XX century, with our lives moving faster and faster, humanity started accelerating toward the speed of sound in the air, and the idea that that value could be reached started appearing in the minds of scientists and engineers. Some thought that the speed of sound was a physical barrier, thus creating the infamous name sound barrier.

The sound barrier lies at about $1200\ \text{km}/\text{h}$, or $770\ \text{mph}$. This speed corresponds to the transition between the subsonic and the supersonic regime, and we indicate it with Mach number $1$.

🙋 As we don't really measure speed with Mach numbers but a ratio, we write this quantity as $\text{Mach}\ 1$ rather than $1\ \text{Mach}$.

## How to calculate Mach number

Calculating Mach number is an easy matter: you only need to know the speed of your object and the local speed of sound. The equation for Mach number is the ratio between these two quantities:

$\text{Mach} = \frac{v}{v_{\text{s}}}$

In our Mach number calculator, you can decide to input both the speed of your object and the speed of sound or to use the preset value (the speed of sound in air at sea level and a temperatureof $20\ \degree\text{C}$.

You can also use our calculator for the conversion from Mach to mph: simply input the Mach number instead of the speed, and we will do the rest.

## Examples of Mach numbers

You already know that Mach $1$ equals the speed of sound. This is also the threshold for supersonic travel. Right before and after Mach 1, at Mach numbers between $0.8$ and $1.2$, we can find the transonic regime, an uncomfortable place where turbulence is intense (and led pilots to think that the sound barrier was a real barrier).

Chuck Yeager proved the skeptics wrong by passing Mach 1 on the Bell X-1 experimental aircraft on October 14th 1947.

For the following few decades, humanity tried to reach ever-increasing speeds. The infamous F-104 Starfighter was the first fighter jet (almost a rocket with tiny wings attached) to routinely reach Mach number 2.

The top speed of the Starfighter was $2,717\ \text{km}/\text{h}$. Try the conversion to Mach number:

$\text{Mach} = \frac{2,717\ \frac{\text{km}}{\text{h}}}{1,235.6\frac{\text{km}}{\text{h}}}=2.2$

🙋 How many miles per hour is that quantity? Visit our speed converter to learn how to convert between more or less known speed measurement units!

In the '60s, engineers were comfortable thinking in terms of Mach 3: in those years, in the sky, the impressive XB-70 and SR-71 were flying three times faster than the speed of sound. The top speed of the SR-71 (as far as we know) was Mach $3.3$. How many miles per hour is this quantity? Invert the Mach number equation:

$v= \text{Mach}\cdot v_\text{s}$

Or ask directly to our Mach number calculator! The Blackbird top speed was $2,533.6\ \text{mph}$.

Davide Borchia
Speed of object
ft/s
Speed of sound
ft/s
Mach number
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