Mach Number Calculator

Q: How to find the Mach number of an aircraft flying at 31,000 feet?

To find the Mach number of a commercial aircraft flying at 31,000 ft , you need to: Take the temperature at 31,000 ft as: T = -46.42 °C (226.73 K) ; Use the temperature in Celsius to calculate the speed of sound: c = 331.3⋅√(1+T/(273.15)) = 301.84 m/s Take the airplane cruise speed as v = 490 kn (252.1 m/s) (Boeing 787); Divide the airplane speed by the speed of sound: M = 252.1/301.84 = 0.84 Well done , you just found the correct answer!

Q: What is the Mach number of the ISS at this instant?

The Mach number of the International Space Station (ISS) is an impressive 22.33! The ISS orbits Earth with a constant speed of 7.66 km/s , which is why we find this huge Mach number . Once this velocity is constant and there is no air or atmosphere in the ISS orbit, the astronauts do not feel any unpleasant effect, and the ISS is safe from structural damage .

Q: What is the Mach number in fluid mechanics?

The Mach number is a dimensionless quantity. In fluid dynamics, it represents the flow velocity ratio past a boundary compared to the local speed of sound . Using the Mach number, the flows can be classified as: Incompressible flow: M = 0 ; Subsonic flow: 0 < M < 1 ; Transonic flow: 0.8 ≤ M ≤ 1.2 ; Supersonic flow: M > 1 ; and Hypersonic flow: M > 3 .

Q: What Mach number is the speed of light?

The Mach number for the speed of light is 873,768 ! You can determine its value by considering the following steps: Take the speed of light in the air as 299,702,547 m/s ; Take the speed of sound in air as 343 m/s ; Divide the speed of light by the speed of sound; and That is it! You found that the Mach number for light is 873,768 .

Q: What could be one result of exceeding a critical Mach number?

Exceeding a critical Mach number may lead to a phenomenon called compressibility . When an aircraft is under compressibility, the shock waves created in the airflow sends it into an unmaneuverable dive and can also cause damage to the structure of the aircraft .

Creators

Rahul Dhari

Research Gate

Rahul is a researcher and engineering expert dedicated to applying his skills to solve complex world problems. He has contributed to impactful projects in advanced material manufacturing and 3D printing failure analysis frameworks, among others. His research is a testament to his devotion to discovery and innovation within mechanical and aerospace engineering. His expertise ranges from 3D printing and computational modeling through advanced engineering simulation to material characterization and additive manufacturing. Whenever he is not revolutionizing engineering research, he enjoys outdoor adventures with his dog, who is his biggest fan. See full profile

Check our editorial policy

Reviewers

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

Check our editorial policy

New

The Mach number calculator returns the Mach number for the given speed. If you wondered how fast an aircraft is flying making those loud noises, this calculator tells you much faster it is than the speed of sound. The calculator will also tell you the meaning of the terms – supersonic and subsonic! Scroll down and read on further to understand what is Mach number and how to calculate Mach number.

What is Mach number?

Sound travels at different speeds in different medium — as we explained in our speed of sound in solids calculator — and at different temperatures. That speed is compared with the speed of an object, say an aircraft or a boat. The ratio of the speed of an object and the speed of sound is known as the Mach number. The Mach number is a dimensionless quantity. Mathematically, the Mach number equation can be written as:

M = \frac{v}{c}

such that $v$ is the speed of the object and $c$ is the speed of sound.

By default, we assume that the air temperature is $20 \degree C$ , but you can change it in the Temperature of air field, and our calculator will make further calculations. The speed of sound in air at different temperature, $T$ (in $\degree C$ ) is given by the speed of sound formula:

c = 331.3 \cdot \sqrt{1+\frac{T}{273.15}}

🙋 If you want to learn more, visit our speed of sound calculator!

How to calculate Mach number?

To calculate Mach number, follow the steps below:

Step 1: Set the appropriate units for speed from the list on the right. If you need any help with conversion, you can also use our speed converter.
Step 2: Enter the speed of the object.
Step 3: Input the speed of sound.
Step 4: The Mach number calculator will now tell you what is the Mach number for the given object.

Example: Using the Mach number calculator

Estimate the Mach number for an aircraft flying at a speed $1,500\ \mathrm{km/h}$ . Given the speed of sound as $343\ \mathrm{m/s}$ .

Step 1: Set the units or convert both speeds into same units, say m/s. Such that,

$v = 1500\ \mathrm{km/h} = 416.67\ \mathrm{m/s}$ .

Step 2: Enter the speed of aircraft as $416.67\ \mathrm{m/s}$ .
Step 3: Enter the speed of sound as $343\ \mathrm{m/s}$ .
Step 4: The Mach number or Mach speed for the aircraft is:

M = \frac{416.67}{343} = 1.21

Alternatively, you can also estimate the speed of an aircraft using its Mach speed. Such as, if the aircraft is travelling at Mach $3$ . What is the speed in meters per second?

Step 1: Enter the Mach number as $3$ .
Step 2: Input the speed of sound as $343\ \mathrm{m/s}$ .
Step 3: The Mach speed calculator will return the speed of the aircraft as $1,\!029\ \mathrm{m/s}$ . Mathematically that's:

v = M \cdot c = 343 \cdot 3 = 1029\ \mathrm{m/s}

🔎 The flying airplane might have a different speed than the speed indicated by a gauge. This difference is also related to the Mach number. Check our true airspeed calculator to learn more!

What are supersonic and subsonic flow?

The Bell X-1B – First manned aircraft to achieve supersonic speeds

The first aircraft ever to break the sound barrier was a Bell X1 aircraft piloted by Chuck Yeager in the year 1947. The sound barrier is the term used when an aircraft is nearing the speed of sound. The Mach speed calculator returns the Mach number. The Mach number is used to characterize the flow speed and mark them in various categories, such as:

Mach number range	Type of flow	Type of objects	Common examples
< 0.8	Subsonic	Passenger aircraft and helicopters	Dornier 228, Boeing 747-400, Airbus A330-300
0.8-1.2	Transonic	Military trainers	M346 Master, T45 Goshawk, B-1B Lancer
1.2-5.0	Supersonic	Military aircraft	MiG 21 Fishbed, F 16 Fighting Falcon, Mirage 2000H
5.0-10.0	Hypersonic	Ballistic missiles, experimental vehicles	Bramhos-II, NASA X15

Please check out the following calculators to learn about the amazing phenomenons that occur in the supersonic flow regime:

FAQs

How to find the Mach number of an aircraft flying at 31,000 feet?

To find the Mach number of a commercial aircraft flying at 31,000 ft, you need to:

Take the temperature at 31,000 ft as: T = -46.42 °C (226.73 K);
Use the temperature in Celsius to calculate the speed of sound:

c = 331.3⋅√(1+T/(273.15)) = 301.84 m/s

Take the airplane cruise speed as v = 490 kn (252.1 m/s) (Boeing 787);
Divide the airplane speed by the speed of sound:

M = 252.1/301.84 = 0.84

Well done, you just found the correct answer!

What is the Mach number of the ISS at this instant?

The Mach number of the International Space Station (ISS) is an impressive 22.33! The ISS orbits Earth with a constant speed of 7.66 km/s, which is why we find this huge Mach number. Once this velocity is constant and there is no air or atmosphere in the ISS orbit, the astronauts do not feel any unpleasant effect, and the ISS is safe from structural damage.

What is the Mach number in fluid mechanics?

The Mach number is a dimensionless quantity. In fluid dynamics, it represents the flow velocity ratio past a boundary compared to the local speed of sound.
Using the Mach number, the flows can be classified as:

Incompressible flow: M = 0;
Subsonic flow: 0 < M < 1;
Transonic flow: 0.8 ≤ M ≤ 1.2;
Supersonic flow: M > 1; and
Hypersonic flow: M > 3.

What Mach number is the speed of light?

The Mach number for the speed of light is 873,768! You can determine its value by considering the following steps:

Take the speed of light in the air as 299,702,547 m/s;
Take the speed of sound in air as 343 m/s;
Divide the speed of light by the speed of sound; and
That is it! You found that the Mach number for light is 873,768.

What could be one result of exceeding a critical Mach number?

Exceeding a critical Mach number may lead to a phenomenon called compressibility. When an aircraft is under compressibility, the shock waves created in the airflow sends it into an unmaneuverable dive and can also cause damage to the structure of the aircraft.