Mach Number Calculator (2024)

Last updated:Apr 16, 2024

Table of contents

What is Mach number?How to calculate Mach number?Example: Using the Mach number calculatorWhat are supersonic and subsonic flow?FAQs

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:

$M = \frac{v}{c}$ M=cv

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

By default, we assume that the air temperature is $20 \degree C$ 20°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, $T$ T (in $\degree C$ °C) is given by the speed of sound formula:

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

🙋 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 $1,500\ \mathrm{km/h}$ 1,500km/h. Given the speed of sound as $343\ \mathrm{m/s}$ 343m/s.

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

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

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

$M = \frac{416.67}{343} = 1.21$ M=343416.67=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 $3$ 3. What is the speed in meters per second?

What are supersonic and subsonic flow?

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:

Oblique shock wave calculator
Prandtl Meyer expansion calculator

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 consistent 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, compressible 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.

FAQs

How do you solve for Mach number? ›

The Mach Number formula is calculated as M = v / c where 'M' is the Mach number, 'v' is the velocity of the object, and 'c' is the speed of sound in the fluid medium.

How fast is 100 Mach? ›

Well, the Mach number is defined as the ratio of the velocity of a body relative to the Speed-of-Sound under the local atmospheric conditions. So, Mach 100 would be about 74,110 mph (miles per hour).

Find Out More ›

What Mach is achievable? ›

The first ever person to break Mach 1 and to break the sound barrier was Chuck Yeager in 1947. And the highest Mach number ever reached was 9.6 achieved by the NASA X-43 in 2004, an experimental unmanned hypersonic aircraft. The highest Mach number ever reached in a manned aircraft was Mach 6.7, achieved by William J.

Read The Full Story ›

What speed is Mach 7? ›

The speed of sound is approximately 767 mph. Varying with air temp, humidity and altitude. The number is just a multiplayer of mach. So 767 x 7 = approximately 5369 mph.

See Details ›

What is the formula for Mach number in aviation? ›

The ratio between the true air speed (TAS) and the local speed of sound (LSS). This ratio, which equals one when the TAS is equal to the LSS, is known as the Mach Number (M) and is very important in aircraft operating at high speed.

What is the formula for exit Mach number? ›

The exit Mach number for compressible isothermal fluid has been shown to be Ma ≠ 1, but 1 / k , where k is the ratio of the fluid-specific heat capacitites at constant pressure to that at constant volume.

Discover More ›

Is 750 mph Mach 1? ›

For example, the speed of sound at 30,000 feet is about 670 miles per hour, but an aircraft must travel at least 750 miles per hour (Mach 1.12, where Mach 1 equals the speed of sound) for a boom to be heard on the ground.

Get More Info ›

What speed is mach 1 mph? ›

Mach 1, then, is the speed of sound, around 761 mph at sea level on a standard day.

Find Out More ›

What is the fastest Mach speed a human has gone? ›

Knight flew at Mach 6.7 at an altitude of 102,100 feet (31,120 m), or 19.34 miles. The Space Shuttle reentered the atmosphere at approximately 17,000 mph—Mach 22. Apollo 10 set the record for the highest velocity attained to date by a piloted vehicle at 24,791 mph (Mach 32.3) during the return from the moon.

Discover More Details ›

Did Tom Cruise fly Mach 10? ›

It Has Never Truly Been Tested. Tom Cruise's character's feat of Mach 10 speed in Top Gun: Maverick is one scientifically improbable stunt out of many featured in the film. That said, is it possible for the human body to be able to withstand such acceleration? The most likely answer is a resounding no.

Learn More ›

Can a human survive Mach 10? ›

Maverick breaks the Mach 10 speed barrier in the movie, a speed that is practically impossible for a human to achieve due to extreme G-forces and potential damage to the body. The real-life SR-72, which the Darkstar prototype is based on, is under development but won't come close to the Mach 10 speed seen in the film.