# Mach Number Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Dec 02, 2022

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.

You can also use the advanced mode of the calculator if you know the temperature of air. The speed of sound in air at different temperature, $T$ (in $\degree C$) is given by the speed of sound formula:

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

## 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 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:

Rahul Dhari
Speed of object
ft/s
Speed of sound
ft/s
Mach number
People also viewed…

### Car crash force

With this car crash calculator, you can find out how dangerous car crashes are.

### DC wire size

Use our DC Wire Size Calculator to know the wire size needed for your DC electric application.

### Photon energy

The photon energy calculator computes the energy of a single photon from its wavelength or frequency.

### Significant figures

The significant figures calculator performs operations on sig figs and shows you a step-by-step solution! 