# Mach Number

Written by Jerry Ratzlaff. Posted in Dimensionless Numbers

Mach number is a dimensionless number that is the ratio of the velocity of flow to the velocity of sound.

## formula

$$Ma = \frac{v}{v_s}$$

Where:

$$Ma$$ or $$M$$ =  mach number

$$v$$ = velocity, object speed

$$v_s$$ = speed of sound

Solve for:

$$v = Ma$$

$$v_s = \frac{v}{Ma}$$

### note about the speed of sound

The speed of sound in this equation is dependent on the density of the medium that the sound is traveling through. For example, the speed of sound through a solid object like a railroad track is much faster than the speed of sound through air at standard conditions.

## Conversion table

Mach Number Conversion Table
MultiplyByTo Get
9.646x107 feet per day
4.0192x105 feet per hour
66,986 feet per minute, fpm
1,116 feet per second, fps
1,225 kilometers per hour
2.94x107 meters per day
1.225x106 meters per hour
20,417 meters per minute
340.29 meters per second
761 miles per hour, mph