Mach number
Dimensionless ratio to the local sound speed.
Fluid mechanics · Fluid dynamics
Mach number calculator
Divide relative speed by the local speed of sound, or recover speed from Mach number. Supply the sound speed for the actual fluid and thermodynamic state.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Relative speed
Speed for the specified local sound speed and Mach number.
Relation and numerical substitution
M = v / a—
Speed and sound speed use the same reference medium; local sound speed is strictly positive.
01Formulas and symbols
Formulas used
M
M = v / aDimensionless ratio to the local sound speed.v
v = M × aSpeed for the specified local sound speed and Mach number.02Assumptions and limits
Scope of validity
- Speed and sound speed use the same reference medium; local sound speed is strictly positive.
03Validation example
Reference numerical case
- With a = 343 m/s, v = 343 m/s gives M = 1; v = 686 m/s gives M = 2.
04References
Technical references
- University Physics 1, §17.8 Shock waves — OpenStax
FAQ
Is Mach 1 a fixed speed?
No. It equals the local sound speed, which depends on the medium and its state.
Can I use kilometres per hour?
Yes. Each velocity is converted before taking the ratio; both need not be entered in the same unit.
05Model and conventions
Divide relative speed by the local speed of sound, or recover speed from Mach number. Supply the sound speed for the actual fluid and thermodynamic state.
06Limits of this model
No temperature-to-sound-speed law, shock strength or compressible-flow solution is included. Conventional regime names do not define universal sharp physical boundaries.
07Common mistakes
Do not use 343 m/s for every medium: it is merely the initial input. Water, other gases and changing temperature need different sound speeds.