💥 Mach Number

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 2 independent reference calculations · how PhDino checks its numbers

How fast something is moving relative to the local speed of sound, which itself depends on air temperature.

Mach number describes speed as a ratio to the local speed of sound, rather than as an absolute value — Mach 1 is "exactly the speed of sound right here, right now," which matters aerodynamically far more than absolute airspeed does, since the physics of airflow changes qualitatively as an aircraft approaches and exceeds the speed sound itself travels at.

The speed of sound isn't a universal constant — it depends on the medium's temperature (for a given gas), which is why the same physical airspeed corresponds to a different Mach number at different altitudes: the stratosphere is much colder than sea level, so the local speed of sound is lower there, and the same true airspeed represents a higher Mach number at altitude than it would at sea level.

Key formula

Speed of sound: a = √(γ × R × T)
Mach number = velocity ÷ speed of sound

Variables

γ

ratio of specific heats for air (≈1.4)

R

specific gas constant for dry air (287.05 J/(kg·K))

T

absolute air temperature, in kelvin

Notes & limitations

• This uses dry-air constants and doesn't account for humidity, which changes the effective gas constant slightly — a reasonable simplification for most purposes, since the effect on speed of sound is small compared to the temperature effect.
• This computes true airspeed's Mach number directly from temperature — in real aviation, Mach number is more commonly derived instrument-side from a ratio of pressures (impact pressure to static pressure), which arrives at the same physical answer through a different, instrument-friendly measurement path.