Method and variables
Mach number: M = V/a, where V is the object or flow speed and a is the local speed of sound. In ideal-gas mode, this page uses a = √(γRT).
- γ — heat-capacity ratio (Cp/Cv)
- R — specific gas constant for the gas
- T — absolute static temperature in kelvin
Worked example
For air approximated as γ = 1.4 and R = 287.05 J/(kg·K) at 15 °C (288.15 K), the calculated sound speed is about 340.3 m/s. A speed of 250 m/s therefore gives M ≈ 0.735.
How to read the result
Mach is a ratio, not a speed unit. Labels such as low subsonic, subsonic, transonic, supersonic and hypersonic are useful shorthand; their exact boundaries vary by application. Near Mach 1, compressibility effects and the details of the geometry quickly become important.
Important limits
The ideal-gas calculation assumes a calorically perfect gas and uses static temperature. It does not model humidity, atmospheric pressure variation directly, shocks, local acceleration around a body, temperature recovery, high-temperature dissociation, real-gas effects or structural/aerodynamic safety margins. Use a validated flow model and applicable standards for design work.
Reference
- NASA Glenn: Mach number and ideal-gas speed-of-sound relation
- NIST Guide for the Use of the International System of Units
Related tools
Reynolds Number Calculator · Prandtl Number Calculator · Dimensionless Numbers Calculators
Frequently asked questions
What is Mach number?
Mach number is the ratio of an object's or flow's speed to the local speed of sound: M = V/a. It is dimensionless.
Why does this calculator ask for static temperature?
In the ideal-gas mode, it calculates the local speed of sound as a = sqrt(gamma R T). That relation requires absolute static temperature, not total or stagnation temperature.
Is Mach 1 always 343 m/s?
No. The speed of sound changes with gas composition and local thermodynamic state. About 343 m/s is a familiar dry-air value near 20 °C, not a universal constant.