Speed of sound
a = √(γRT)
Ideal-gas acoustic speed at the entered static temperature.
Mach Number Calculator
Calculate local acoustic speed and Mach number for a calorically perfect gas from velocity and static temperature.
Access: Free to use, no installation, and No account required.
Inputs
For air, γ ≈ 1.4 and R ≈ 287 J/(kg·K) near ordinary temperatures. Real-gas and high-temperature property variation are not included.
Results
Mach number
Mach number is velocity divided by local speed of sound. In the ideal-gas model, acoustic speed is a = √(γRT), so temperature changes the Mach number corresponding to a given physical velocity.
Engineering reference
Mach Number Calculator: background and worked detail
Use the Mach Number Calculator to calculate ideal-gas speed of sound and Mach number from flow velocity, static temperature, heat-capacity ratio, and specific gas constant.
Speed of sound and compressibility regimes
Mach number is the ratio of flow speed to the local acoustic speed. For an ideal gas, speed of sound depends on γRT, so a fixed physical velocity corresponds to different Mach numbers at different temperatures or gas compositions.
This calculation uses static thermodynamic temperature and constant ideal-gas properties. High-temperature chemistry, real-gas effects, humidity, varying composition, and shock/expansion relations require a more complete compressible-flow model.
Equations used by this calculator
Mach number
M = V/a
Flow speed normalized by local speed of sound.
340 m/s in standard-temperature air
Use V = 340 m/s, T = 288.15 K, γ = 1.4, and R = 287.05 J/(kg·K).
- The ideal-gas speed of sound is about 340.3 m/s.
- Mach number is therefore approximately 1.00.
- Changing temperature changes a even when physical velocity is unchanged.
Result: The example lies near sonic conditions under the entered air properties.
Validation checks
Sea-level standard-atmosphere values anchor these checks.
Zero velocity
Case: Set V = 0.
Expected: Mach number should be zero while speed of sound remains finite.
Temperature increase
Case: Raise T while holding V, γ, and R fixed.
Expected: Speed of sound should increase and Mach number should decrease.
Assumptions and model boundaries
Assumptions
- Ideal gas with constant γ and R.
- Entered temperature is static absolute temperature in kelvin.
- Velocity and acoustic speed refer to the same local state.
Limitations
- Does not calculate stagnation properties, shocks, area-Mach relations, nozzle flow, real-gas chemistry, or humidity effects.
- At extreme temperatures, constant γ and ideal-gas assumptions can become inaccurate.
Mach Number Calculator FAQ
Is Mach 1 always the same speed?
No. Mach 1 equals the local speed of sound, which changes with temperature and gas properties.
Should I use static or stagnation temperature?
Use static local temperature for a = √(γRT) in this calculator.
Does altitude directly determine Mach number?
Not directly. Altitude influences atmospheric temperature and therefore speed of sound; Mach is still velocity divided by the local acoustic speed.
Where this calculation comes from
Shared with the Flight and Aerodynamics Workbench, which adds atmosphere models and compressible flow relations.
Open the source workbench →Read calculation and source methodology →