Mach Number Calculator
Free calculate mach number from velocity and speed of sound. m = v/a Get instant, accurate results with our easy-to-use calculator.
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What is Mach Number?
The Mach number (M) is a dimensionless quantity representing the ratio of an object's speed to the speed of sound in the surrounding medium. It's named after Austrian physicist Ernst Mach.
Mach number is crucial in compressible flow analysis. M < 1 is subsonic, M = 1 is sonic (sound speed), and M > 1 is supersonic. At high Mach numbers, compressibility effects become significant, and flow behavior changes dramatically.
The speed of sound in air depends on temperature: a = √(γRT), where γ = 1.4 (for air), R = 287 J/(kg·K), and T is absolute temperature. At 20°C, sound speed ≈ 343 m/s.
Mach Number Formula
Where:
- • M = Mach number (dimensionless)
- • v = Object velocity (m/s)
- • a = Speed of sound (m/s)
Speed of sound in air:
a = √(γRT) = √(1.4 × 287 × T)
At 20°C: a ≈ 343 m/s
How to Calculate
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1
Convert velocity to m/s
Convert km/h or mph to meters per second for consistent units.
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2
Calculate speed of sound
From temperature: a = √(1.4 × 287 × T) where T is in Kelvin. Or use direct input.
-
3
Calculate Mach number
M = v / a. This gives the ratio of speed to sound speed.
Practical Examples
Example 1: Commercial Aircraft
Aircraft at 250 m/s, air temperature 20°C (a = 343 m/s).
Solution:
M = 250 / 343
M ≈ 0.73 (subsonic)
Example 2: Supersonic Jet
Jet at 686 m/s, a = 343 m/s.
Solution:
M = 686 / 343
M = 2.0 (Mach 2 - twice the speed of sound!)
Applications
Aerospace
Designing aircraft, understanding compressible flow, analyzing supersonic flight, and optimizing aerodynamic performance.
Propulsion
Designing nozzles, analyzing jet engines, understanding shock waves, and optimizing propulsion systems.
Fluid Dynamics
Analyzing compressible flows, understanding wave propagation, and studying high-speed fluid behavior.
Education
Teaching compressible flow, understanding speed regimes, and learning about supersonic and hypersonic flight.
Frequently Asked Questions
What are the different Mach regimes?
Subsonic: M < 0.8 (compressibility negligible). Transonic: 0.8 < M < 1.2 (mixed flow). Supersonic: 1.2 < M < 5 (shock waves). Hypersonic: M > 5 (extreme heating).
Why does speed of sound depend on temperature?
Sound is a pressure wave. Warmer air has higher molecular speeds, so pressure disturbances propagate faster. a = √(γRT) increases with √T.
What happens at Mach 1?
At sonic speed (M = 1), the object moves as fast as sound waves. This creates a shock wave (sonic boom). Flow behavior changes dramatically - compressibility becomes dominant.
Can Mach number be greater than 1?
Yes! Supersonic aircraft (M > 1) exceed sound speed. The SR-71 reached M ≈ 3.3. Hypersonic vehicles can reach M > 5. Spacecraft re-entering can reach M > 20.
How does altitude affect Mach number?
At higher altitude, temperature decreases, so speed of sound decreases. The same true airspeed gives a higher Mach number at altitude. Aircraft often fly at constant Mach number, not constant speed.