Mach Number Calculator
How fast is it compared to sound? Calculate the Mach number for aircraft, projectiles, or any object moving through air or other gases.
M = v / c
At sea level (20°C): 343 m/s
Mach Number Regimes:
- Subsonic: M < 0.8
- Transonic: 0.8 ≤ M < 1.2
- Supersonic: 1.2 ≤ M < 5
- Hypersonic: M ≥ 5
How the Mach Number Calculator Works
Enter the object's speed and the speed of sound in the medium. You can input speed in various units (m/s, km/h, mph, knots) and the calculator converts automatically. Specify the medium and temperature for accurate sound speed.
The calculator applies the Mach number formula: M = v / a, where v is object speed and a is the speed of sound. Mach number is dimensionless - it's a ratio, not a speed itself.
Results show the Mach number and classify the flow regime: subsonic (M < 0.8), transonic (0.8-1.2), supersonic (1.2-5), or hypersonic (M > 5). The speed of sound calculation accounts for temperature and medium properties.
When You'd Actually Use This
Aircraft performance analysis
Determine if an aircraft is flying subsonic or supersonic. Mach number affects drag, lift, and control surface effectiveness.
Rocket and missile design
Calculate Mach number during ascent. Rockets pass through transonic regime where aerodynamic forces are complex and unpredictable.
Wind tunnel testing
Match Mach number for scale model testing. Dynamic similarity requires matching Mach number between model and full-scale vehicle.
Bullet and projectile ballistics
Analyze supersonic projectile behavior. Bullets typically travel at Mach 2-3. Shock waves affect trajectory and create sonic booms.
Jet engine inlet design
Ensure proper airflow into engines. Supersonic aircraft need inlet designs that slow air to subsonic before it reaches the compressor.
Atmospheric re-entry analysis
Calculate Mach number for spacecraft re-entry. Vehicles enter at hypersonic speeds (Mach 25+), creating intense shock heating.
What to Know Before Using
Speed of sound varies with temperature.In air, sound speed ≈ 331 + 0.6T m/s (T in °C). At sea level (15°C), it's about 340 m/s. At altitude, colder air means slower sound speed.
Mach 1 isn't a fixed speed.Mach 1 at sea level is ~767 mph. At 35,000 ft, it's ~660 mph. Aircraft can exceed Mach 1 without changing true airspeed by climbing.
Compressibility matters at high Mach.Above M ≈ 0.3, air compressibility affects aerodynamics. Shock waves form at M > 1, dramatically changing flow behavior.
Different regimes have different physics.Subsonic: smooth flow. Transonic: mixed sub/supersonic with shock waves. Supersonic: shock cones. Hypersonic: extreme heating and chemical effects.
Pro tip: The "sound barrier" isn't a physical barrier. It's the region around Mach 1 where drag increases sharply due to shock wave formation. Modern aircraft pass through it routinely.
Common Questions
What creates a sonic boom?
Shock waves from supersonic objects merge into a cone. When this cone passes over you, you hear a sudden pressure change - the sonic boom.
Can Mach number be negative?
No. Mach number is a ratio of speeds, both positive. Direction doesn't matter - only the magnitude of velocity relative to sound speed.
Why is transonic flight problematic?
Some airflow is subsonic, some supersonic. Shock waves form and move unpredictably, causing control issues and buffeting.
What's the highest Mach number achieved?
The X-15 reached Mach 6.7 (crewed). Spacecraft re-enter at Mach 25+. Parker Solar Probe reaches Mach 500+ relative to solar corona.
Does Mach number apply underwater?
Yes, but sound travels ~4.3× faster in water. A submarine would need ~3300 mph to reach Mach 1. Cavitation is a bigger concern underwater.
What's critical Mach number?
The freestream Mach number where airflow first reaches Mach 1 somewhere on the aircraft. Usually occurs on the wing's upper surface.
How does altitude affect Mach number?
Colder air at altitude means slower sound speed. At constant true airspeed, Mach number increases with altitude. Pilots monitor Mach at high altitude.
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