Mach Number Calculator

Mach number is the ratio of object speed to the local speed of sound. M<1 is subsonic, M=1 is sonic, M>1 supersonic, M>5 hypersonic. It changes with altitude since sound speed varies with temperature.

💨 Fluid Dynamics📐 M = v/vₛ✈️ Aerodynamics

Object Speed v (m/s)

Speed of Sound vs (m/s)

Default sound speed 343 m/s (sea level 20°C)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Mach Number	M	M = v / v_s	dimensionless
Object Speed	v	v = M × v_s	m/s
Speed of Sound	v_s	331.3√(T/273.15)	m/s
At sea level 20°C	v_s	343 m/s	m/s

Step-by-Step Examples

Example 1

Commercial Jet

Boeing 747 at 900 km/h, vs=295 m/s at cruise altitude.

v = 900/3.6 = 250 m/s
M = 250/295 = 0.847

✓ Mach 0.847 — high subsonic

Example 2

Concorde

Mach 2.04 target, vs=295 m/s.

v = 2.04 * 295 = 601.8 m/s = 2166 km/h

✓ 2166 km/h supersonic

Example 3

Rifle Bullet

v = 900 m/s, vs = 343 m/s.

M = 900/343 = 2.62

✓ Mach 2.62 — supersonic bullet

Real-World Applications

✈️

Aircraft Design

Wings designed for specific Mach regime — subsonic and supersonic require very different shapes.

🚀

Rocket Nozzles

Nozzle throat reaches Mach 1, supersonic flow in diverging section via de Laval geometry.

💥

Sonic Boom

Shock wave forms when M=1 is crossed. Boom heard when cone passes observer.

🌡️

Altitude Effect

Sound speed drops with altitude — Mach 1 at 10 km is 299 m/s vs 343 m/s at sea level.

Common Mistakes to Avoid

⚠️

Speed of sound varies with altitude

At 10,000 m altitude, vs ~299 m/s due to colder air. Always use correct vs for altitude.

⚠️

Mach 1 is not a fixed speed

Mach 1 = local sound speed. An aircraft at Mach 1 flies slower at sea level than the statement implies.

⚠️

Transonic regime is complex

Between M=0.8 and 1.2, mixed subsonic/supersonic flow creates complex shock patterns requiring special aerodynamic design.

Frequently Asked Questions

What happens exactly at Mach 1? ▾

A normal shock wave forms at the nose. Pressure, density, and temperature jump discontinuously across it. This creates the sonic boom.

Why do jets not cruise at Mach 1? ▾

Wave drag peaks near M=1 (transonic drag rise). Requires too much fuel. Commercial jets cruise at M=0.83-0.89 to avoid this.

What is hypersonic flight? ▾

M > 5. Aerodynamic heating becomes extreme (SR-71 skin reached 300 deg C). Chemical reactions in air must be considered.

How does a Mach cone form? ▾

At supersonic speed, object outruns sound waves. Cone half-angle theta satisfies sin(theta) = 1/M.

What was the first supersonic aircraft? ▾

Chuck Yeager in the Bell X-1 broke Mach 1 on October 14, 1947, reaching Mach 1.06 at 13,000 m altitude.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects pressure, velocity, density, viscosity, geometry or transport in a fluid system. Assumption: Check whether flow is steady, incompressible, laminar, fully developed or one-dimensional. Reynolds and Mach regimes determine whether simplified formulas are valid.

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