Physics

Mach Number Calculator

Calculate Mach number from velocity and the speed of sound.


Mach Number Calculator

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Calculates how many times the local speed of sound an object is traveling.

How it works

The object’s velocity is divided by the local speed of sound to give the Mach number.

What this does not include

This does not include computing the speed of sound itself from temperature — for that, use this site’s speed of sound calculator first, then enter the result here.

How to use this calculator

  1. Enter the object’s velocity and the local speed of sound.

A worked example

An object traveling 686 m/s where the speed of sound is 343 m/s → 686 ÷ 343 = Mach 2 — twice the speed of sound.

1,000 m/s against a speed of sound of 340 m/s → Mach 2.9412.

What the variables mean

Variable Meaning
Velocity The object’s actual speed
Speed of sound The local speed of sound, which varies with air temperature and altitude

Edge cases worth knowing

The speed of sound isn’t a fixed constant — it changes with temperature and altitude, which is why this calculator takes it as an input rather than assuming a single sea-level value.

Mach 1 is the speed of sound itself, not a fixed velocity. The same aircraft speed can be a different Mach number at different altitudes, since the speed of sound itself changes.

Frequently asked questions

What does “Mach 1” mean?

Traveling at exactly the local speed of sound — Mach 2 means twice the speed of sound, and so on.

Why does “the” speed of sound vary?

The speed of sound depends on air temperature (and to a lesser extent, humidity and altitude), so the same aircraft speed corresponds to a different Mach number depending on conditions.

What’s the difference between subsonic and supersonic?

Subsonic means traveling slower than the speed of sound (Mach number under 1); supersonic means faster (Mach number over 1).

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Written by

R. Solano

Physics writer

R. Solano writes the physics calculators, spanning mechanics, electricity, optics and thermodynamics. Each page names the physical model it uses and the conditions under which that model holds — ideal gas, no air resistance, small-angle approximation — because a physics result without its assumptions is a number without a meaning. Formulas are given in symbols first, then in the calculator.

Reviewed by

V. Kowalski

Calculator reviewer — physics and engineering

V. Kowalski reviews the physics and engineering calculators, checking that each page states the physical model it assumes and that the stated model matches the formula actually implemented. Review covers unit consistency throughout a calculation and whether approximations are flagged where the underlying physics is more complicated than the formula suggests.

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