What Is the Mach Number?
The Mach number is a dimensionless quantity that expresses the ratio of the speed of an object to the local speed of sound. It is named after Austrian physicist Ernst Mach. Whether you're analyzing an aircraft, a bullet, or a spacecraft, the Mach number tells you how fast an object moves relative to the speed at which sound propagates through the surrounding medium.
The Mach number equation is:
M = v / c
where v is the speed of the object and c is the local speed of sound.
How to Calculate the Mach Number?
Follow these steps to use the Mach number calculator:
- Choose the calculation mode. Select "Find Mach Number" to convert a known speed to Mach, or "Find Object Speed" to work backwards from a known Mach number.
- Enter the object's speed and choose the unit (km/h, m/s, mph, or ft/s).
- Enter the air temperature (default 20 °C). The speed of sound changes with temperature — the calculator uses this to determine the local speed of sound.
- Click Calculate. The result shows the Mach number, flow regime, and full unit conversion for both the object speed and the speed of sound.
Speed of Sound Formula
The speed of sound in air at temperature T (in degrees Celsius) is given by:
c = 331.3 × √(1 + T / 273.15) [m/s]
At the standard temperature of 20 °C, the speed of sound in air is approximately 343 m/s (1,235 km/h or 767 mph). At 0 °C it drops to about 331 m/s, and at −50 °C to about 299 m/s.
Example: Using the Mach Number Calculator
Estimate the Mach number for an aircraft flying at a speed of 1,500 km/h. Assume an air temperature of 20 °C.
- Convert the speed: 1,500 km/h ÷ 3.6 = 416.67 m/s
- Speed of sound at 20 °C: c = 331.3 × √(1 + 20 / 273.15) ≈ 343.21 m/s
- Mach number: M = 416.67 / 343.21 ≈ Mach 1.214
The aircraft is flying at Mach 1.214 — well into the supersonic regime.
Flow Regimes: Subsonic, Transonic, Supersonic, Hypersonic
| Regime | Mach Range | Examples |
|---|---|---|
| Subsonic | M < 0.8 | Commercial airliners, propeller aircraft, birds |
| Transonic | 0.8 ≤ M < 1.2 | High-speed jets near the sound barrier |
| Supersonic | 1.2 ≤ M < 5.0 | Concorde, fighter jets, rifle bullets |
| Hypersonic | M ≥ 5.0 | Space shuttle re-entry, ICBMs, experimental vehicles |
Unit Systems Supported
This Mach number calculator supports both the metric system and the US customary (American imperial) system:
- Metric: m/s (meters per second), km/h (kilometers per hour), °C (Celsius), K (Kelvin)
- US / Imperial: ft/s (feet per second), mph (miles per hour), °F (Fahrenheit)
Results are always displayed in all four speed units simultaneously — m/s, km/h, ft/s, and mph — so you can compare across systems instantly.
Frequently Asked Questions
What does Mach 1 mean?
Mach 1 means the object is traveling at exactly the speed of sound. At sea level and 20 °C, this is approximately 343 m/s (1,235 km/h / 767 mph). When an object breaks the sound barrier and crosses Mach 1, it produces a sonic boom.
Is the speed of sound always the same?
No. The speed of sound depends on the temperature and medium. In air, higher temperatures mean faster sound. It also travels much faster in water (~1,480 m/s) and in solids like steel (~5,100 m/s).
What is the fastest Mach number ever recorded?
The fastest recorded speed was achieved by the NASA X-43A unmanned scramjet aircraft at approximately Mach 9.6 (about 10,600 km/h) in 2004. The Space Shuttle re-entered the atmosphere at around Mach 25.
Can sound travel in space?
No. Sound requires a medium (gas, liquid, or solid) to propagate. In the vacuum of space, there is no medium, so the Mach number concept does not apply there in the traditional sense.
What is a sonic boom?
A sonic boom is a loud shockwave produced when an object travels through air faster than the speed of sound (M ≥ 1). The shockwave forms a cone shape (Mach cone) and spreads outward, creating the characteristic loud "boom" heard on the ground.