# Mach Number Calculator

URL: https://speedycalculator.com/calculators/physics/mach-number/
Last updated: 2026-10-30

> The Mach number calculator finds the Mach number of an object from its speed and the speed of sound – entered directly or computed from the air temperature – and classifies the flow regime.

## Inputs

- Speed v (km/h, m/s, mph, knots, ft/s)
- Speed of sound from
- Air temperature (°C, K, °F)
- Speed of sound (m/s, km/h, mph, ft/s, knots, km/s)

## Results

- Speed of sound
- Mach number
- Regime

## Formula

```
M = v / a,  a = √(γ·R·T) (air: γ = 1.4, R = 287.05 J/(kg·K))
```

## Explanation

Mach 1 is the local speed of sound – about 1,225 km/h at sea level but only 1,062 km/h at airliner cruise altitude, where it is colder. Concorde cruised at Mach 2.04.

### How to use the Mach Number Calculator

- **Speed v**
- **Speed of sound from**
- **Air temperature**
- **Speed of sound**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the speed and either the air temperature or the speed of sound.

### Inputs explained

FieldWhat to enterSpeed vUnits: km/h, m/s, mph, knots, ft/sSpeed of sound fromChoose one: Air temperature, Direct valueAir temperatureUnits: °C, K, °FSpeed of soundUnits: m/s, km/h, mph, ft/s, knots, km/s

### Example values

How the main result changes when **Speed v** changes and everything else stays at the example values above:

Speed v (km/h)Mach number4500.42366750.63549000.84731,1251.05911,3501.27091,8001.6945

## Worked example

Inputs — Speed v: 900 km/h; Speed of sound from: Air temperature; Air temperature: -56.5 °C.

Results — Speed of sound = 295.06802 m/s; **Mach number = 0.8473**; Regime = Transonic.

## Key terms

- **Mach number**: Speed divided by the local speed of sound.

## FAQ

**Why does the speed of sound change with altitude?**
It depends on temperature, which falls with height.

**What Mach do airliners cruise at?**
About 0.78–0.85.

**What is hypersonic?**
Above about Mach 5.

**Does air pressure affect Mach 1?**
Not directly – temperature dominates.


## Sources

- [NASA Glenn – Beginner's Guide to Aeronautics](https://www.grc.nasa.gov/www/k-12/airplane/)
- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)