About this tool
The Mach Number Calculator converts between true airspeed (TAS) and Mach number using the outside air temperature, and reports the local speed of sound. Pick TAS → Mach to get the Mach ratio from a speed, or Mach → TAS to find the speed for a target Mach. It computes instantly in your browser.
The local speed of sound in knots is a = 38.968 × √(OAT °C + 273.15), where the term in the root is the absolute temperature in kelvin. Mach number is then TAS ÷ a, and the inverse is TAS = Mach × a. Because the speed of sound depends only on temperature, colder air lowers it and raises the Mach for a given TAS.
The tool also classifies the flight regime: subsonic below Mach 0.8, transonic from 0.8 to 1.2, supersonic above that, and hypersonic at Mach 5 and beyond. For example, 500 kt TAS at −40 °C gives a speed of sound near 595 kt and a Mach around 0.84.
Frequently asked questions
How is the speed of sound found?
It depends only on temperature: a = 38.968 × √(OAT in °C + 273.15) knots. The 38.968 constant folds in the ratio of specific heats and gas constant for air and converts metres per second to knots.
How do I get Mach from TAS?
Divide true airspeed by the local speed of sound: Mach = TAS ÷ a. In Mach → TAS mode the tool reverses this as TAS = Mach × a, using the same temperature-based speed of sound.
Why does colder air raise the Mach number?
The speed of sound falls as temperature drops, so at a fixed true airspeed you are a larger fraction of that lower speed of sound. That is why aircraft near the tropopause can be at high Mach even at moderate TAS.
What do the regime labels mean?
Subsonic is below Mach 0.8, transonic runs from Mach 0.8 to 1.2 where mixed sub/supersonic flow appears, supersonic is above 1.2, and hypersonic begins around Mach 5. They are broad aerodynamic bands, not sharp boundaries.
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