Mach Number Calculator - Speed, Sound, and Temperature

A Mach number calculator solves M = v / c, where v is the object speed and c is the local speed of sound, and tags the flow as subsonic, transonic, supersonic, or hypersonic. It accepts the object speed, the speed of sound, or the air temperature, so the same page covers sea-level checks and high-altitude jet estimates.

• • Aircraft Mach checks: Confirm whether a commercial jet at cruise altitude is flying subsonic or transonic by entering the indicated airspeed and the air temperature.
• • Hypersonic vehicle estimates: Convert a kilometre-per-second figure for a re-entry vehicle or scramjet into a Mach number against the local sound speed.
• • Compressible-flow homework: Solve textbook problems that mix Mach, speed, and temperature without doing the square root of 1 + T / 273.15 by hand.

The same 0.8 reads the same whether v is in m/s, km/h, or knots, as long as c uses the same unit. The mach number calculator keeps everything in m/s internally and lets you toggle c between a manual value and the air-temperature formula.

For dry air the speed of sound follows c = 331.3 * sqrt(1 + T_C / 273.15) m/s, so a 20 C cabin gives the textbook 343 m/s reference and a -40 C winter morning drops c to about 306 m/s.

When the wave behind a Mach number is described as frequency times wavelength, wave speed calculator returns v = f * lambda in one panel.

The calculator reads v, T, and the toggle that controls c, forms M = v / c, cross-checks the implied speed, and tags the flow regime.

• v (object speed): Object speed in m/s, from the object-speed field.
• c (speed of sound): Local speed of sound in m/s, from the speed-of-sound field or recomputed from air temperature.
• T_C (air temperature): Air temperature in degrees Celsius, used by c = 331.3 * sqrt(1 + T_C / 273.15) when the toggle is on.
• useTemperature (toggle): When on, the calculator overwrites c with the temperature-derived value. When off, c is the manual entry.

With the temperature toggle on, the panel shows the recomputed speed of sound so you can see c dropping as T falls.

According to Wikipedia - Mach number, the Mach number is defined as M = v / a, where v is the flow velocity and a is the local speed of sound, and the value is used to classify subsonic, transonic, supersonic, and hypersonic flow regimes.

According to NOAA National Weather Service, the speed of sound in dry air at 20 C is approximately 343 m/s and follows c = 331.3 * sqrt(1 + T_C / 273.15).

Once the Mach number is known, the Reynolds number calculator takes the same density, velocity, and characteristic length and tags the flow as laminar, transitional, or turbulent.

Four ideas sit behind Mach number: M = v / c, the air-temperature speed of sound, the regime bands, and the difference between Mach and true airspeed.

For dry air the speed of sound is a function of T_C alone. Humid air is slightly faster than dry air at the same temperature because water vapour has a lower molecular weight and lowers the gas density more than it shifts the heat-capacity ratio, nudging c up by about 0.1% to 0.3%.

For the wave-physics cousin that turns density into a sound-wave impedance using the same c, acoustic impedance calculator returns Z = rho * c in Pa.s/m and MRayl.

Five steps read a Mach number and a flow regime from any combination of speed, c, and air temperature.

1. 1 Enter the object speed v: Type the speed of the moving object in m/s. The default 250 m/s covers a fast passenger jet on approach.
2. 2 Decide where the speed of sound comes from: Leave the 'Derive c from temperature' toggle on to use the air-temperature formula, or switch it off to use the speed-of-sound value you typed.
3. 3 Type the air temperature T in Celsius: Use 20 C for a textbook check, 15 C for a standard day at sea level, or -40 C for a high-altitude jet.
4. 4 Override c manually if you need to: Type the local speed of sound in m/s when you already have a measured or reference value, for example 1482 m/s for water or 5960 m/s for steel.
5. 5 Read M, the implied speed, and the flow regime: The result panel shows M to four decimals, the speed of sound used in m/s, the object speed implied by M and c, and the flow regime label.

For a 787 at 31,000 ft, type 252.1 m/s as v, leave the toggle on, set T = -46.4 C, and read M = 0.8352 with the flow regime Transonic.

Before computing M, the speed converter translates knots, km/h, and mph into m/s so c and the object speed share one unit.

These benefits cover the workflow gains when M = v / c and c = 331.3 * sqrt(1 + T_C / 273.15) are no longer done by hand. The calculator keeps one panel for sea-level and high-altitude checks, so the same inputs work for a takeoff roll and a cruise climb.

• • Three inputs in one panel: Object speed, speed of sound, and air temperature live in one form, so you can swap between a measured c and the temperature-derived value on the same page.
• • Speed of sound from temperature: The c = 331.3 * sqrt(1 + T_C / 273.15) formula runs in the background, so entering T in Celsius recomputes c and M at the same time.
• • Flow regime label: Subsonic, Transonic, Supersonic, and Hypersonic tags give an immediate read of whether the flow is compressible, which is the practical question behind Mach number.
• • Implied speed cross-check: The object speed implied by M and c sits next to v, so rounding or unit mistakes show up the moment you type them.
• • Real-time updates on input change: Edit any field and the panel refreshes M, c, the implied speed, and the flow regime, useful when scanning many altitude bands.

The same Mach number feeds the compressible Bernoulli equation, the Prandtl-Meyer expansion, and the oblique-shock relations, so a clean M is a starting point for those too.

For the compressible-flow extension of M = v / c, the Bernoulli equation calculator returns pressure, density, and temperature changes across a nozzle or venturi.

Four factors decide the Mach number you read, plus two limitations when M = v / c models a real flow.

• • The c = 331.3 * sqrt(1 + T_C / 273.15) formula is for dry air. For other gases use the medium-specific formula, and for water or metals use the tabulated c.
• • Mach number alone does not capture viscous or shock losses. Above about M = 0.3, use the compressible Bernoulli or Rayleigh relations instead of the incompressible form.

The implied object speed is a fast unit check: if v and the implied speed disagree by more than 1 m/s, one is in the wrong unit.

According to Wikipedia - Hypersonic speed, aerodynamicists classify flow regimes as subsonic below M = 0.8, transonic between 0.8 and 1.2, supersonic from 1.2 up to about 5, and hypersonic above M = 5, where the chemistry of the air starts to matter.

For the resistive counterpart of M = v / c, the drag equation calculator returns the drag force from the same density, velocity, frontal area, and drag coefficient.