Mach Number Calculator

Origin of the name Mach number is named after Austrian physicist Ernst Mach, who in 1887 photographed the shock waves trailing a supersonic bullet, one of the first images of a shock wave ever captured. The dimensionless ratio became standard usage in aerodynamics after WWII.

Speed of Sound in Air The speed of sound depends on temperature, not pressure: a = √(γ × R × T) = 20.05 × √T (m/s) where T is in Kelvin At sea level (15°C = 288.15 K): a = 340.3 m/s = 661.5 knots = 1225.4 km/h = 761.2 mph For every °C temperature drop, sound speed decreases by ~0.6 m/s.

ISA Standard Atmosphere International Standard Atmosphere (ISA) defines temperature vs altitude: Sea level: 15°C (288.15 K), pressure 1013.25 hPa Lapse rate: −6.5°C per 1000 m up to 11,000 m (tropopause) Tropopause (11,000–20,000 m): constant −56.5°C (216.65 K) Above 20,000 m: temperature increases again

Mach Number M = V / a Where V = true airspeed (TAS), a = local speed of sound. Subsonic: M < 1 | Transonic: 0.8 < M < 1.2 | Supersonic: 1 < M < 5 | Hypersonic: M > 5

Mach Regimes M < 0.3: incompressible flow, simple Bernoulli applies M 0.3–0.8: compressible subsonic, correction factors needed M 0.8–1.2: transonic, shock waves begin forming M > 1: supersonic, oblique shock waves, sonic boom M > 5: hypersonic, extreme heating and plasma effects

Critical Mach Number (Mcrit) For aircraft with subsonic design, airflow over the wing can reach M=1 locally. This causes control problems and buffeting, the so-called “coffin corner.” Airliners typically cruise at M 0.78–0.86 to stay below Mcrit.

Notable Mach numbers

• Boeing 737 cruise: M 0.785
• Boeing 787 cruise: M 0.85
• Concorde cruise: M 2.04
• SR-71 Blackbird: M 3.2 (still the air-breathing record)
• X-15 rocket plane: M 6.7 in 1967 (William J. Knight, United States)
• Space Shuttle re-entry: peak M ≈ 25 (the orbital reentry envelope)

The sonic boom is a cone, not a one-time event A sonic boom is not the moment of crossing Mach 1. It’s a continuous shock wave shaped like a cone trailing the aircraft, called the Mach cone, with a half-angle of arcsin(1/M). At M 2 the half-angle is 30°; at M 5 it narrows to 11.5°. Anyone within the cone hears the boom as the cone sweeps past them, which is why supersonic transports were banned over land in 1973. Every populated area along the flight path would otherwise get boomed.