Mach Number Calculator — Speed of Sound Ratio
Find the Mach number for any speed and air temperature, and see which aerodynamic regime — subsonic, transonic, supersonic or hypersonic — it falls into.
Speed unit
°C
Transonic (0.8 ≤ M < 1.2)
- 1
Speed of sound
331.3 × √(1 + 15 ÷ 273.15) = 340.275Speed of sound in dry air rises with temperature. - 2
Mach number
340 ÷ 340.275 = 0.9992
How does this calculator work?
M = v ÷ c where c = 331.3 × √(1 + T/273.15) m/s is the speed of sound at temperature T °C. At 15 °C, Mach 1 ≈ 340 m/s ≈ 1,225 km/h. Regimes: subsonic M < 0.8, transonic 0.8–1.2, supersonic 1.2–5, hypersonic ≥ 5.
Formula
How this is calculated
The Mach number is the dimensionless ratio of an object's speed (v) to the local speed of sound (c). A Mach number of 1 means the object travels at exactly the speed of sound; M = 2 means twice the speed of sound; M = 0.5 means half. Because the units cancel in the ratio, Mach number is the same whether you work in m/s, km/h, or mph.
The speed of sound in dry air is temperature-dependent. Warmer air has faster-moving molecules that transmit pressure waves more quickly. The standard formula c = 331.3 × √(1 + T/273.15) m/s (T in Celsius) captures this dependence precisely over the range −60 °C to +40 °C. At sea-level standard atmosphere (15 °C), c ≈ 340.3 m/s = 1,225 km/h. At typical cruising altitude (−56.5 °C), c ≈ 295 m/s — 15% slower — which is why aircraft achieve higher Mach numbers at altitude for the same true airspeed.
Aerodynamicists divide flight into four regimes: subsonic (M < 0.8), where compressibility effects are small; transonic (0.8–1.2), where mixed subsonic and supersonic flow coexists around an object; supersonic (1.2–5), dominated by shock waves and wave drag; and hypersonic (M ≥ 5), where aerodynamic heating and chemical dissociation of air become critical. This calculator uses dry air and does not account for humidity (which slightly raises the speed of sound) or altitude-dependent air density.
Frequently asked questions
At 15 °C (standard atmosphere), the speed of sound is about 340.3 m/s = 1,225 km/h = 761 mph. This is Mach 1. The exact value depends on temperature — cold air gives a lower Mach 1 in absolute speed.
Temperature controls the speed of sound: warmer air transmits pressure waves faster (higher c), so the same true airspeed gives a lower Mach number in warm air and a higher Mach number in cold air at altitude.
Yes, slightly. Moist air has a lower average molecular mass than dry air, raising the speed of sound by up to ~0.6% at 100% humidity and 20 °C. This calculator uses dry air as the reference; for most practical purposes the difference is negligible.
TG we-Calculate Editorial Team. (2026). Mach Number Calculator — Speed of Sound Ratio [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/mach-number-calculator
TG we-Calculate Editorial Team. "Mach Number Calculator — Speed of Sound Ratio." TG we-Calculate. 2026. https://we-calculate.com/calculator/mach-number-calculator.
TG we-Calculate Editorial Team, "Mach Number Calculator — Speed of Sound Ratio," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/mach-number-calculator
@misc{wecalculate_mach_number_calculator, title = {Mach Number Calculator — Speed of Sound Ratio}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/mach-number-calculator}}, year = {2026}, note = {TG we-Calculate} }
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