Mach Number Calculator
At 11 km, where the speed of sound is 295.1 m/s, a true airspeed of 250 m/s is Mach 0.847258.
Air 1.4; hot combustion gases about 1.3; helium 1.667.
0.847258037511472
Full answer, then cut to fewer decimals (not rounded):
- 0.847258037511472
- 0.84725803751147
- 0.8472580375114
- 0.847258037511
- 0.84725803751
- 0.8472580375
- 0.847258037
- 0.84725803
- 0.8472580
- 0.847258
- 0.84725
- 0.8472
- 0.847
- 0.84
- 0.8
- Speed of sound a = √(γRT)
- 295.0694935 m/s
- Speed of sound
- 1062.250177 km/h
- Temperature
- 216.65 K
- Regime
- transonic
Step-by-step solution
- a = √(γRT) = √(1.4 × 287.05287 × 216.65) = 295.0694935 m/s
- M = V ÷ a = 250 ÷ 295.0694935 = 0.8472580375
Mach Number Formula
M = V / a, a = √(γRT)
γ = 1.4 and R = 287.05 J/(kg·K) for air; T in kelvin
Worked Example
An aircraft at 250 m/s true airspeed at 11 km:
- a = √(γRT) = √(1.4 × 287.05287 × 216.65) = 295.0694935 m/s
- M = V ÷ a = 250 ÷ 295.0694935 = 0.8472580375
Speed of sound: 1062.250177 km/h · Temperature: 216.65 K · Regime: transonic
GATE tip
Critical Mach number is where the local flow first reaches M = 1 somewhere on the wing, typically 0.7–0.8 for subsonic airliners; drag divergence follows shortly after.
More Atmosphere and Airspeed Calculators
-
Standard Atmosphere Calculator
T = 288.15 − 0.0065h, p = 101325 (T/288.15)^5.2559
troposphere to 11 km; isothermal 216.65 K from 11 to 20 km; ρ = p/(RT), a = √(γRT)
Example: The standard atmosphere at 5000 m: Temperature T = 255.65 K.
-
Airspeed Calculator
EAS = TAS √(ρ/ρ₀), q_c = p[(1 + 0.2M²)^3.5 − 1]
CAS = a₀√(5[(q_c/p₀ + 1)^(2/7) − 1]); a₀ = 340.294 m/s, p₀ = 101325 Pa
Example: 250 knots calibrated airspeed at 10,000 ft pressure altitude: True airspeed TAS = 288.702 kn.
Frequently asked questions
Why does the speed of sound fall with altitude?
It depends only on temperature for a given gas: a = √(γRT). From 340 m/s at 15 °C it drops to 295 m/s at −56.5 °C above 11 km.
When does compressibility matter?
Above about M = 0.3 density changes exceed 5 %, so incompressible Bernoulli no longer holds and compressible relations are needed.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Mach Number Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/mach-number-calculator/
IEEE
Scientific Converters, "Mach Number Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/mach-number-calculator/