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Mach Number Calculator
Solve any side of M = v / a: enter speed and conditions to get Mach number, or enter Mach to get true airspeed. The local speed of sound comes from physics — a = √(γRT) from temperature, or from altitude via the ISA model (0–20 km) — with a live subsonic / transonic / supersonic / hypersonic readout.
Mach number (M = v / a)
1.9983
Supersonic
Breakdown
| Speed of sound | 340.29 m/s |
|---|---|
| … in km/h | 1,225.05 |
| … in mph | 761.21 |
| Object speed | 680.00 m/s |
| … in km/h | 2,448.00 |
| … in mph | 1,521.12 |
| Air temperature | 15.00 °C |
| ISA layer | — |
Presets
ISA reference: speed of sound vs altitude
| Altitude | Temp | Speed of sound | Mach 1 in km/h |
|---|---|---|---|
| 0 km (sea level) | 15.0 °C | 340.29 m/s | 1,225.05 |
| 2 km | 2.0 °C | 332.53 m/s | 1,197.10 |
| 4 km | −11.0 °C | 324.58 m/s | 1,168.48 |
| 6 km | −24.0 °C | 316.43 m/s | 1,139.14 |
| 8 km | −37.0 °C | 308.06 m/s | 1,109.02 |
| 10 km | −50.0 °C | 299.46 m/s | 1,078.06 |
| 12 km | −56.5 °C | 295.07 m/s | 1,062.24 |
| 14 km | −56.5 °C | 295.07 m/s | 1,062.24 |
| 16 km | −56.5 °C | 295.07 m/s | 1,062.24 |
| 18 km | −56.5 °C | 295.07 m/s | 1,062.24 |
| 20 km | −56.5 °C | 295.07 m/s | 1,062.24 |
ISA: 288.15 K at sea level, −6.5 K/km to 11 km, then 216.65 K (−56.5 °C) constant to 20 km. Values computed from a = √(1.4 × 287.05 × T).
Worked examples
1. Fighter jet: 680 m/s at 15 °C
a = √(1.4 × 287.05 × 288.15) = 340.29 m/s
M = 680 / 340.29 = 1.9983 → supersonic
M = 680 / 340.29 = 1.9983 → supersonic
2. Airliner: Mach 0.85 at 35,000 ft
ISA: 10,668 m → T = 288.15 − 0.0065 × 10,668 = 218.81 K (−54.34 °C)
a = √(1.4 × 287.05 × 218.81) = 296.53 m/s
v = 0.85 × 296.53 = 252.05 m/s = 907.39 km/h (563.83 mph)
a = √(1.4 × 287.05 × 218.81) = 296.53 m/s
v = 0.85 × 296.53 = 252.05 m/s = 907.39 km/h (563.83 mph)
3. Same speed, different altitude: 250 m/s
At sea level (15 °C): M = 250 / 340.29 = 0.7347 (subsonic)
At 11 km (−56.5 °C): M = 250 / 295.07 = 0.8473 (transonic)
At 11 km (−56.5 °C): M = 250 / 295.07 = 0.8473 (transonic)
Method
- Definition
- M = v / a (dimensionless)
- Speed of sound
- a = √(γ · R · T), γ = 1.4 (dry air), R = 287.05 J/(kg·K), T in kelvin
- ISA 0–11 km
- T = 288.15 − 0.0065 × h (h in meters)
- ISA 11–20 km
- T = 216.65 K (−56.5 °C), isothermal
- Regimes
- Subsonic < 0.8 · Transonic 0.8–1.2 · Supersonic 1.2–5 · Hypersonic > 5
ISA constants spot-checked against the ICAO International Standard Atmosphere table (sea level 288.15 K, lapse rate 6.5 K/km, tropopause 11,000 m at 216.65 K, sea-level speed of sound 340.294 m/s). Humidity, wind and non-standard days shift real values by a few m/s; dry-air γ = 1.4 is assumed.
Scope boundary: this tool is the Mach-number headline calculator (3-way M/v/a solver with regime readout). For a deep dive on the speed of sound itself — humidity correction, other gases and media (water, steel, helium), echo ranging — see our Speed of Sound Calculator.
Frequently asked questions
What is Mach number?
Mach number is the ratio of an object's speed to the local speed of sound: M = v / a. Mach 1 means you are traveling at exactly the speed of sound; Mach 2 is twice the speed of sound, and so on. It is named after the physicist Ernst Mach.
How do you calculate Mach number?
Divide the object's speed by the local speed of sound: M = v / a. Example: an aircraft flying at 680 m/s where the air is 15 °C. The speed of sound is a = √(1.4 × 287.05 × 288.15) = 340.29 m/s, so M = 680 / 340.29 = 1.9983 — just under Mach 2.
How does temperature affect the speed of sound?
The speed of sound in air grows with the square root of absolute temperature: a = √(γRT), with γ = 1.4 and R = 287.05 J/(kg·K). At 0 °C (273.15 K) it is 331.32 m/s, and at 20 °C (293.15 K) it is 343.23 m/s — roughly 0.6 m/s faster per degree Celsius near room temperature.
What is Mach 1 in mph and km/h?
It depends on temperature. At 15 °C at sea level the speed of sound is 340.29 m/s, so Mach 1 = 1,225.05 km/h = 761.21 mph = 661.48 knots = 1,116.44 ft/s.
How fast is Mach 2 in km/h?
At 15 °C at sea level, Mach 2 is 2 × 340.29 m/s = 680.58 m/s, which equals 2,450.10 km/h (1,522.42 mph). At altitude the same Mach number means a lower true airspeed, because cold air carries sound more slowly.
What are subsonic, transonic, supersonic and hypersonic speeds?
Subsonic is below Mach 0.8; transonic is Mach 0.8–1.2, where airflow around the aircraft is mixed subsonic and supersonic; supersonic is Mach 1.2–5; hypersonic is anything above Mach 5.
Why is Mach number more useful than airspeed at high altitude?
Aerodynamic effects such as shock waves and wave drag depend on Mach number, not raw speed. Because cold high-altitude air carries sound more slowly, the same true airspeed is a higher Mach number up high: 250 m/s is Mach 0.7347 at sea level (15 °C) but Mach 0.8473 at 11 km — nearly transonic.
What is the speed of sound at 35,000 ft?
In the International Standard Atmosphere, 35,000 ft (10,668 m) has a temperature of −54.34 °C and the speed of sound is 296.53 m/s. That is why an airliner cruising at Mach 0.85 up there flies at 252.05 m/s — 907.39 km/h (563.83 mph) true airspeed.
What is the International Standard Atmosphere (ISA)?
The ISA is a standard model of how air temperature falls with altitude: 288.15 K (15 °C) at sea level, dropping 6.5 K per kilometre up to 11 km, then constant at 216.65 K (−56.5 °C) from 11 to 20 km. This calculator uses it to derive the speed of sound directly from altitude.
Is there a maximum Mach number?
There is no theoretical limit — Mach number is just a speed ratio. Practical limits come from heat and materials: above Mach 5 (hypersonic), air friction heats vehicles to thousands of degrees, which is why re-entry capsules need heat shields.
Educational tool. Results use the ideal-gas / ISA model for dry air; always use certified flight-planning data for real aviation decisions. Calculations run 100% in your browser — no data leaves your device.
Free tool by NRTechStudio