KPH to Mach
Convert km/h to Mach number for aircraft speed. Mach number depends on altitude — enter km/h and get Mach at sea level and cruise altitude.
Enter your values above to see the results.
Tips & Notes
- ✓The speed of sound is NOT constant — it depends on temperature, not altitude directly. At sea level (15°C): c = 340.3 m/s = 1,225 km/h = 761.2 mph. At 35,000 ft (−55°C): c = 295.1 m/s = 1,062 km/h = 660 mph. So the same aircraft at 900 km/h TAS is at Mach 0.73 at sea level but Mach 0.85 at cruise altitude.
- ✓Subsonic (Mach < 0.8), transonic (0.8-1.2), supersonic (1.2-5.0), hypersonic (5.0+). Commercial airliners cruise at Mach 0.78-0.86. Concorde cruised at Mach 2.04. SR-71 Blackbird: Mach 3.3+. Space Shuttle reentry: ~Mach 25.
- ✓Critical Mach (Mcrit): the speed at which airflow over the wing first goes supersonic locally — typically Mach 0.72-0.84 for modern transport aircraft. Above Mcrit, shockwaves form on wings causing drag rise (wave drag). Swept wings delay Mcrit.
- ✓Mach buffet: commercial aircraft avoid flying above Mach 0.82-0.86 (depending on type) where compressibility effects cause buffeting. The "coffin corner" is the narrow speed range between low-speed stall and high-speed Mach buffet at very high altitudes.
- ✓Sound barrier: Mach 1.0 is not a physical barrier but a flight regime change. The dramatic drag increase near Mach 1.0 (transonic drag rise) required specially designed aircraft to break it. Chuck Yeager first exceeded Mach 1.0 in 1947 in the Bell X-1, reaching Mach 1.06 = 1,299 km/h at altitude.
Common Mistakes
- ✗Using sea-level speed of sound for cruise-altitude calculations — at 35,000 ft cruise altitude, the speed of sound is 1,062 km/h (not 1,235 km/h). A cruising aircraft at 910 km/h TAS: at sea level = 910/1,235 = Mach 0.737; at 35,000 ft = 910/1,062 = Mach 0.857. Always use the altitude-appropriate speed of sound.
- ✗Using indicated airspeed (IAS) instead of true airspeed (TAS) for Mach calculation — Mach = TAS / c, not IAS / c. At altitude, TAS is much higher than IAS due to lower air density. A 737 showing 250 KIAS at 35,000 ft has a TAS of approximately 460 knots = 852 km/h = Mach 0.80.
- ✗Assuming Mach 1.0 at sea level equals Mach 1.0 at altitude in km/h terms — Mach 1.0 at sea level = 1,235 km/h; Mach 1.0 at 35,000 ft = 1,062 km/h. A jet breaking the sound barrier at altitude is going slower in km/h than one breaking it at sea level.
- ✗Treating Mach numbers as proportional at different altitudes — Mach 2.0 at cruise altitude (2 × 1,062 = 2,124 km/h) is not the same speed as Mach 2.0 at sea level (2 × 1,235 = 2,470 km/h). The aerodynamic forces depend on Mach number, but the actual speed (km/h) differs.
- ✗Applying Mach to water/liquid speeds — Mach number is defined for compressible fluids (gases). The concept of Mach number does not apply to ships or submarines in the usual aeronautical sense, though similar compressibility effects occur in cavitation at high underwater speeds.
KPH to Mach Overview
Mach number expresses speed as a multiple of the speed of sound — a variable quantity that changes with altitude and temperature. Converting km/h to Mach reveals the aerodynamic regime an aircraft is operating in, which determines its drag, stability characteristics, and structural loads far more meaningfully than absolute speed alone.
KPH to Mach formula (altitude-dependent):
Mach = km/h ÷ c(altitude) | c sea level (15°C) = 1,225 km/h | c cruise (35,000 ft, −56°C) = 1,062 km/h
EX: Boeing 787 cruise speed 905 km/h at 35,000 ft → Mach = 905/1,062 = 0.852. Same speed at sea level → Mach = 905/1,225 = 0.739. The aerodynamic regime is determined by Mach, not absolute speed.Speed of sound vs. altitude:
c (m/s) = 331.3 × √(T/273.15) where T in Kelvin | Decreases with altitude in troposphere
EX: At 10,000 m (T = −50°C = 223 K): c = 331.3 × √(223/273.15) = 331.3 × 0.904 = 299.5 m/s = 1,078 km/h. Aircraft doing 900 km/h here: Mach = 900/1,078 = 0.835Mach regimes and speed of sound at altitude:
| Altitude (m) | Temp (°C) | c (km/h) | Mach 1.0 in mph |
|---|---|---|---|
| 0 (sea level) | 15°C | 1,225 km/h | 761 mph |
| 3,000 m | 4.5°C | 1,190 km/h | 739 mph |
| 6,000 m | −24°C | 1,148 km/h | 713 mph |
| 10,000 m | −50°C | 1,078 km/h | 670 mph |
| 11,000 m+ | −56.5°C | 1,062 km/h | 660 mph |
| Aircraft | Speed (km/h) | Mach (at altitude) | Notes |
|---|---|---|---|
| Boeing 737-800 | 840 km/h | Mach 0.79 | Normal cruise |
| Boeing 787-9 | 906 km/h | Mach 0.85 | Long-haul cruise |
| Airbus A380 | 903 km/h | Mach 0.85 | Standard cruise |
| Concorde | 2,179 km/h | Mach 2.04 | Supersonic cruise |
| SR-71 Blackbird | 3,540 km/h | Mach 3.3+ | Reconnaissance |
| X-43A scramjet | 11,843 km/h | Mach 9.6 | Experimental record |
Frequently Asked Questions
Mach = km/h / speed of sound. At sea level (15°C): speed of sound = 1,235 km/h, so Mach = km/h / 1,235. Examples: 900 km/h / 1,235 = Mach 0.729; 1,235 km/h / 1,235 = Mach 1.0 (sound barrier, sea level); 2,470 km/h / 1,235 = Mach 2.0. At cruise altitude 35,000 ft (−55°C): speed of sound = 1,062 km/h. 900 km/h / 1,062 = Mach 0.848. A Boeing 787 at 905 km/h cruise: Mach = 905/1,062 = 0.852.
Mach number = speed / speed of sound. The speed of sound depends on temperature: c = 331.3 × √(1 + T/273.15) m/s where T is in Celsius. As altitude increases, temperature decreases (in the troposphere), so the speed of sound decreases. At sea level (15°C): c = 340.3 m/s = 1,225.1 km/h. At 10,000 m (−49.9°C): c = 299.5 m/s = 1,078.2 km/h. At 11,000 m and above (−56.5°C): c = 295.1 m/s = 1,062 km/h. Same aircraft at 800 km/h: Mach 0.65 at sea level but Mach 0.75 at 10,000 m.
Subsonic (Mach < 0.8): normal airflow, no shockwaves. Commercial cruise: Mach 0.78-0.86. Transonic (Mach 0.8-1.2): mixed subsonic/supersonic airflow; shockwaves form on wings; wave drag increases sharply; stability and control changes. Aircraft must be designed for transonic flight (swept wings, area ruling). Supersonic (Mach 1.2-5.0): full supersonic flow; attached oblique shockwaves; sonic boom. Concorde Mach 2.0; fighter jets Mach 1.5-2.5. Hypersonic (Mach 5-10): extreme aerodynamic heating; special materials required. SR-71 Mach 3.3 is high supersonic. Space Shuttle reentry Mach 25 is hypersonic.
Speed of sound (Mach 1.0) vs. altitude: sea level (15°C): 1,225 km/h = 761.2 mph; 3,000 m (9,000 ft, 4.5°C): 1,190 km/h = 739.5 mph; 6,000 m (19,685 ft, -24°C): 1,148 km/h = 713.4 mph; 9,000 m (29,528 ft, −44°C): 1,101 km/h = 684.2 mph; 11,000 m (36,089 ft, −56.5°C): 1,062 km/h = 660 mph; 20,000 m (65,617 ft, −56.5°C): 1,062 km/h = 660 mph (isothermal stratosphere). Most commercial aircraft break the sound barrier only inadvertently in steep dives; their certified speeds are well below Mach 1.0.
A sonic boom occurs when an aircraft exceeds the local speed of sound (Mach 1.0). At subsonic speeds, the aircraft and its pressure waves travel at different speeds, allowing waves to propagate ahead. At Mach 1.0, the aircraft outruns its own pressure waves, creating a shockwave that builds into a conical Mach cone. The boom is not a one-time event at the moment of crossing Mach 1.0 — it is continuous as long as the aircraft flies supersonically. The boom reaches the ground as a double crack (one from nose shockwave, one from tail). Concorde at Mach 2 at 17,000 m produced a sonic boom radius of approximately 50-75 km (31-47 miles) on either side of its track.
Record speeds by aircraft: X-43A scramjet (NASA, 2004): Mach 9.6 = 11,843 km/h = 7,366 mph — fastest air-breathing aircraft. X-15 rocket plane (1967): Mach 6.70 = 7,274 km/h = 4,520 mph at 102,100 ft altitude. SR-71 Blackbird (operational record): Mach 3.3 = 3,540 km/h = 2,200 mph. MiG-25 fighter: Mach 3.2 = 3,395 km/h = 2,110 mph (official). Concorde: Mach 2.04 = 2,179 km/h = 1,354 mph at cruise altitude (35,000 ft). Boeing 747 maximum speed: Mach 0.92 = 977 km/h = 607 mph (Vmo/Mmo never-exceed speed). Space Shuttle reentry: Mach 25 ≈ 26,544 km/h = 16,500 mph.