Knot to Mach Converter

Mach 1 is 661.48 knots at sea level and 576.42 knots at 35,000 feet

Mach is not a unit of speed. It is the ratio of an aircraft's true airspeed (TAS) to the speed of sound where it is flying. The speed of sound is set by air temperature, so the same Mach number corresponds to a different number of knots at a different altitude and temperature. In the standard atmosphere at sea level (15 °C), sound travels at 340.29 m/s, or 661.48 kn, so Mach 1 = 661.48 kn. At 35,000 ft, a typical airliner cruising altitude, the temperature falls to −54.3 °C and the speed of sound drops to 576.42 kn, which makes Mach 1 about 85 kn slower.

The converter above calculates the other field when you type a number in either the knots field or the Mach field. Enter a pressure altitude and an outside air temperature and it converts with the speed of sound for those conditions. Switch the knots field to the calibrated airspeed (CAS) shown by the airspeed indicator and it also accounts for the air pressure at that altitude. The altitude–speed chart marks your current position and the Mach lines, and the speed band shows the regimes from subsonic to hypersonic along with reference aircraft such as the Boeing 787 and Concorde.

How to use the converter

1. Type a number in the knots field or the Mach field. The field you typed in last is the one being used as the input and gets a stronger border. The other field is filled in rounded to two decimals for knots and three for Mach, and a rounded field has '≈' at the end of its label.
2. Under 'Speed in the knots field', choose true airspeed (TAS) or calibrated airspeed (CAS). Use TAS for values given as TAS in aviation data, and CAS for a cockpit airspeed indicator reading (indicated airspeed, IAS) or a speed in an air traffic control instruction. IAS and CAS differ only by instrument and position error.
3. Enter a pressure altitude in ft or m, or press one of the 'Sea level · 10,000 ft · FL350 · 11 km · 60,000 ft' buttons. If the altitude is empty, sea level is used.
4. The outside air temperature is filled in automatically with the standard atmosphere (ISA) temperature for that altitude. If you know the actual temperature, type it in. Press 'Reset to ISA' to go back to the automatic value.
5. Tap or drag the altitude–speed chart to calculate at that altitude and true airspeed. The heavy line on the chart is the speed of sound (Mach 1), and the orange dashed line shows the true airspeed at the current Mach as the altitude changes. With CAS selected, a black dotted line adds the true airspeed for the same calibrated airspeed at each altitude.
6. Each press of 'Example' fills in the next case: airliner cruise, calibrated 280 kn, then Concorde cruise. 'Copy result' copies the conditions and values as text, and 'Copy link' copies an address that holds the current state.

How it is calculated: temperature → speed of sound → Mach

The converter takes temperature and pressure at each altitude from the U.S. Standard Atmosphere 1976. Like the International Standard Atmosphere (ISA) used in aviation, it starts at 15 °C and 1,013.25 hPa at sea level. The FAA Pilot's Handbook summarizes this ICAO standard as air that cools by about 2 °C per 1,000 ft and reaches roughly −55 °C near 36,000 ft.

1. Temperature at altitude: it starts at 15 °C (288.15 K) at sea level and falls 6.5 °C per km up to a geopotential altitude of 11 km (36,089 ft). From 11 to 20 km it stays constant at −56.5 °C, and from 20 to 32 km it rises 1 °C per km.
2. Speed of sound: a = √(γRT). The ratio of specific heats γ of air is 1.4, the gas constant R is 8,314.32 ÷ 28.9644 = 287.05 J/(kg·K), and T is the absolute temperature. Since one knot is 1,852 m/h, the speed of sound in knots is a = 38.968 × √T kn.
3. Mach: M = true airspeed ÷ speed of sound. To go from Mach to knots, multiply by the speed of sound instead.
4. Example: 35,000 ft is 10.668 km, so the temperature is 288.15 − 6.5 × 10.668 = 218.808 K (−54.3 °C) and the speed of sound is 38.968 × √218.808 = 576.42 kn. A true airspeed of 450 kn is then 450 ÷ 576.42 = Mach 0.781.

If you enter a temperature yourself, only T in step 2 changes. At the same altitude, a temperature 10 °C above standard raises the speed of sound by about 2%, so the same true airspeed gives a correspondingly lower Mach number.

Standard atmosphere and speed of sound by altitude

Between 11 km (36,089 ft) and 20 km (65,617 ft) the temperature is constant, so the speed of sound stays at 573.57 kn. In this layer, changing altitude does not change the relation between Mach number and true airspeed. The FAA Pilot's Handbook likewise gives the speed of sound as 661 kn at sea level and 574 kn at 40,000 ft.

Common Mach values

Finding Mach from calibrated airspeed

The U.S. Federal Aviation Regulations (14 CFR 1.1) define true airspeed as 'the airspeed of an aircraft relative to undisturbed air', calibrated airspeed (CAS) as 'indicated airspeed of an aircraft, corrected for position and instrument error', and Mach number as 'the ratio of true airspeed to the speed of sound'. An airspeed indicator is scaled for compressible flow in sea-level standard air, so in thin air at altitude the same calibrated airspeed means a much higher true airspeed.

1. Find the impact pressure qc from the calibrated airspeed. When CAS is at or below the sea-level speed of sound a0 (661.48 kn), qc = p0 × [(1 + 0.2 × (CAS ÷ a0)²)^3.5 − 1], with p0 = 1,013.25 hPa.
2. Use the standard pressure p at that altitude to find Mach. In subsonic flight, M = √(5 × [(qc ÷ p + 1)^(2/7) − 1]).
3. In supersonic flight a shock wave forms ahead of the pitot tube, so the Rayleigh pitot formula replaces those two equations. It reads qc ÷ p + 1 = 166.92 × M⁷ ÷ (7M² − 1)^2.5, and the calibrated airspeed side has the same form. The converter solves this backward to find Mach.
4. True airspeed is the Mach number found this way multiplied by the speed of sound where the aircraft is flying. The relation between calibrated airspeed and Mach is set by pressure alone, while true airspeed also depends on temperature.

The same calibrated airspeed of 300 kn is Mach 0.541 at 10,000 ft but Mach 0.874 at 35,000 ft. That is why jet airliners hold a maximum speed in calibrated airspeed at low altitude and in Mach number at high altitude. The FAA handbook explains that a maximum operating Mach of 0.82 corresponds to about 306 KCAS at 31,000 ft and 261 KCAS at 38,000 ft, and the converter gives 305.56 kn and 260.83 kn.

From subsonic to hypersonic, and reference aircraft

The FAA Pilot's Handbook roughly divides flight speeds into subsonic below Mach 0.75, transonic from 0.75 to 1.20, supersonic from 1.20 to 5.00 and hypersonic above 5.00. The transonic range begins when airflow over some part of the aircraft first reaches the speed of sound, and civil jets usually cruise at Mach 0.7 to 0.90. NASA educational material also calls Mach 1 to 3 supersonic and Mach 3 to 5 high supersonic, so the boundaries are approximate.

The speed band compares the current Mach number with these five aircraft and shows how many times the reference just below and the one just above it you are going. The reference Mach numbers were each set at different altitudes, so comparing them after converting to knots gives different ratios.

Common mistakes

• Using 661.48 kn at every altitude: it is correct only at sea level and 15 °C. At 35,000 ft, a true airspeed of 450 kn divided by the sea-level value gives Mach 0.680, but divided by the speed of sound at that altitude it gives Mach 0.781.
• Entering calibrated airspeed as true airspeed: at 33,000 ft, entering an indicator reading of 280 kn as true airspeed gives Mach 0.481, while entering it as calibrated airspeed gives Mach 0.789. If the number comes from an airspeed indicator, choose 'Calibrated CAS'.
• Using ground speed as true airspeed: the speed shown on flight tracking sites is usually ground speed (GS), which differs from true airspeed by the wind. In a 100 kn headwind, ground speed is 100 kn lower than true airspeed.
• Reading knots as mph or km/h: 1 kn is 1.852 km/h, or about 1.151 mph. 500 kn is 926 km/h, or about 575 mph.
• Remembering Mach as a fixed speed per hour: 'Mach 1 = 1,225 km/h' is the value at sea level and 15 °C. At 35,000 ft, Mach 1 is 1,067.5 km/h.
• Mixing geometric and pressure altitude: the altitude in the converter is pressure altitude in the standard atmosphere, which is what an altimeter shows when set to 1,013.25 hPa (29.92 inHg). It can differ from the elevation on a map or from GPS altitude, depending on that day's pressure and temperature.

Limits and cautions

• The atmosphere is treated as dry standard air. If you enter a temperature, the speed of sound is calculated from it, but the pressure at each altitude still uses the standard atmosphere value.
• Altitude is geopotential pressure altitude from −2,000 to 100,000 ft (−609.6 to 30,480 m). Layers of the standard atmosphere above 32 km are not covered.
• The ratio of specific heats of air is fixed at 1.4. In hypersonic flight above Mach 5 or at very high temperatures the properties of air change, so results are approximate.
• Calibrated airspeed means CAS, which is corrected for instrument and position error. The actual indicated airspeed (IAS) can differ a little because each aircraft has its own errors.
• The calculation is for study, comparison and simulation. For actual operations, follow the flight manual and the values from the aircraft's instruments and flight management computer.

Basis: the standard atmosphere and the calibrated airspeed formulas are definitions and do not change. The FAA handbook, the Federal Aviation Regulations, NASA, Boeing and Smithsonian material were checked on October 20, 2026.

Sources

• 01NOAA·NASA·USAF — U.S. Standard Atmosphere, 1976 (NASA-TM-X-74335)Page 3, Table 4: −6.5 K/km from 0 to 11 km, 0 from 11 to 20 km, +1.0 K/km from 20 to 32 km; sea level 288.15 K and 101,325 Pa; γ 1.400
• 02William Gracey — Measurement of Aircraft Speed and Altitude (NASA RP-1046, 1980)Pages 14–15, equations 3.14 to 3.17: impact pressure and subsonic and supersonic calibrated airspeed, a0 = 1,116.45 ft/s
• 03eCFR — 14 CFR 1.1 General definitionsDefinitions of indicated, calibrated and true airspeed and of Mach number
• 04FAA — Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C)Pages 4-3 and 4-4: standard atmosphere (ISA) and pressure altitude / pages 5-44 and 5-45: speed of sound 661 kn at sea level and 574 kn at 40,000 ft, speed regimes, civil jet cruise Mach 0.7 to 0.90, MMO 0.82 = about 306 KCAS at FL310 and 261 KCAS at FL380 / page 8-9: CAS and TAS
• 05NIST Guide to the SI — Appendix B.8knot = 0.514 444 m/s, nautical mile = 1,852 m
• 06NASA Glenn Research Center — Mach Number1 < M < 3 supersonic, 3 < M < 5 high supersonic, M > 5 hypersonic
• 07NASA — First Generation X-1Mach 1.06 at 43,000 ft on October 14, 1947, the first crewed supersonic flight
• 08Boeing — Boeing Products (787)speeds similar to today's fastest wide bodies (Mach 0.85)
• 09Smithsonian National Air and Space Museum — Concorde, Fox Alpha, Air FranceCruised at twice the speed of sound at 55,000 to 60,000 ft
• 10NASA — SR-71 Blackbird fact sheetDesigned to cruise at Mach 3.2 at altitudes up to 85,000 ft
• 11NASA — X-154,520 mph (Mach 6.7) on October 3, 1967

Frequently asked questions

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