Airspeed
Convert TAS to Mach number, Mach to TAS, or CAS to Mach at any altitude and temperature. Computes speed of sound in knots, m/s, mph, and km/h simultaneously. Covers subsonic, transonic, and supersonic regimes with a full ISA reference table.
Three modes — TAS ↔ Mach, CAS to Mach, or speed of sound only
Usage Guide
Four modes — TAS to Mach, Mach to TAS, CAS to Mach, or speed of sound only.
Enter your true airspeed and pressure altitude. If OAT is known, enter it to override the ISA calculation — this gives the most accurate result. If OAT is blank, the calculator uses ISA standard temperature for the entered altitude. The result tells you your Mach number, the local speed of sound, and your flight regime.
When an ATC clearance or FMS gives you a Mach number and you need the TAS for wind triangle planning, enter the Mach and altitude. The calculator returns TAS in knots — the value to use in the E6B wind triangle. Useful for high-altitude routing where speeds are expressed in Mach.
For flight operations where you read a CAS from the ASI, enter CAS, altitude, and OAT. The calculator converts CAS to TAS using the temperature ratio, then divides by the local speed of sound to give Mach. This is the complete CAS → TAS → Mach chain in one step.
Enter an altitude (and optionally an OAT) to see just the speed of sound in all four unit systems — knots, m/s, mph, and km/h. Useful for understanding how the acoustic environment changes with altitude and temperature. At the tropopause (36,089 ft), speed of sound reaches its ISA minimum of 573.6 kt.
ISA Reference Table
The speed of sound decreases from 661.5 kt at sea level to 573.6 kt at the tropopause, then stays constant through the stratosphere where temperature is fixed.
Above the tropopause (36,089 ft), ISA temperature is constant at −56.5°C — speed of sound stays constant through the stratosphere. Values computed using a = 661.47 × √(T/288.15) kt.
Flight Regimes
Aerodynamics changes fundamentally at different Mach regimes. Understanding which regime you are in determines what aerodynamic effects to expect.
Aerodynamic Effects
As Mach number increases toward and beyond Mcrit, the aircraft experiences a sequence of aerodynamic changes that every high-altitude pilot must understand.
Normal subsonic operation. Drag follows the familiar polar. No shock waves. Lift and drag coefficients are predictable. Full control authority. This is the design operating regime for all subsonic aircraft — performance data in the POH/AFM applies throughout this range.
The local airflow over the wing crest first reaches Mach 1.0. A small, weak shock wave appears. Wave drag begins to rise. The pilot notices no change at this point — the effect is microscopic initially. Mcrit is typically 0.72–0.85 for modern swept-wing designs.
Shock waves strengthen and move across the wing. The buffet boundary is reached — vibration is felt through the airframe as turbulent flow behind the shock strikes the tail. Drag coefficient rises steeply (drag divergence). Mach tuck begins as the centre of pressure moves aft. Pilots must apply back pressure to maintain altitude.
Both subsonic and supersonic zones coexist. Shock waves are unstable and move rapidly. Control effectiveness changes unpredictably. This is the most hazardous regime for an aircraft not specifically designed for it. Early jet aircraft lost to "unexplained" accidents were entering this regime in dives.
A stable bow shock forms ahead of the aircraft. Flow over the entire aircraft is supersonic. Wave drag is still significant but behaviour is more predictable than transonic. Aerodynamic heating becomes a factor above ~M2.0. Control surfaces work differently — moving shocks rather than circulating flow.
Sweeping the wing backward reduces the component of airflow perpendicular to the leading edge. A wing swept at 35° sees an effective Mach number of only cos(35°) × M_aircraft ≈ 0.82 × M_aircraft. This raises the effective Mcrit and delays drag divergence, allowing higher cruise speeds for the same thrust. Most commercial jets have sweep angles of 25–35°.
A supercritical aerofoil has a flatter upper surface than a conventional section. This reduces the acceleration of airflow over the upper surface, delaying the onset of local supersonic flow and raising Mcrit. Developed by Richard Whitcomb at NASA in the 1960s and now used on virtually all commercial transports. Allows cruise at M0.80–0.86 without severe wave drag.
The transonic wave drag of an aircraft depends on how its total cross-sectional area changes along its length. Area ruling minimises this drag by ensuring the area distribution is as smooth as possible — typically by waisting the fuselage where the wings add cross-sectional area. The result is the "coke bottle" fuselage shape seen on the Convair F-102 and other early supersonic aircraft.
At high subsonic Mach numbers, nacelle shape, pylon design, and engine placement all affect local flow acceleration. Modern engine nacelles are carefully contoured to avoid creating flow that reaches Mach 1 prematurely. Wing-mounted engines also interact with wing airflow — engine position is optimised to delay flow separation.
High-Altitude Operations
At extreme altitudes, the margin between stall speed and MMO shrinks to almost nothing. Understanding the coffin corner is essential for high-altitude jet operations.
As altitude increases, air density decreases. The stall IAS remains nearly constant because stall depends on dynamic pressure — but the TAS at stall grows. Meanwhile, the TAS corresponding to MMO also grows (higher TAS to reach M0.82 at lower density). However, the IAS corresponding to MMO decreases because the same Mach number at lower density = lower dynamic pressure = lower IAS.
At some altitude, stall IAS and MMO-equivalent IAS converge. This is the coffin corner. In practice, operators set maximum operating altitudes (service ceilings) well below the theoretical coffin corner, but high-performance aircraft and U-2 reconnaissance operations approach it closely.
Commercial jets don't fly to their service ceiling immediately — they step climb as fuel burns and weight decreases. At initial cruise weight (full fuel), the optimum altitude is lower. As fuel burns, the aircraft can step to higher, more fuel-efficient altitudes while maintaining adequate margins.
Turbulence in the coffin corner is dangerous because it can simultaneously push the aircraft toward stall (if speed is reduced in a gust) or toward Mach buffet (if speed is gained). At FL410+, the appropriate response to moderate turbulence is immediate descent, not speed adjustment.
The standard upset recovery (push, roll, pull — or PARE) must be modified at high altitude. Pushing (gaining speed) risks Mach buffet or MMO exceedance. Pulling (reducing speed) risks stall. Recovery requires simultaneous careful speed management and altitude reduction before standard recovery inputs.
Reduced Vertical Separation Minima (RVSM) allows 1,000 ft vertical separation above FL290, enabling efficient use of high-altitude airspace. RVSM requires very accurate altitude keeping (±200 ft), which is why autopilots and precise altimetry are mandatory — hand-flying in the coffin corner regime to RVSM standards is extremely demanding.
Common Questions
Mach number (M) is the ratio of an aircraft's true airspeed (TAS) to the local speed of sound: M = TAS / a. The speed of sound (a) depends solely on the temperature of the air, not on pressure or density: a = 661.47 × √(T/288.15) knots, where T is the ambient temperature in Kelvin. At sea level in ISA conditions (15°C), the speed of sound is 661.5 kt (340.3 m/s, 761.2 mph). At 35,000 ft in ISA conditions (−54.3°C), the speed of sound drops to 576.4 kt. Mach 1 therefore represents different speeds in knots at different altitudes — flying at Mach 1 at sea level requires 661.5 kt TAS, while at 35,000 ft it requires only 576.4 kt TAS. Mach number is used as the primary speed reference at high altitudes because aerodynamic phenomena (compressibility effects, shock wave formation) depend on the ratio of airspeed to the speed of sound, not on absolute airspeed.
The speed of sound in air depends only on temperature — not on pressure or density. This is because sound is a pressure wave that travels by compressing and expanding the air molecules, and the speed at which this disturbance propagates depends on the molecular kinetic energy, which is directly related to temperature. Speed of sound a = √(γ × R × T), where γ is the ratio of specific heats (1.4 for air), R is the specific gas constant for air (287 J/kg·K), and T is absolute temperature in Kelvin. Simplified to standard aviation units: a = 661.47 × √(T/288.15) knots. Since temperature decreases with altitude in the troposphere (at 1.98°C per 1,000 ft in ISA), the speed of sound decreases with altitude up to the tropopause. Above the tropopause (approximately 36,089 ft in ISA), temperature is constant at −56.5°C, so the speed of sound is constant at 573.6 kt from the tropopause through the lower stratosphere.
Critical Mach number (Mcrit) is the aircraft TAS at which the airflow over some part of the aircraft (typically the upper surface of the wing) first reaches Mach 1.0 locally. Because the airflow accelerates over a curved wing surface, the local airflow velocity exceeds the aircraft TAS. For a typical swept wing airliner, Mcrit is typically 0.78–0.85 — the aircraft may be flying at Mach 0.82, but the airflow over the wing crest is already supersonic. Above Mcrit, shock waves form on the wing surface. These shock waves create wave drag (a dramatic increase in drag), cause flow separation behind the shock (which can cause buffet and loss of lift), and change the aircraft's pitch characteristics (Mach tuck — a nose-down pitching moment). Maximum operating Mach number (MMO) is set conservatively below the speed at which these effects become unsafe.
Mach tuck (also called tuck under) is a nose-down pitching moment that develops as an aircraft accelerates beyond its critical Mach number. When shock waves form on the upper wing surface, they cause flow separation behind the shock, reducing the lift coefficient of the wing. The centre of lift moves rearward (further aft on the wing chord). Additionally, shock waves can form on the horizontal stabilizer, reducing its downward force and further contributing to nose-down pitch. The net result is a significant nose-down pitching moment that the pilot must counteract with back pressure. As speed increases further, the Mach tuck intensifies and the control forces required can exceed the pilot's ability to recover. Without proper understanding and early intervention (immediate power reduction and speed brakes), Mach tuck can lead to a fatal high-speed dive. This is why MMO is a hard limit and why aircraft are equipped with Mach warning systems (the "clacker" in older jets).
For practical purposes, compressibility effects on the airspeed indicator become significant above approximately Mach 0.3 (about 200 KIAS at sea level, or higher indicated speeds at altitude). Below Mach 0.3, air can be treated as incompressible and CAS ≈ EAS ≈ TAS (ignoring density). Above Mach 0.3, the compressibility correction — the difference between CAS and EAS — grows noticeably. For most piston and turboprop GA aircraft that operate below 250 KIAS and below 20,000 ft, the compressibility correction is less than 5 kt and is typically ignored. High-performance turboprop aircraft (King Air, PC-12) at their maximum speeds (around Mach 0.4–0.5) may see corrections of 5–10 kt between CAS and EAS. The full TAS formula (TAS = CAS × √(T_actual/T_ISA)) already accounts for density effects but not for compressibility separately — for speeds below Mach 0.6, this is an acceptable approximation.
Subsonic flight is where all airflow around the aircraft is below Mach 1.0. No shock waves form and drag is relatively predictable. Most commercial aviation operates in the high subsonic regime (Mach 0.75–0.90). Transonic flight is the regime where some airflow is subsonic and some is supersonic — typically between aircraft Mach 0.8 and 1.2. In this regime, shock waves form and move across the aircraft as speed changes, creating complex drag, buffet, and handling characteristics. Supersonic flight is where all airflow around the aircraft is above Mach 1.0 (aircraft Mach typically > 1.2). A bow shock forms ahead of the aircraft and the aerodynamics become more predictable again — drag decreases from its transonic peak. Supersonic transport aircraft (Concorde, SR-71) and military aircraft operate in this regime. The "sound barrier" was a challenge to overcome precisely because the transonic regime had characteristics that were unpredictable with pre-supersonic aerodynamic theory.
Wave drag is a form of pressure drag that appears when shock waves form on an aircraft flying at or above its critical Mach number. Shock waves represent a sudden discontinuity in pressure, temperature, and density — the energy required to maintain this discontinuity against the oncoming flow manifests as drag. Wave drag can be very large — at Mach 1.0, wave drag typically exceeds all other forms of drag combined. The "sound barrier" effect — a sharp drag rise near Mach 1.0 — is primarily wave drag. Aircraft designers minimise wave drag through: swept wings (the sweep angle delays the onset of compressibility by reducing the component of airflow perpendicular to the leading edge), supercritical wing sections (wing profiles optimised for high-subsonic flight with a flatter upper surface to reduce local acceleration), area ruling (the Whitcomb "coke bottle" fuselage shape that minimises transonic wave drag by ensuring the total cross-sectional area distribution is smooth), and waisted fuselages.
MMO (Maximum Operating Mach Number) is the maximum certificated Mach number for normal aircraft operations. It is analogous to VNE for subsonic aircraft but expressed in Mach because at high altitudes, TAS-based limits are impractical. MMO is set by the manufacturer based on: the speed at which Mach buffet (from shock-wave-induced flow separation) first becomes unacceptable; the speed at which Mach tuck forces exceed pilot ability to correct; the speed at which control effectiveness or structural integrity is compromised; and certification margins required by the airworthiness authority. For commercial jets, MMO is typically in the range of 0.82–0.92 Mach. The actual MMO for a specific aircraft is determined during flight testing and must provide adequate margin below the speed at which dangerous characteristics appear. MMO is displayed on some aircraft as a moveable Mach limit indicator on the airspeed indicator, and exceedance is typically indicated by an audible warning.
As Mach number increases toward MMO, several handling characteristics change. Longitudinal stability decreases — the aircraft becomes less stable in pitch because the aerodynamic centre moves aft as shock waves develop. Buffet onset (low-speed stall buffet at the bottom, Mach buffet at the top) defines the coffin corner — the narrow altitude/speed envelope where the margin above stall and the margin below Mach buffet converge. At very high altitudes (above FL400 for many jets), the coffin corner can be as narrow as 10–15 KIAS. Control effectiveness changes — ailerons may become less effective as shock waves alter the flow over the control surfaces. Aircraft with older designs may experience roll coupling — a tendency to roll when pitching — due to the swept wing effects at high Mach. Modern fly-by-wire systems provide Mach number-dependent control laws that compensate for these handling changes, giving the pilot a consistent feel across the flight envelope.
The coffin corner (also called the Q corner or aerodynamic ceiling) is the altitude at which the stall speed (in terms of IAS) and the Mach number limit (MMO expressed as IAS) converge to the same value, leaving no margin for safe flight. As altitude increases, the stall IAS remains approximately constant (stall depends on dynamic pressure), but the TAS at which MMO occurs decreases in terms of IAS because air density decreases. At approximately FL450–FL500 for a typical commercial jet, the IAS at which the aircraft stalls and the IAS corresponding to MMO are the same — there is literally no safe operating speed. In practice, operators set maximum operating altitudes well below the coffin corner. High-altitude reconnaissance aircraft like the U-2 operate close to the coffin corner and pilots must fly at precisely the right speed with no margin for error. An unusual attitude recovery at coffin corner altitude can be fatal if speed is gained (approaching MMO) or lost (approaching stall) during recovery.