An airspeed indicator does not measure speed. It measures a pressure difference — the difference between the pitot's total pressure and the static pressure — and its dial is marked in knots on the assumption that the air is at sea-level standard density. Climb, and the air thins, so the same dynamic pressure now corresponds to a much higher speed through the air than the dial shows. True airspeed is that real speed through the air mass, and it is what navigation, fuel planning and every performance figure quoted against distance depend on. This calculator takes the chain properly: indicated airspeed to calibrated airspeed with your aircraft's position error correction, then calibrated to true using pressure altitude and outside air temperature and the compressible relation, not the two-per-cent-per-thousand-feet approximation.
Arb Digital publishes this alongside the free ground speed calculator, and the boundary between them is exact and deliberate. That page solves the wind triangle: it takes true airspeed as a given input, along with the course and the wind, and returns ground speed, the heading to fly and the drift. This page produces the true airspeed that page needs. It does not touch the wind triangle at all — no wind, no drift, no heading, no wind correction angle. If you need the whole picture, run this first and take the result across to the ground speed page.
What This True Airspeed Calculator Does
It performs the full published conversion chain. Indicated airspeed plus your position error correction gives calibrated airspeed. Calibrated airspeed and the standard sea-level pressure give the impact pressure through the compressible subsonic relation. Impact pressure and the actual static pressure at your pressure altitude give the Mach number. Mach number and the local speed of sound, which depends only on temperature, give true airspeed. Along the way it reports equivalent airspeed, the density altitude implied by your pressure altitude and temperature, the local speed of sound and the deviation of your temperature from the standard atmosphere.
It uses the compressible relation throughout rather than the incompressible density-ratio shortcut. Below about 200 knots the two agree closely, but the difference grows with speed and altitude, and by the mid-200s at high level the simple square-root-of-density-ratio method is noticeably optimistic. The tool also handles total air temperature: if your probe reads TAT rather than SAT, enter its recovery factor and the ram rise is removed before the speed of sound is computed.
How to Use It
- Enter indicated airspeed and the position error correction. The correction comes from the airspeed calibration table in the approved flight manual for your aircraft, at the configuration you are flying. It is often only a knot or two in cruise and much larger in the landing configuration.
- Set the altimeter subscale to 29.92 or 1013.25 and read pressure altitude. This is not your indicated altitude on a local setting, and it is not your true altitude; the US National Weather Service publishes a Pressure Altitude Calculator if you need to derive it from station pressure. Getting this wrong is the most common source of a wrong TAS.
- Enter the outside air temperature. Static air temperature if you have it. If your gauge reads total air temperature, enter the probe's recovery factor and let the tool remove the ram rise.
- Read true airspeed, and check the Mach number. If the Mach number is above about 0.3 the compressibility correction is doing real work, and any rule of thumb you might have used instead is now materially wrong.
- Take the TAS to the wind triangle. This page stops at speed through the air. Ground speed, heading and drift are the job of the ground speed calculator.
The Formulas: The Full IAS to TAS Chain
Start with CAS = IAS + position error correction. The impact pressure follows from the compressible relation with sea-level standard pressure P0 = 101,325 Pa and the sea-level speed of sound a0 = 661.4788 kt:
qc = P0[(1 + 0.2(CAS/a0)2)3.5 − 1]. Static pressure at pressure altitude comes from the standard atmosphere: below the tropopause, P = P0(1 − 6.87535×10−6h)5.2559 with h in feet; above it the atmosphere is isothermal and the pressure decays exponentially. NASA Glenn's Earth Atmosphere Model sets out the same layered model in metric form.
Mach number then follows from M = √(5[(qc/P + 1)2/7 − 1]), and the local speed of sound from the static air temperature alone: a = 38.967854√T in knots with T in kelvin. Finally TAS = Ma. Equivalent airspeed is TAS multiplied by the square root of the density ratio, and the gap between EAS and CAS is precisely the compressibility effect that the shortcut methods ignore.
Worked example, matching the defaults. At 120 KIAS with no position error, 8,000 ft pressure altitude and −5 °C: the pressure ratio is (1 − 0.0550028)5.2559 = 0.742779, so P = 75,264 Pa. CAS/a0 = 0.181427, giving qc = 101,325 × 0.0232314 = 2,354.0 Pa. Then qc/P + 1 = 1.031277, whose 2/7 power is 1.008838, so M = √(5 × 0.008838) = 0.21021. At 268.15 K the speed of sound is 638.09 kt, so TAS = 134.1 kt. Density altitude works out at 7,504 ft, below the pressure altitude because the air is colder than standard. Every figure there was computed by hand before the code was written. Note that the familiar two-per-cent-per-thousand-feet rule would have given about 139 kt — five knots optimistic, which is a real navigation error over a long leg.
Four Airspeeds, and Why Each One Exists
Indicated is the raw dial reading, uncorrected. It is the speed the aircraft is flown by, because stall speed, flap limits and manoeuvring speed are all functions of dynamic pressure, and dynamic pressure is what the instrument responds to. That is why an aeroplane stalls at very nearly the same indicated airspeed at any altitude, while its true airspeed at the stall is far higher up high.
Calibrated removes the position and instrument error — the fact that the static port does not sit in perfectly undisturbed air, and that the disturbance changes with angle of attack and configuration. The correction is measured in flight test for each type and published as a table in the flight manual; the FAA sets the airspeed definitions out in the Pilot’s Handbook of Aeronautical Knowledge.
Equivalent removes compressibility. Air piling up at the pitot is compressed, so at speed the instrument over-reads relative to a true dynamic-pressure measurement. Below about 200 kt EAS and CAS are within a knot; at 300 kt and altitude the difference matters, and structural limits such as maximum design speeds are properly expressed in EAS.
True removes density. It is the actual speed through the air mass and the only one of the four that belongs in navigation arithmetic. It is also the one that has no direct instrument: it is always computed, on a flight computer, in an air data computer, or on a page like this one.
Temperature Matters More Than Pilots Expect
Pressure altitude gets the attention, but temperature enters twice and in opposite ways. It sets the local speed of sound, which scales as the square root of absolute temperature, and it sets the air density along with pressure. Two aircraft at the same pressure altitude and the same calibrated airspeed on a hot day and a cold day have measurably different true airspeeds: warmer air is thinner, so the same dynamic pressure means a higher true speed.
The effect is large enough to matter operationally. Twenty degrees warmer than standard adds roughly three to four per cent to true airspeed at the same CAS and pressure altitude, which on a two-hour leg is several minutes of flight time and a corresponding fuel difference in the wrong direction, since the higher density altitude also reduces engine power output. Our density altitude calculator works that side of the problem from elevation, altimeter setting, temperature and dew point, and the temperature at altitude calculator gives the standard-atmosphere temperature at a level so you can see how far off-standard your day is.
Total Air Temperature and the Ram Rise Trap
A temperature probe sitting in the airflow does not read the ambient temperature of the air. The air is brought partly or wholly to rest against the probe, and that stagnation converts kinetic energy into heat. The relation is Ttotal = Tstatic(1 + 0.2KM2), where K is the probe's recovery factor. At Mach 0.2 the rise is under three kelvin and can reasonably be ignored; at Mach 0.8 it is around 35 kelvin, which is far too large to ignore in any TAS calculation.
The convenient part is that Mach number falls out of impact pressure and static pressure alone, with no temperature term in it, so the correction is a single step rather than a loop: the tool computes Mach first, divides out the ram rise, and only then uses the static temperature for the speed of sound. Enter a recovery factor of zero and no correction is applied at all, which is the right setting when your gauge already gives static air temperature.
Where This Page Stops
This is a standard-atmosphere calculation using published relations and your entered figures. It assumes a subsonic, correctly calibrated pitot-static system in undisturbed flight, and it says nothing about a blocked or partially blocked pitot or static port, which produces indications that no correction chain can rescue. It assumes the standard atmosphere's lapse structure for the pressure-to-altitude relation, which is exactly what a pressure altitude is defined against, but it means the pressure altitude you enter must genuinely be a pressure altitude.
It is not a substitute for the aircraft flight manual or pilot's operating handbook, and it is not an approved flight-planning tool. Certificated performance figures come from the approved manual, and operational planning is done with approved tools and current data. Speeds this page produces are for study and cross-checking. If you want the Mach side on its own, the Mach number calculator and the speed of sound calculator cover it, the air pressure at altitude calculator gives the pressure model directly, and the crosswind component calculator handles the runway wind problem, which is a different question again.
Arb Digital builds reference calculators and documentation for aviation, engineering and technical sites — the kind that earn links because the maths is correct and the assumptions are stated.
Browse the free tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using indicated altitude instead of pressure altitude. Pressure altitude is read with 29.92 inHg or 1013.25 hPa in the subscale. A local altimeter setting gives a different number, and the error propagates straight into TAS.
- Trusting the two-per-cent-per-thousand-feet rule. It ignores temperature entirely and ignores compressibility, so it drifts off at altitude and at speed. On the defaults here it is five knots optimistic.
- Feeding total air temperature in as static. Ram rise is a few kelvin at low Mach but tens of kelvin in the high subsonic range. Use the recovery factor input rather than ignoring the difference.
- Skipping the position error correction. Calibrated is not indicated. The difference is small in cruise and can be several knots in the landing configuration, where it matters most.
- Using true airspeed to fly the aeroplane. Stall, flap and manoeuvring speeds are indicated-airspeed numbers because they depend on dynamic pressure. True airspeed belongs in navigation, not on the approach.
Related Free Tools From Arb Digital
Once you have a true airspeed, the ground speed calculator solves the wind triangle and gives ground speed, heading and drift — it takes TAS as an input and this page supplies it. The density altitude calculator covers aircraft and engine performance from elevation, altimeter setting, temperature and dew point, and the temperature at altitude calculator gives the standard-atmosphere temperature at any level. For the compressibility side, use the Mach number calculator and the speed of sound calculator; for the atmosphere itself, the air pressure at altitude calculator and the air density calculator. Browse the full free online tools hub for the rest.
Frequently Asked Questions
It is the aircraft's actual speed through the air mass it is flying in. An airspeed indicator cannot show it directly because the instrument responds to dynamic pressure and is calibrated for sea-level standard density, so true airspeed is always computed from calibrated airspeed, pressure altitude and temperature.
Apply the position error correction from the flight manual to get calibrated airspeed, convert that to impact pressure with the compressible relation, divide by the static pressure at your pressure altitude to get Mach number, and multiply by the local speed of sound, which depends only on the static air temperature.
Only roughly, and only at low speed near standard temperature. It ignores temperature and compressibility entirely. In the worked example on this page it overestimates true airspeed by about five knots at 8,000 feet, and the error grows with altitude and speed.
Pressure altitude, which is the altimeter reading with 29.92 inches of mercury or 1013.25 hectopascals set in the subscale. It is not the indicated altitude on a local setting and not true altitude, and using either of those instead is the most common cause of a wrong result.
Equivalent airspeed has compressibility removed but not density; it is the speed that would produce the same dynamic pressure at sea-level standard density. True airspeed additionally accounts for the actual air density, so it equals equivalent airspeed divided by the square root of the density ratio.
Because it sets both the air density and the local speed of sound. Warmer air is less dense, so the same calibrated airspeed corresponds to a higher true airspeed. Roughly twenty degrees above standard adds three to four per cent to true airspeed at the same pressure altitude.
It is the temperature increase a probe reads because the airflow is brought to rest against it, converting kinetic energy into heat. It is under three kelvin at Mach 0.2 and around thirty-five kelvin at Mach 0.8, so it can be ignored at low speed but never in the high subsonic range.
No. It stops at speed through the air. Ground speed, the heading to fly and the drift caused by wind are wind triangle problems, and the ground speed calculator on this site solves them from a true airspeed you supply.
This tool is provided for education and flight-planning study only. It applies published standard-atmosphere and airspeed relations to figures you enter and is not an approved flight-planning tool. It does not replace the approved flight manual or pilot's operating handbook, which is the sole source of certificated performance and airspeed calibration data for any aircraft, and operational planning should be carried out with approved tools and current data.
