True airspeed (TAS) calculator.
Turn calibrated airspeed into true airspeed for any altitude and temperature, with the density ratio and the Mach number alongside.
True airspeed (TAS)
Enter calibrated airspeed (use IAS if that is all you have), pressure altitude, and OAT. Leave OAT blank to assume ISA. The Mach number is worked out from CAS and pressure altitude with the subsonic compressible relations, and TAS is that Mach number times the local speed of sound.
Enter CAS and a pressure altitude to see the true airspeed.
In the EASA ATPL exam
CAS-to-TAS conversion is a core mechanical skill in ATPL General Navigation (subject 061), where it is normally done on the CRP-5 navigation computer as the first step of a triangle-of-velocities problem, and it reappears in Instrumentation (022) through the airspeed indicator's density error. If the conversion is slow or shaky, every downstream heading and groundspeed answer inherits the error, so examiners can test one skill and harvest mistakes across the whole question.
Exam-style example
Your CAS is 180 kt at FL150 with a standard (ISA) temperature. What is the TAS, roughly?
- Rule of thumb: TAS rises about 2% over CAS per 1,000 ft, so at 15,000 ft add about 30%.
- 180 kt × 1.30 = 234 kt as the quick mental figure.
- The exact density-ratio method (or the CRP-5) gives about 227 kt; the exam's answer options are spaced widely enough that either route identifies the correct one.
TAS ≈ 230 kt (mental check 234 kt, computed 227 kt).
Common trap: Feeding the wrong inputs into the conversion. The density correction needs pressure altitude and outside air temperature, not indicated altitude and cabin-comfortable guesses. The second trap is forgetting that above roughly 300 kt the CAS ÷ √σ shortcut reads HIGH, because it treats CAS as EAS: at FL350 and 280 kt CAS it gives 503 kt where the true answer is 473.5 kt.
How to calculate true airspeed
The definition, the formula, a worked example and how it shows up in the ATPL exams.
How to calculate true airspeed
The definition, the formula, a worked example and how it shows up in the ATPL exams.Indicated, calibrated and true airspeed
Indicated airspeed (IAS) is what the airspeed indicator shows. Correct it for instrument and position error and you get calibrated airspeed (CAS). Correct CAS for air density and you get true airspeed (TAS), the speed of the aircraft through the air mass, which is what you combine with the wind to get groundspeed.
Because the airspeed indicator is really a dynamic-pressure gauge, it under-reads as the air thins out. That is why TAS is always higher than CAS once you leave sea level.
The density ratio and the formula
TAS = CAS ÷ √σ, where σ (sigma) is the density ratio: the actual air density divided by sea-level ISA density. SkyStudy builds σ from the pressure altitude (which sets the pressure ratio) and the outside air temperature (which sets the temperature ratio), so warmer or higher air both reduce σ and increase TAS.
Square-rooting the density ratio is the key step: a density ratio of 0.69 (roughly FL100 on a standard day) gives √0.69 ≈ 0.83, so TAS ≈ CAS ÷ 0.83 ≈ CAS × 1.20.
Worked example
CAS 250 kt at a pressure altitude of 10,000 ft on a standard day. The density ratio is about 0.74, and √0.74 ≈ 0.86, so TAS = 250 ÷ 0.86 ≈ 291 kt. The 2% per 1000 ft rule of thumb predicts +20% (300 kt), close enough for a quick mental check and a good way to sanity-test the calculator.
The compressibility correction and the next step
CAS ÷ √σ quietly assumes CAS and EAS are the same thing, which stops being true once the air starts to compress at the pitot. The error is always in the same direction: the shortcut reads HIGH, and the gap grows with speed and altitude. At FL300 and 250 kt CAS it is +15 kt; at FL350 and 280 kt CAS it is +30 kt (503 kt against a true 473.5 kt); at FL390 and 300 kt CAS it is +47 kt, which is enough to report a routine cruise as Mach 1.03 when the aircraft is actually at Mach 0.95. This calculator applies the correction, so the figure it shows is the one to trust at cruise levels. Work the CRP-5 the exam way and expect it to sit a little high up there.
Once you have TAS, take it to the wind component calculator to turn it into the runway, track and groundspeed picture you actually fly.
Good to know
Background and tips for getting the most out of this calculator.
Good to know
Background and tips for getting the most out of this calculator.Why TAS climbs
Thinner air at altitude means the same calibrated airspeed corresponds to a higher true airspeed, roughly 2% more per 1000 ft as a rough check.
Density ratio σ
σ combines the pressure and temperature ratios. The exam formula TAS = CAS ÷ √σ reads high at cruise; the compressibility correction brings it back.
Then the wind
Once you have TAS, the wind component calculator turns it into the runway and track picture you actually fly.
Frequently asked questions
Tap to read the full background and answers.
Frequently asked questions
Tap to read the full background and answers.- How do you convert CAS to TAS?
- The exam formula is TAS = CAS divided by the square root of the density ratio, and SkyStudy derives that density ratio from the pressure altitude and outside air temperature. The calculator goes one step further and works the Mach number out of CAS and pressure altitude first, then multiplies it by the local speed of sound, which is the same answer at low speed and the correct one at cruise.
- What is a quick rule of thumb for TAS?
- TAS increases by roughly 2% over CAS for every 1000 ft of altitude as a rough mental check. At 10,000 ft that is about +20%, so 250 kt CAS is around 300 kt TAS. Use the calculator for accurate figures.
- What if I only have IAS and no OAT?
- Enter IAS in place of CAS for a close estimate, and leave OAT blank to assume standard (ISA) temperature at the pressure altitude you enter.
- Is this exact?
- It includes the compressibility correction, so it stays exact across the subsonic range rather than drifting at cruise levels. It is a study tool for ATPL-level work and quick checks, not for primary navigation.
- Which speed do I use for navigation questions?
- True airspeed. The triangle of velocities in General Navigation combines TAS with the wind vector to produce heading and groundspeed. Using IAS or CAS in the triangle is a classic way to get a plausible-looking wrong answer.
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