# What is CAS and EAS and how to calculate from IAS? [duplicate]

I am trying to understand IAS, CAS, EAS, and TAS. I was under the impression that CAS is IAS corrected for instrumentation error and position error. The error is specific to the type of aircraft. Why then on the wikipedia page for CAS is there a formula to calculate CAS which is a function of just dynamic pressure? Where did this formula come from and how can it be valid if the correction for CAS is aircraft specific?

Also, EAS is CAS corrected for compressibility. What does this really mean? How can I convert a speed in CAS to EAS?

• Interesting article but I still don’t get how CAS can be calculated based solely on impact pressure like the Wikipedia article suggests. Where did this formula come from? The article you linked says the error becomes greater with higher angle of attack yet angle of attack is not a term in the equation? Apr 23, 2020 at 1:35
• How? By definition. "CAS is defined as a function of impact pressure alone". This is the value, the truth, that we want to measure. But given imperfect instruments, we can only get IAS. From there, we can use all our engineering knowledge, lab testing with more accurate instruments, etc, to get correction tables from measured IAS to the true CAS. They can be as complicated as you'd bear, but their sole aim is to arrive at a simple (but theoretical) truth.
– Zeus
Apr 23, 2020 at 5:46

If you don´t mind, I´ll keep it in simple terms.

We start off with IAS - that´s the airspeed you see on your instruments. You have static port - registering pressure around your aircraft, pitot tube, registering how many molecules of air getting inside. And by subtracting one from another, you get your IAS. Dummy example: Static registers 100 molecules around. Pitot registers 200 molecules, which would equal to speed of 100kts.

CAS - it the speed corrected for instrument error. Because no instruments are perfect. Again, just one example, since a/c is moving through the air, pushing the air aside, it does create lower pressure around the a/c. Which in term, does affect reading of static and pitot tubes (registering wrong amount of molecules). As a pilot, CAS is less relevant speed, as it will be used mostly for certification process.

CAS - EAS is made by allowing for compressibility effects. At very high altitude and very high speeds (jet fighters/bombers/space shuttle), there are different rules in action.

There is another speed, TAS. If you want to do everything perfect, first you need to convert IAS to CAS, (by using special table for a given airplane) and then convert CAS to TAS. TAS is your real airspeed, moving through the air. It might differ greatly from IAS depending on pressure and temperature. In standard (ISA) conditions CAS will be equal to TAS. But what happens when you fly at an altitude of 40.000 feet? Well, air is a lot less dense. For a given cube of air, there are a lot less molecules. In order to fly and not to stall, you must see "100kts IAS" on your airspeed indicator. Ssince there are so fewer molecules in the air, your real airspeed through the air must be 2-3 times higher, in order to hit all those 100 molecules. Does it make sense?

As a pilot, greatest importance for you is IAS. It shows you how many molecules of air you are hitting (dynamic pressure). Stall speed, never exceed - all based on IAS. Your TAS can be whatever, but IAS is the one affects your airplane.

So why do we care about TAS? Well, based on TAS and wind, we can derive our GS - ground speed. And GS is important! It will tell you, how long time will it take for you to get from A to B. Based on time, you know how much fuel you will need. Perhaps, you would need to make an extra refuelling stop on your way. Or you calculate and see that airport will be closed by the time you arrive there? Later on, as an airline pilot, you know if you are early/late, duty times, etc, etc.

There is Mach number as well, but since you didn´t ask, I´ll just say you will need it flying at higher altitudes (approx. above 25,000 feet) and at those altitudes, it will take over IAS.

• Thanks I appreciate your response. Like you said, I have heard there are tables to convert IAS to CAS for a given aircraft. Now the Wikipedia article I linked gives an equation to calculate CAS based on dynamic pressure but how can CAS only depend on dynamic pressure and not anything else? Then all conversion tables from IAS to CAS would be the same and not dependent on the type of aircraft. Apr 23, 2020 at 2:22
• Perhaps if you think of it this way: there is no instrument on board the aircraft that can give a direct measurement of dynamic pressure. The only thing you get is IAS, which you can then convert to CAS using the correction tables from the flight manual. Now you can calculate dynamic pressure.
– Ugo
May 18, 2020 at 13:41
• continued comment ... by using the Wikipedia formula you quote to solve for Qc (dynamic pressure). You would theoretically need Qc to calculate Mach number from CAS if flying at supersonic speed. Theoretically, because in practice these aircraft will have a Machmeter that will do this mechanically for the pilot. (or an air data computer, which knows these formulas).
– Ugo
May 18, 2020 at 14:05