Atmosphere and performance workbench, one page.
The atmosphere and performance windows of the manual flight computer as direct calculators, in the order you actually use them, plus a drill that generates fresh time, speed, distance and fuel problems with the worked method, because those are drilled here rather than calculated: the exam tests whether you can work them on the wheel.
Turn calibrated or indicated airspeed into the true airspeed the navigation triangle needs. The airspeed window: set pressure altitude against temperature, then read TAS opposite CAS.
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.
Headwind, tailwind and crosswind for a runway, plus the gust case you brief against the limit. The wind side: the sliding grid behind the rotating disc, the same face used for drift and groundspeed.
The altitude the aircraft actually feels once it is hot or high, the figure performance charts want. The density-altitude window, right next to the airspeed window on the same disc.
Field elevation plus QNH into the entry figure every performance table is indexed by. The altitude window: the pressure correction you apply before anything else.
Standard temperature at any level, and how far today sits above or below it. The temperature scale the other windows are indexed against; get this wrong and every later window is wrong.
Convert between true airspeed and Mach from temperature alone, the way Principles of Flight expects. The Mach index on the airspeed window, the arrow marked for compressible speeds.
Distance, speed, mass, pressure, and fuel volume to mass at the right density. The conversion marks printed around the rim: litres, gallons, kilos, pounds, nautical and statute miles.
Flight computer drill
Eight original problems per set, drawn from the same generators behind the timed aptitude exercises. Pick an answer and the worked method appears with the flight-computer equivalent, so you learn the shortcut rather than just the number.
Untimed here on purpose: get the method right first. For speed training, run the same maths against the clock in speed, distance and time, fuel planning or the mixed cockpit maths drill.
Every window has its own page
Each tab above is the same calculator that lives on its own page, with the full explanation, worked example and exam context alongside it.
- True airspeedTurn calibrated or indicated airspeed into the true airspeed the navigation triangle needs.
- Wind componentsHeadwind, tailwind and crosswind for a runway, plus the gust case you brief against the limit.
- Density altitudeThe altitude the aircraft actually feels once it is hot or high, the figure performance charts want.
- Pressure altitudeField elevation plus QNH into the entry figure every performance table is indexed by.
- ISA deviationStandard temperature at any level, and how far today sits above or below it.
- Mach numberConvert between true airspeed and Mach from temperature alone, the way Principles of Flight expects.
- Unit converterDistance, speed, mass, pressure, and fuel volume to mass at the right density.
"E6B" is used here as the generic term for the manual flight computer. SkyStudy is not affiliated with, endorsed by, or connected to any manufacturer or vendor of physical flight computers, and this page is not an approved exam device. Check with your ATO or national authority which flight computer is permitted in your exam sitting.
In the EASA ATPL exam
Flight-computer work runs through three ATPL subjects at once. General Navigation (061) uses it for the triangle of velocities, true airspeed and every time and distance leg. Flight Planning and Monitoring (033) uses it for trip fuel, contingency, endurance and the point of equal time. Performance (032) leans on pressure altitude, ISA deviation and density altitude before any chart can be entered. The individual sums are small; the marks are lost to speed, to unit slips, and to feeding one window with the output of the wrong one.
Exam-style example
You are holding a groundspeed of 240 kt with 80 NM to run and a burn rate of 1,800 kg/h. How long is the leg, and how much fuel does it take?
- Convert the speed to a per-minute rate: 240 ÷ 60 = 4 NM per minute. This is the same thing the rate index does mechanically.
- Time for the leg: 80 ÷ 4 = 20 minutes.
- Fuel: 20 minutes is a third of an hour, so 1,800 ÷ 3 = 600 kg.
20 minutes and 600 kg, from one alignment on the computer.
Common trap: Putting true airspeed where groundspeed belongs. The rate index does not know which speed you fed it, so a leg time worked from TAS looks perfectly reasonable and is wrong by the whole wind component. Resolve the wind first, then work the time and the fuel from groundspeed.
How the atmosphere and performance windows work
The definition, the formula, a worked example and how it shows up in the ATPL exams.
How the atmosphere and performance windows work
The definition, the formula, a worked example and how it shows up in the ATPL exams.What the flight computer really is
Strip away the aviation markings and an E6B is two tools glued back to back. One face is a circular slide rule: two logarithmic scales that turn multiplication and division into a single rotation. The other face is a wind grid, a piece of graph paper you slide behind a rotating compass rose to add two vectors by drawing rather than by trigonometry.
Almost every planning figure a pilot needs is one of those two operations. That is why one small disc replaces a page of formulas, and why learning the disc is really learning to recognise which of the two operations a question is asking for.
The rate index, and why one setting answers three questions
The black 60 on the inner scale is the rate index: it represents one hour in minutes. Line your hourly rate up against it (240 kt, or 1,800 kg/h) and the two scales are now locked in that proportion for good. Every pair of numbers around the rim is then a valid answer to the same question.
That is the insight most students miss. You do not do a separate calculation for time, for distance and for fuel. You set the rate once, and read whichever pair you were asked for. A groundspeed of 240 kt sitting against the index means 4 NM against 1 minute, 80 NM against 20 minutes, and 240 NM against 60 minutes, all visible at the same time.
The wind side comes first
The calculator face works in the air mass. The moment wind is involved, the wind face has to run first: it converts true airspeed and the wind vector into drift and groundspeed, and only then does the rate index have the right speed to work with.
The same ordering applies to performance. Field elevation and QNH give pressure altitude; pressure altitude and temperature give ISA deviation and density altitude; only then can you enter a performance chart. Each window is fed by the one before it, which is why the tabs above are laid out in the order you actually use them.
Drilling beats reading
Reading about the rate index takes two minutes and does nothing for an exam sat under time pressure. What moves the needle is repetition on original problems until the per-minute conversion is automatic and the fuel arithmetic no longer needs a scratch pad.
The drill on this page generates fresh time, speed, distance and fuel problems every set, each with the worked method and the flight-computer equivalent. When those feel easy, take the same maths against the clock in the timed aptitude exercises, where speed is scored as well as accuracy.
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.One rate, three answers
Set the hourly rate against the 60-minute index and time, distance and fuel are all readable from the same alignment. That is the whole trick of the calculator face.
Order matters
Wind before groundspeed, pressure altitude before density altitude. Each window feeds the next, so an early slip produces a wrong answer that still looks sensible.
Drill, then time it
Work the drill below until the per-minute conversion is automatic, then repeat it against the clock in the timed aptitude exercises.
Frequently asked questions
Tap to read the full background and answers.
Frequently asked questions
Tap to read the full background and answers.- What is an E6B flight computer?
- It is the circular slide rule pilots use for flight planning. One face is a rotating logarithmic scale that solves any rate problem (time, speed and distance, fuel burn, unit conversion) from a single alignment against the 60-minute rate index. The other face is a sliding wind grid for drift, heading and groundspeed. The name comes from a US Army Air Forces form number and is now used generically for the whole family of manual flight computers.
- Is this page a simulator of the rotating disc?
- No, and it does not pretend to be. Turning a picture of a disc with a mouse teaches nothing you can carry into an exam hall. This page covers the atmosphere and performance windows of the disc, true airspeed, wind components, density altitude, pressure altitude, ISA deviation, Mach and unit conversion, each as a direct calculator. Time, speed and distance, and fuel, are drilled rather than calculated here, because the exam tests whether you can work them on the wheel, not whether a screen can do it for you. If you want the feel of the full disc, buy the physical computer; the drills here are what transfer to it.
- Can I use this in the ATPL exam?
- No. Exam centres allow a specific list of calculators and manual flight computers, and a phone or laptop is not on it. Ask your ATO or your national authority which model is permitted for your sitting, and practise on that exact device. Use this page for the maths and the drilling between study sessions.
- What is the difference between an E6B and a CRP-5?
- They are the same idea in two shapes. The classic E6B is rectangular with a sliding wind card; the CRP-5 and its relatives are round with a rotating wind disc and add scales for higher speeds and metric fuel. The computations are identical, so anything you drill here works on either. SkyStudy is not affiliated with, endorsed by, or connected to any manufacturer of physical flight computers.
- Which window do I use for what?
- Pressure altitude first, then ISA deviation, then density altitude for performance work. For navigation, true airspeed, then wind components for the runway limit. Time, speed, distance and fuel are not calculators on this page; they are drilled below, because the exam tests whether you can work them on the wheel. Doing the calculator windows out of order is the most common way to get a plausible but wrong answer, because each one feeds the next.
- Do I still need to learn the manual computer?
- Yes, if your exam allows it and your school teaches it, because the exam is timed and a practised computer user is faster than someone reasoning from formulas. The value of an on-screen version is that it removes the mechanical fumbling while you learn which quantity goes where, which is the part most students get wrong.
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