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e6b calculator

The wind triangle, true airspeed, fuel and endurance, and every aviation unit conversion. No whizz wheel, no batteries.

Keep the references consistent: a true course with a true wind, or magnetic with magnetic. A written METAR wind is true; an ATIS wind is magnetic.

Wind corr. angle

-8.0°

turn left of course

Heading to fly

082°

Groundspeed

96 kt

slower than still air

N8.0° WCA
White is the heading and 110 kt true airspeed you fly, purple the 20 kt wind, and blue the course and 96 kt groundspeed the two add up to. The shaded wedge is the correction.

Headwind component 12.9 kt, crosswind 15.3 kt from the left. Point the aeroplane 8.0° left of course and the wind carries you back onto it.

WCA = arcsin(crosswind ÷ TAS); groundspeed = TAS × cos(WCA) − headwind component. That is the triangle above: the two vectors you can measure, added head to tail, give the one you actually travel along.

For training and reference only: always use approved sources and your aircraft’s performance charts for operational decisions.

An E6B solves the four calculations that make up basic flight planning: the wind triangle (heading and groundspeed from course, true airspeed and wind), true airspeed from calibrated airspeed and density altitude, fuel endurance and range, and unit conversions. This online E6B does all four instantly.

Key takeaways

  • The wind triangle gives you wind correction angle, heading to fly and groundspeed from course, TAS and wind.
  • TAS = CAS ÷ √σ, where σ is the density ratio at your density altitude. The 2% per thousand feet rule is a shortcut that over-reads by roughly 3% of your airspeed.
  • Endurance = usable fuel ÷ burn rate. Range = endurance × groundspeed, and groundspeed is the part the wind changes.
  • Always plan fuel to a reserve, not to dry tanks. The tool shows you when you start eating into it.
  • Learn the mental approximations too: examiners and real cockpits both reward a pilot who can sanity-check a gadget.

The four functions, and when you use each

Wind triangle. The core navigation calculation. You know where you want to go (course), how fast you fly through the air (TAS) and what the air itself is doing (wind). It returns the heading you must fly to track the course, and the groundspeed that results. Use it in planning for every leg, and in the air whenever the actual wind turns out to differ from the forecast.

True airspeed. Your airspeed indicator reads indicated airspeed, which understates your true speed through the air as you climb. TAS is what you use for navigation and flight planning, and it comes from the density ratio at your density altitude.

Fuel and endurance. How long you can stay airborne, how far that takes you, and the number that actually matters: how long until you are into your reserve.

Conversions. Knots to miles per hour, gallons to litres, feet to metres, Celsius to Fahrenheit, inches of mercury to hectopascals, and all of them the other way round. Aviation mixes unit systems more than almost any other field, and most mistakes are conversion mistakes.

How the wind triangle actually works

The wind triangle is a vector problem. Your aircraft’s movement through the air is one vector (heading and true airspeed); the air’s movement over the ground is another (wind direction and speed); the sum of the two is your track and groundspeed over the ground.

The wind correction angle comes from the crosswind element: WCA = arcsin(wind speed × sin(angle between wind and course) ÷ TAS). Then groundspeed = TAS × cos(WCA) − wind speed × cos(angle between wind and course).

You do not need to hold that formula in your head, but two consequences are worth knowing. Turning into wind costs you groundspeed disproportionately, because you lose both the headwind component and some airspeed to the correction angle. And a wind stronger than your TAS has no solution at all: you cannot hold a course against it, which is exactly what the tool tells you if you try.

True airspeed: the exact figure and the rule of thumb

Air density falls with altitude, so at a fixed indicated airspeed you are moving through the air faster and faster the higher you go. The exact relation is TAS = CAS ÷ √σ, where σ is the ratio of the local air density to sea-level standard density. In the standard atmosphere σ follows from density altitude alone, which is why this calculator asks for pressure altitude and temperature and works the density altitude out for you.

A whizz wheel cannot take a square root, so the classic teaching shortcut is to add 2 per cent of calibrated airspeed per thousand feet of density altitude. It is a straight line drawn through a curve, so it drifts, always upwards: at 5,000 feet it over-reads by about two knots on a 105 knot aeroplane, at 10,000 feet by nearly four, and at 15,000 feet by rather more. That is fine for a mental check and not fine as a flight plan figure, so this page shows both, exact first.

One caveat on the exact figure: it ignores compressibility, which begins to matter above roughly 200 knots or 20,000 feet. Below that it agrees with a certified flight computer.

Calibrated, indicated, true: keeping airspeeds straight

Indicated airspeed is what the instrument reads. Calibrated airspeed is indicated airspeed corrected for position and instrument error, usually a knot or two, and listed in your flight manual. True airspeed is calibrated airspeed corrected for air density. Groundspeed is true airspeed corrected for wind.

The aeroplane flies on indicated airspeed: your stall speed, your rotation speed and your approach speed are all indicated values, and they do not change with altitude. Navigation runs on true airspeed and groundspeed. Confusing the two is the classic student error, and it leads to flying an approach far too fast at a high-elevation airfield.

Fuel planning: the number that matters is time to reserve

Endurance to dry tanks is an interesting number. Endurance to your required reserve is an operational one. The tool shows both, because the gap between them is your actual decision-making margin.

Two habits keep fuel planning honest. Use a burn rate from your own recent experience rather than the flight manual figure, because engines, mixtures and pilots vary. And plan the reserve as fuel you will land with, not fuel you might dip into: the moment the reserve becomes usable in your planning, it stops being a reserve.

Note also that range depends on groundspeed, so a headwind reduces your range in exactly the proportion it reduces your groundspeed. A 20-knot headwind on a 100-knot aeroplane costs you a fifth of your range, which on a marginal leg is the whole discussion.

Do you still need a physical E6B?

For examinations, often yes. Many authorities still require a manual flight computer in the exam room, and there is real value in understanding the wind triangle as geometry rather than as a black box. The mechanical E6B teaches the relationship between the numbers in a way an app does not.

For flying, an online or app-based E6B is faster, less error-prone and always legible in turbulence. Most pilots learn the wheel, use the app, and keep the mental approximations, 60-to-1, the clock method and groundspeed × 5 for a 3° descent, for the times when neither is to hand.

Frequently asked questions

What is an E6B used for?

An E6B flight computer solves the standard flight planning calculations: the wind triangle to find heading and groundspeed, true airspeed from calibrated airspeed and density altitude, fuel burn, endurance and range, time-speed-distance problems, and unit conversions. It is the core planning tool taught in every private pilot syllabus.

How do you calculate wind correction angle?

Wind correction angle equals the arcsine of the crosswind component divided by true airspeed. In practice you enter your course, true airspeed, wind direction and wind speed into an E6B and it returns the correction angle, the heading to fly and the resulting groundspeed. A useful mental approximation is that the correction angle in degrees is roughly the crosswind component divided by TAS, multiplied by 60.

How do you calculate true airspeed from indicated airspeed?

Correct indicated airspeed for instrument and position error to get calibrated airspeed, then correct for air density. Exactly, true airspeed is calibrated airspeed divided by the square root of the density ratio at your density altitude, which is what this calculator uses. At 8,000 feet density altitude a calibrated 100 knots is 113 knots true. The whizz-wheel shortcut of adding 2 per cent per thousand feet would say 116, so it over-reads by about 3 per cent of your airspeed.

Is an online E6B allowed in pilot exams?

Usually not. Most aviation authorities require a manual flight computer or an approved non-programmable electronic version in written examinations, and personal devices are generally prohibited in the exam room. Use an online E6B for study, practice and real flight planning, and learn the wheel for the exam itself.

What is the difference between groundspeed and true airspeed?

True airspeed is how fast you are moving through the air mass. Groundspeed is how fast you are moving over the ground, which is true airspeed adjusted for the wind. With a 100 knot true airspeed and a 20 knot headwind your groundspeed is 80 knots, and it is groundspeed that determines how long the flight takes and how far your fuel goes.

How do I calculate fuel endurance?

Divide your usable fuel by your fuel burn rate per hour. Forty usable gallons at nine and a half gallons per hour gives about four hours and 13 minutes. The more useful figure is endurance to your required reserve: subtract the reserve fuel first, then divide by the burn rate.

Why does my groundspeed drop more than the headwind component?

Because a crosswind element forces you to angle into wind, and the component of your true airspeed spent on that correction is no longer contributing to progress along your course. The stronger the crosswind relative to your true airspeed, the more of your speed is consumed holding the track.

What units should I use for fuel in this calculator?

Whatever you fly in. The calculator is unit-agnostic for fuel, so long as your fuel quantity and your burn rate use the same unit: US gallons with gallons per hour, or litres with litres per hour. The conversions tab will translate between them in either direction if you need it to.

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