How the E6B wind triangle works
The wind triangle is the vector relationship between true airspeed (the airplane’s speed through the air), the wind, and groundspeed (the speed over the ground). To stay on a chosen true course, you point the nose into the wind by a wind correction angle (WCA). The heading you fly is the course plus that WCA, and your groundspeed is whatever is left after the wind is added to the airspeed vector.
With wind reported as the direction it is coming from:
crosswind = wind speed × sin(wind direction − course)
headwind = wind speed × cos(wind direction − course)
WCA = arcsin(crosswind / TAS)
true heading = course + WCA
groundspeed = √(TAS² − crosswind²) − headwind
A positive crosswind is from the right and needs a right correction (heading greater than course). A negative headwind is a tailwind and increases groundspeed. The same convention is used on a mechanical E6B, an electronic flight computer, and the crosswind component calculator.
Worked example
True course 090°, TAS 120 kt, wind 225° at 20 kt:
- The wind is 135° from the right of the nose, so the crosswind is 20 × sin 135° ≈ 14.1 kt from the right, and there is a 14.1 kt tailwind.
- WCA = arcsin(14.1 / 120) ≈ 6.8° right, so the true heading is 097°.
- Groundspeed ≈ 133 kt.
Running the same numbers in reverse — heading 097°, TAS 120, course 090, GS 133 — recovers a wind of 225° at 20 kt.
True airspeed and units
The triangle uses true airspeed, not indicated or calibrated airspeed. If you only have an indicated number, convert it first with the true airspeed calculator. All speeds in one calculation must use the same unit; switch freely between knots and miles per hour and the values will convert.
How to use it
- Choose “Heading & GS” to plan a leg, or “Find the wind” to solve for winds aloft.
- Enter the true course, true airspeed, and (in the forward mode) the wind direction and speed.
- Read WCA, true heading, groundspeed, and the crosswind and headwind components.
- Use the groundspeed in the time, speed, and distance calculator or the fuel planner to finish the leg.
Frequently asked questions
How do I calculate wind correction angle and groundspeed?
Find the crosswind and headwind components of the wind relative to your true course. The wind correction angle is the inverse sine of crosswind divided by true airspeed. Groundspeed is the remaining along-track airspeed minus the headwind (or plus the tailwind). This calculator uses that standard flight-computer convention.
Should I enter true or magnetic directions?
Use one reference consistently. If the course is a true course, enter a true wind and read a true heading. If you are working from a magnetic course and a magnetic wind (for example an ATIS wind), the heading will be magnetic as well. Do not mix true and magnetic in the same triangle.
Why is my groundspeed negative or the course impossible?
If the crosswind is stronger than true airspeed, or the headwind is stronger than the along-track component of TAS, you cannot make the course good. Slow down, accept a different track, or wait for a lighter wind.
Can I use this to find winds aloft from my GPS groundspeed?
Yes. Switch to “Find the wind,” enter true heading, TAS, true course (or track), and groundspeed, and the calculator returns the wind direction the wind is coming from and the wind speed.