E6B: heading and ground speed?
Type the true course, the true airspeed and the wind. The E6B calculator works the wind triangle like the wind side of an E6B flight computer and gives the true heading to fly, the wind correction angle, the ground speed, and the time and fuel for the leg.
- True heading
- 81.7
Fly a true heading of 81.7° (-8.3° correction) for a ground speed of 108.7 kn.
- Ground speed
- 108.7 kn
- Wind correction angle°
- -8.3
- Correct
- Left
- Headwind
- 10 kn
- Crosswind
- 17.3 kn
- Time en routemin
- 82.8
True heading: 81.7. Fly a true heading of 81.7° (-8.3° correction) for a ground speed of 108.7 kn.
How to calculate
E6B calculator, the wind side of the flight computer: true heading, wind correction angle and ground speed from the true course, true airspeed and wind, with headwind, crosswind, time en route and fuel.
Example with the default inputs (True course 90, True airspeed 120 kn, Wind direction 30, Wind speed 20 kn, Distance 150 nmi): Fly a true heading of 81.7° (-8.3° correction) for a ground speed of 108.7 kn.
Method: SWC = (WS ÷ TAS) × sin(WD − TC); WCA = asin(SWC); heading = TC + WCA; GS = TAS × √(1 − SWC²) − WS × cos(WD − TC); time = distance ÷ GS; fuel = burn per hour × time.
- The course, wind direction and heading are all true (winds aloft forecasts are true). Apply magnetic variation and deviation to get a compass heading.
- A steady wind over the whole leg; no answer when the crosswind is stronger than the airspeed or the headwind is at least the airspeed.
Worked examples
Each example is checked against the calculator on every build.
- True course 90, True airspeed 120 kn, Wind direction 0, Wind speed 20 kn, Distance 150 nmi gives Wind correction angle -9.594068, True heading 80.405932, Ground speed 118.3 kn, Headwind 0 kn, Time en route 76.063883.Source: Ed Williams, Aviation Formulary V1.47, In-flight wind calculations (SWC = (WS/TAS) sin(WD − CRS); HD = CRS + asin(SWC); GS = TAS √(1 − SWC²) − WS cos(WD − CRS)), https://edwilliams.org/avform147.htm (retrieved 2026-10-05); Wikipedia, E6B (wind correction angle = sin⁻¹((Vw ÷ Va) sin(w − d))), https://en.wikipedia.org/wiki/E6B (retrieved 2026-10-05)
- True course 360, True airspeed 100 kn, Wind direction 360, Wind speed 25 kn, Distance 150 nmi, Fuel burn per hour 8 gives Wind correction angle 0, True heading 0, Ground speed 75 kn, Headwind 25 kn, Time en route 120, Fuel for the leg 16.Source: Ed Williams, Aviation Formulary V1.47, In-flight wind calculations (SWC = (WS/TAS) sin(WD − CRS); HD = CRS + asin(SWC); GS = TAS √(1 − SWC²) − WS cos(WD − CRS)), https://edwilliams.org/avform147.htm (retrieved 2026-10-05)
- True course 270, True airspeed 150 kn, Wind direction 300, Wind speed 30 kn gives Wind correction angle 5.73917, True heading 275.73917, Ground speed 123.3 kn.Source: Ed Williams, Aviation Formulary V1.47, In-flight wind calculations (SWC = (WS/TAS) sin(WD − CRS); HD = CRS + asin(SWC); GS = TAS √(1 − SWC²) − WS cos(WD − CRS)), https://edwilliams.org/avform147.htm (retrieved 2026-10-05)
How it works
With true course TC, true airspeed TAS, wind from WD at speed WS (angles in degrees):
- SWC = (WS ÷ TAS) × sin(WD − TC).
- Wind correction angle WCA = asin(SWC), from −90° to 90°; positive means turn right of the course, negative left.
- True heading = TC + WCA, brought into 0° to 360° (360° shows as 0°).
- Ground speed GS = TAS × √(1 − SWC²) − WS × cos(WD − TC).
- Headwind = WS × cos(WD − TC) (negative is a tailwind); crosswind = WS × |sin(WD − TC)|.
- Time en route = distance ÷ GS, in minutes; fuel for the leg = fuel burn per hour × time ÷ 60.
Unit sizes: 1 kn = 1,852 m per hour; 1 nmi = 1,852 m; 1 mi = 1,609.344 m; 1 mph = 0.44704 m/s.
Rules
- Course and wind direction from 0 to 360 degrees; TAS from 1 to 2,000 kn; wind speed from 0 to 2,000 kn; distance more than 0 and at most 20,000 nmi; fuel burn more than 0 and at most 100,000 per hour.
- No answer when |SWC| > 1 (the crosswind is stronger than the airspeed) or when GS ≤ 0.
- Time needs a distance; fuel needs a distance and a fuel burn.
Output format
Heading and WCA in degrees to 1 decimal; speeds in knots to 1 decimal; time in minutes to 1 decimal; fuel to 1 decimal in the unit you typed. All arithmetic is in floats (trigonometry).
Worked examples by hand
A crosswind from the left. TC 090°, TAS 120 kn, wind 360° at 20 kn: WD − TC = −90°, SWC = −1/6, WCA = asin(−1/6) = −9.594° (left), heading 080.4°. GS = 120 × √(35/36) − 20 × cos(−90°) = 118.32 kn. 150 nmi takes 150 ÷ 118.32 × 60 = 76.06 min.
A direct headwind. TC 360°, TAS 100 kn, wind 360° at 25 kn: SWC = 0, heading 360° (shown as 0°), GS = 100 − 25 = 75 kn. 150 nmi takes 2 h = 120 min; at 8 gal/h that is 16 gal.
A quartering headwind. TC 270°, TAS 150 kn, wind 300° at 30 kn: SWC = 0.2 × sin 30° = 0.1, WCA = 5.739° (right), heading 275.7°. GS = 150 × √0.99 − 30 × cos 30° = 149.2481 − 25.9808 = 123.267 kn.
Other questions people ask
How do you find the wind correction angle?
WCA = asin((wind speed ÷ true airspeed) × sin(wind direction − course)). Flying course 090° at 120 kn with wind from 360° at 20 kn: (20 ÷ 120) × sin(−90°) = −1/6, so WCA = −9.6°, a heading of 080.4°.
How do you calculate ground speed with wind?
GS = TAS × √(1 − SWC²) − wind speed × cos(wind direction − course), where SWC = (wind speed ÷ TAS) × sin(wind direction − course). A direct 25 kn headwind on a 100 kn airplane gives 75 kn.
What is an E6B?
The E6B is a circular slide rule flight computer. One side does time, speed, distance and fuel sums; the other side, the wind side, solves the wind triangle for heading and ground speed. The name comes from its US Army Air Corps part number.
Should I use true or magnetic directions?
Use true for the course and the wind when the wind comes from a winds aloft forecast, as here. Then apply magnetic variation to the true heading to get a magnetic heading.
Why does a crosswind lower ground speed?
To hold the course you point partly into the wind, so only TAS × cos(WCA) of your airspeed is along the course. A pure 20 kn crosswind on 120 kn costs about 1.7 kn of ground speed.
When is there no answer?
When the crosswind part of the wind is stronger than the airspeed, no heading holds the course; when the headwind is at least the airspeed, the aircraft makes no progress.