# E6B: heading and ground speed?

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.

- Page: https://www.acalculator.org/physics/e6b-calculator
- JSON spec: https://www.acalculator.org/physics/e6b-calculator.json
- Version: a92e24af3d9d

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| tc | True course | The course over the ground you want to fly, in degrees true (0 to 360). |
| tas | True airspeed | The aircraft’s true airspeed. |
| wd | Wind direction | The direction the wind blows from, in degrees true (winds aloft are true). |
| ws | Wind speed | The wind speed. |
| d | Distance | The distance of the leg, for the time en route. Leave empty to skip. |
| ff | Fuel burn per hour | Fuel used per hour in any unit (gal, L, lb), for the fuel for the leg. Leave empty to skip. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| heading | True heading | The heading to fly: true course + wind correction angle, 0 to 360. |
| groundSpeed | Ground speed | The speed over the ground. |
| wca | Wind correction angle | Degrees to turn into the wind: positive to the right of the course, negative to the left. |
| correction | Correct | Which way to turn from the course into the wind. |
| headwind | Headwind | The wind along the course: WS × cos(WD − course); negative is a tailwind. |
| crosswind | Crosswind | The wind across the course: WS × \|sin(WD − course)\|. |
| minutes | Time en route | Distance ÷ ground speed, in minutes. |
| fuelUsed | Fuel for the leg | Fuel burn per hour × time en route, in the fuel unit you typed. |

## 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.

## Assumptions

- 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

1. tc = 90, tas = 61.733333, wd = 0, ws = 10.288889, d = 277,800 gives wca = -9.594068, heading = 80.405932, groundSpeed = 60.869888, headwind = 0, minutes = 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).
2. tc = 360, tas = 51.444444, wd = 360, ws = 12.861111, d = 277,800, ff = 8 gives wca = 0, heading = 0, groundSpeed = 38.583333, headwind = 12.861111, minutes = 120, fuelUsed = 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).
3. tc = 270, tas = 77.166667, wd = 300, ws = 15.433333 gives wca = 5.73917, heading = 275.73917, groundSpeed = 63.414205. 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).

## FAQ

### 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.

## Sources

- Ed Williams, Aviation Formulary V1.47, in-flight wind calculations (heading and ground speed from course, TAS and wind), retrieved 2026-10-05. https://edwilliams.org/avform147.htm
- Wikipedia, E6B: the flight computer, its wind side and the wind correction angle formula, retrieved 2026-10-05. https://en.wikipedia.org/wiki/E6B
- NIST Special Publication 811 (2008), Appendix B.8: 1 nautical mile = 1,852 m, 1 knot = 1,852 m/h, retrieved 2026-10-05. https://www.nist.gov/pml/special-publication-811