Wind Correction Angle Calculator

What the wind correction angle calculator does

To fly a straight path in a crosswind, an aircraft must angle slightly into the wind. This calculator finds that angle, the wind correction angle, from the aircraft's true airspeed, its intended course, and the wind's speed and direction, and it also gives the heading the pilot must actually fly.

Below is what the wind correction angle is, the equation behind it, how heading differs from course, and a worked example.

How to use it

1. Enter the true airspeed and the intended course, the direction you want to travel.
2. Enter the wind speed and the wind direction, the direction the wind is coming from.
3. Press Calculate for the wind correction angle and the required heading, or Reset to clear them.

What the wind correction angle is

When an aircraft flies through moving air, the wind pushes it sideways off its intended path. To compensate, the pilot points the aircraft's nose slightly into the wind, so that the sideways push of the wind exactly cancels the sideways drift, and the aircraft tracks straight along its desired route. The angle between where the nose points and where the aircraft actually travels is the wind correction angle, sometimes called the crab angle, because the aircraft moves somewhat sideways like a crab.

This correction is a fundamental part of air navigation. Without it, a crosswind would steadily blow an aircraft off course, so that a pilot aiming straight at a destination would end up far to one side. By calculating the wind correction angle before or during a flight, a pilot knows exactly how much to angle into the wind to stay on track. The same idea applies to boats crossing a current and even to swimmers, but it is most precisely used in aviation, and this calculator computes it.

The equation it uses

The wind correction angle comes from balancing the sideways component of the wind against the aircraft's airspeed:

WCA = arcsin(wind speed × sin(wind angle) ÷ true airspeed)

Here the wind angle is the angle between the wind and the aircraft's course, so that wind speed times the sine of that angle is the crosswind, the part of the wind blowing sideways across the path. Dividing the crosswind by the true airspeed and taking the inverse sine gives the angle the aircraft must turn into the wind. The required heading is then the course adjusted by this correction. The calculator works out the wind's angle relative to the course from the directions you enter, then applies this relationship.

Heading versus course

Two directions are easy to confuse but crucial to keep separate in navigation. The course, sometimes called the track, is the direction the aircraft actually travels over the ground, the path from start to destination. The heading is the direction the aircraft's nose points. In still air the two are identical, but in any crosswind they differ, and the wind correction angle is precisely the gap between them.

This is why a pilot in a crosswind appears to fly slightly sideways, the nose aimed off to one side of the actual direction of travel. To a passenger it can look as though the aircraft is pointed the wrong way, yet it is tracking perfectly toward its destination. The calculator gives both numbers: the wind correction angle, which is how much to crab, and the heading, which is the compass direction the pilot actually steers to make good the intended course. Knowing the heading is what lets a pilot set the aircraft up correctly for the wind.

Why only the crosswind matters

The wind correction angle depends only on the sideways part of the wind, the crosswind, not on the whole wind. A wind blowing straight along your path, whether a headwind slowing you or a tailwind speeding you, pushes you forward or back but never sideways, so it needs no correction angle at all. Only wind blowing across your path drifts you off course and must be corrected for.

This is why the formula uses the sine of the wind's angle, which picks out exactly the sideways component. A wind directly ahead or behind has no sideways component and produces no correction, while a wind blowing straight across your path is entirely crosswind and demands the largest correction. Most real winds are somewhere in between, partly along the path and partly across it, and the calculator extracts just the crosswind part to find the angle. The stronger the crosswind relative to your airspeed, the larger the angle you must crab into it.

Units and precision

The calculator takes the true airspeed and wind speed in knots, the standard unit in aviation, and the course and wind direction in degrees, with wind direction given as the direction the wind blows from, following aviation convention. It returns the wind correction angle and the required heading in degrees. The calculation is an exact application of the navigation triangle, and results are given to a fraction of a degree.

A worked example

Suppose an aircraft has a true airspeed of 100 knots and wants to fly a course due east, while a 20-knot wind blows from the south, straight across the path.

The crosswind is the full 20 knots, so the wind correction angle is WCA = arcsin(20 ÷ 100) ≈ 11.5 degrees, meaning the aircraft must point its nose about 11.5 degrees into the wind. The required heading is the course adjusted by this amount. If the same wind were blowing partly along the path rather than straight across, only its sideways component would count, and the correction angle would be smaller.

Questions people ask

How do you calculate the wind correction angle?

Use WCA = arcsin(crosswind ÷ true airspeed), where the crosswind is the sideways component of the wind. Dividing it by the airspeed and taking the inverse sine gives the angle.

What is the difference between heading and course?

Course is the direction you actually travel over the ground; heading is the direction the nose points. In a crosswind they differ by the wind correction angle.

Why do aircraft fly slightly sideways in wind?

To counter a crosswind. By pointing the nose into the wind by the correction angle, the aircraft cancels the sideways drift and tracks straight toward its destination.

Does a headwind need a correction angle?

No. A headwind or tailwind blows along your path and only affects your speed, not your direction. Only a crosswind drifts you sideways and needs a correction angle.

References

A quick note on where this comes from. The wind correction angle and the navigation triangle are standard air navigation, set out in the Federal Aviation Administration's Pilot's Handbook of Aeronautical Knowledge. The relationship is the same one mechanized by the classic E6B flight computer. The trigonometry follows standard vector navigation.

1. Federal Aviation Administration (FAA), Pilot's Handbook of Aeronautical Knowledge, Navigation. https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak
2. FAA, Aeronautical Chart Users' Guide and navigation principles. https://www.faa.gov/air_traffic/flight_info/aeronav
3. Wikipedia, E6B and the wind triangle. https://en.wikipedia.org/wiki/E6B