Wind Correction Angle Calculator (Wind Triangle: Heading and Ground Speed)
The heading to fly or steer to hold a desired course in a crosswind, the drift correction angle and the resulting ground speed.
Results
What this tool does
A crosswind pushes you sideways, so to travel along your course you must point partly into the wind. The wind triangle gives the correction angle, asin(wind speed × sin(angle between wind and course) ÷ your own speed), and the ground speed that results. It is solved here for an aircraft, but the maths is the same for a boat crossing a current or a swimmer in a river: use the direction the current comes from. If the crosswind component is as large as your own speed, no heading holds the course, and the tool says so. Headwind is positive; a negative value is a tailwind.
Formula
WCA = asin(W × sin α ÷ V) · heading = course + WCA · GS = V × cos WCA − W × cos α (α = wind direction − course)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
va | Speed through the air or water | kt |
tk | Course you want to make good (degrees true) | ° |
wd | Direction the wind comes from (degrees) | ° |
ws | Wind speed | kt |
HD | Heading to steer (degrees) | ° |
WC | Wind correction angle (+ = to the right) | ° |
GS | Ground speed | kt |
HW | Headwind component | kt |
CW | Crosswind component (+ = from the right) | kt |
OK | Can the course be held? | — |
Worked example
- Speed through the air or water110 kt
- Course you want to make good (degrees true)90 °
- Direction the wind comes from (degrees)150 °
- Wind speed20 kt
- Heading to steer (degrees)99 °
- Wind correction angle (+ = to the right)9.1 °
- Ground speed99 kt
- Headwind component10.0 kt
- Crosswind component (+ = from the right)17.3 kt
- Can the course be held?Yes
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.