Wind Correction Angle Calculator

What Is a Wind Correction Angle Calculator?

The wind correction angle (WCA) is the angle a pilot must turn the aircraft into the wind so the ground track stays on the desired course. Without it, a crosswind pushes the aircraft sideways and it drifts off track. The Wind Correction Angle Calculator returns the WCA, the heading to fly, and the resulting ground speed from true airspeed, wind speed, and wind direction.

How the Calculation Works

The wind triangle relates course, heading, and wind. First the wind angle is formed from the course and the direction the wind blows from:

$$\delta = \alpha - \left(180^\circ + \beta\right)$$

The wind correction angle then follows from the sine rule, and the heading adds the correction to the course. Ground speed comes from the law of cosines:

$$\theta = \arcsin\!\left(\frac{WS}{TAS} \sin \delta\right)$$

$$\psi = \alpha + \theta, \qquad GS = \sqrt{TAS^2 + WS^2 + 2\,TAS\,WS\cos\!\left(\psi - (\beta + 180^\circ)\right)}$$

Where:

• α is the desired course in degrees clockwise from north
• β is the wind direction the wind blows from, in degrees
• WS is wind speed in knots
• TAS is true airspeed in knots
• δ is the wind angle, θ is the wind correction angle, and ψ is the heading

Worked Example

An aircraft flies at 100 knots on a course of 090° with a 20 knot wind from 045°. The wind angle is 90 − 225 = −135°, so the WCA is arcsin((20/100) × sin(−135°)) = −8.1°. The heading is 081.9°, crabbed into the wind, and the ground speed is about 84.9 knots because the wind has a headwind component.

For related aviation tools, see the True Airspeed Calculator, Wing Loading Calculator, and Weight on Other Planets Calculator.