The crosswind component formula

The formula

Angle, Δ

wind direction − runway heading

Crosswind

wind speed × sin Δ

Headwind

wind speed × cos Δ

The wind direction is where the wind blows from. The runway heading is the runway number times ten. Use the same kind of degrees for both (magnetic, for a runway number and a tower wind; see METAR wind and your runway).

Why sine and cosine

The wind is one arrow. Split it into a part along the runway and a part across it, and you have a right triangle with the wind as the long side. The Airplane Flying Handbook puts the two parts like this:

It has a headwind component acting along the airplane’s ground track and a crosswind component acting 90° to its track. [AFH p. 9-18]

The part along the runway is next to the angle, so it is the speed times the cosine. The part across it is opposite the angle, so it is the speed times the sine.

Step 1: find the angle

Subtract the runway heading from the wind direction. If the answer is more than 180, subtract 360; if it is −180 or lower, add 360. The angle then always lands between −180° and 180°, with 180° itself included.

Example: wind from 010° on runway 33 (heading 330°). 10 − 330 = -320, and adding 360 gives 40°. The wind is 40° off the nose, to the right.

Step 2: which side

A positive angle means the wind is on the right of the nose, a negative angle on the left. A crosswind of zero has no side.

Step 3: headwind or tailwind

The cosine is positive while the angle is under 90° either way, so the wind is in your face. Past 90° the cosine is negative and the headwind is a tailwind of the same size. At exactly 90° there is neither, only crosswind.

A worked example

Wind 300° at 20 knots, runway 27. Angle = 300 − 270 = 30°.

• Crosswind = 20 × sin 30° = 20 × 0.5000 = 10.0 knots, from the right.
• Headwind = 20 × cos 30° = 20 × 0.8660 = 17.3 knots.

More cases, including a left crosswind, a tailwind and a gust, are on the worked examples page.

Three angles worth knowing

At 0° the crosswind is none and the headwind is all of the wind. At 30° the crosswind is exactly half the wind speed, because sin 30° = 0.5. At 90° the crosswind is all of it. The crosswind component chart has the values in between.

Try it

The calculator does these three steps, with the gust and the side, for any wind and runway.