How to Find the Crosswind Component (and the Headwind)

Before landing, pilots compare the wind with the runway. The part of the wind straight down the runway is the headwind (or tailwind), and the part blowing across it is the crosswind component. Every airplane’s handbook gives a maximum demonstrated crosswind.

For learning only. This lesson is for studying and ground-school work, not for planning a real flight. Use official weather, charts and flight-planning tools, and the numbers in your aircraft’s handbook (POH).

Try it with your own problem ↓

The steps

Turn the runway number into a direction by adding a zero: runway 27 points 270°, runway 9 points 090°.
Find the angle between the wind and the runway: wind direction − runway direction. Use the smaller angle (at most 180°).
Crosswind = wind speed × sin(angle). It comes from the side the wind is on.
Headwind = wind speed × cos(angle). If the angle is more than 90°, the answer is negative: a tailwind.
Round to whole knots. With gusts, work out the crosswind for the gust speed too.

A worked example

You are landing on runway 27. The tower reports the wind from 310° at 20 knots. Find the crosswind and headwind components.

Runway 27 points 270°.
Angle: 310° − 270° = 40°. A plus angle means the wind is from the right.
Crosswind: 20 × sin 40° = 20 × 0.6428 = 12.86, about 13 kt from the right.
Headwind: 20 × cos 40° = 20 × 0.766 = 15.32, about 15 kt.
Check: √(15.32² + 12.86²) = 20, the whole wind. ✓

About 13 knots of crosswind from the right and a 15 knot headwind.

Why it works

The wind is an arrow that can be split into two arrows at right angles: one along the runway and one across it. Those two parts and the wind make a right triangle, with the wind as the hypotenuse. SOH CAH TOA gives the parts: the side opposite the angle is wind × sin, and the side next to it is wind × cos.

Try it with your own problem

Open The Flight Computer (free) with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: runway 27, wind 310° at 20 ktOpens The Flight Computer with this example

Or try these

More aviation math, every step written out: open The Flight Computer.

Common mistakes

Comparing a METAR wind with a runway number. Tower and ATIS winds are magnetic, like runways, but METAR and TAF winds are true. Convert first.
Swapping sine and cosine. Crosswind uses sine. At 0° there is no crosswind (sin 0° = 0), and at 90° it is all crosswind (sin 90° = 1).
Forgetting the gusts. With a wind of 20 gusting 30, the crosswind in the gusts is bigger. Check that against the airplane’s limit.
Missing a tailwind. An angle over 90° means the wind is from behind, which makes the landing roll longer. The other end of the runway is usually better.

Questions people ask

What is the clock rule for crosswind?

Read the angle as minutes on a clock: 15° is a quarter of the wind, 30° is half, 45° is three-quarters, and 60° or more is all of it. For 40°, about two-thirds of 20 kt is 13 kt.

What does runway 27 mean?

The runway points about 270° magnetic: the number is the direction divided by 10 and rounded. The other end of the same strip is runway 9 (090°).

What if the wind is from 360° at 15 knots on runway 27?

The angle is 90°, so it is all crosswind: 15 × sin 90° = 15 kt from the right, and no headwind.

Keep learning

Show The Steps is free, with no accounts or ads, and everything is worked out in your own browser. Start at the home page.