Split the wind into two components
Any wind hitting a runway at an angle splits into two parts. The crosswind pushes across the runway and uses the sine of the angle; the headwind (or tailwind) runs along it and uses the cosine. Here θ is the angle between the wind direction and the runway heading, taking the shorter way round if it exceeds 180°.
Crosswind by wind angle
The crosswind is a fixed fraction of the total wind for each angle. A useful mental anchor: at 30° you get half, at 45° about 70%, and by 60° nearly all of it.
| Angle θ | Crosswind (sin) | Headwind (cos) |
|---|---|---|
| 0° | 0% of wind | 100% of wind |
| 15° | 26% | 97% |
| 30° | 50% | 87% |
| 45° | 71% | 71% |
| 60° | 87% | 50% |
| 90° | 100% | 0% |
Example: a 20-knot wind 45° off the runway gives 20 × 0.71 ≈ 14 knots of crosswind and 14 knots of headwind at the same time.
Headwind, tailwind and the sign
- Angle under 90° means the wind has a component toward you — a headwind, which shortens landing and lengthens takeoff.
- Angle over 90° means the along-runway part points with the aircraft — a tailwind, usually limited to about 10 knots for landing.
- Wind direction is where it comes from. "Wind 270°" blows from the west toward the east; get this backwards and the whole split flips.
Common questions
How do I calculate the crosswind component?
Multiply the wind speed by the sine of the angle between the wind and the runway. At a 30-degree angle, sine is 0.5, so a 20-knot wind gives a 10-knot crosswind. The rest of the wind acts along the runway as headwind or tailwind.
What is the difference between crosswind and headwind?
Crosswind is the part of the wind blowing across the runway, found with sine of the angle. Headwind is the part blowing straight down it toward you, found with cosine. At 90 degrees the wind is all crosswind; at 0 degrees it is all headwind.
Why do pilots prefer a headwind for landing?
A headwind lowers the aircraft ground speed, so it slows down and stops in less runway. A tailwind does the opposite and needs more room, which is why most aircraft cap tailwind at about 10 knots for landing.
