Formula
The crosswind is the part of the wind blowing across the runway. The headwind is the part blowing down it. FAA flying handbooks draw this as one right triangle.
angle = wind direction − runway heading
crosswind = wind speed × sin(angle)
headwind = wind speed × cos(angle)
The angle is wrapped to sit between −180 and 180. Positive means the wind is from the right. Runway 36 is heading 0. A cosine below zero is a tailwind.
Worked examples
Runway 27, wind 300 at 20. Heading 270. Angle +30°. Crosswind = 20 × sin 30° = 10, from the right. Headwind = 20 × cos 30° = 17.32.
Runway 18, wind 360 at 15. The wind is on the tail. Crosswind is 0. Tailwind is 15.
Reference
A 20 knot wind, for an angle off the nose. The components are in the same unit as the wind. At 90 degrees the crosswind is the whole wind and the headwind is zero.
| Angle | Crosswind | Headwind |
|---|---|---|
| 15° | 5.18 kt | 19.32 kt |
| 30° | 10 kt | 17.32 kt |
| 45° | 14.14 kt | 14.14 kt |
| 60° | 17.32 kt | 10 kt |
| 90° | 20 kt | 0 kt |
Questions
How do you calculate a crosswind component?
Crosswind = wind speed × sin(wind direction − runway heading). Headwind = wind speed × cos(that angle). Runway 27 is heading 270. Wind from 300 at 20 knots is 30 degrees off the nose, 10 knots of crosswind from the right, and 17.3 knots of headwind.
Is the wind the direction it is going, or coming from?
Coming from. That is how a METAR and an ATIS say it. Wind 300 at 20 is arriving from 300 degrees. A positive angle on this page is wind from the right of the nose.
What is runway 36?
Heading 360, which is the same as 0. The runway number is the heading divided by 10, and 36 wraps to north. You can also type a heading directly if you are not on a numbered runway.
Does the unit of wind speed matter?
The trigonometry does not. Knots in, knots out. The menu converts the number when you change units, so a 20 knot wind becomes about 23 mph, not a different wind.
Sources
- FAA Pilot’s Handbook of Aeronautical Knowledge and Airplane Flying Handbook. Crosswind component = wind × sin(angle). Headwind = wind × cos(angle). Wind is the direction it comes from.