Formula and directions
For wind speed V and signed relative angle θ, crosswind = V sin θ and headwind = V cos θ. Positive crosswind comes from the pilot’s right; negative headwind is tailwind. Magnitudes are displayed with a separate direction. Default wind 15 knots from 270° and runway heading 180° produces 15 knots from the right and zero headwind. The reciprocal runway 36 has wind from the left.
Use wind direction and runway heading in the same north reference; do not mix true and magnetic bearings. The numeric heading determines the components. The optional designation supplies the diagram label and reciprocal number, including swapped L/R suffixes; a mismatch prompts a check. A blank designation is derived by rounding the heading to the nearest 10°, using 36 for north.
The diagram shows the runway axis in blue and wind source in green. Orange and pink separate the along-runway and crosswind projections. The wind blows from the green endpoint towards the centre. The diagram is normalised to direction, not speed; calm wind omits its components. Results and tables supply the magnitudes.
Aircraft limits have their own unit selector. One knot is exactly 1.852 km/h; conversions use that definition. Reciprocal crosswind magnitude and its distance from the limit are identical, while the side and headwind/tailwind signs reverse.
Why your number may differ
The reference site computes components in knots but labels the main values with the selected wind unit. We calculate and display components in the actual selected unit, converting the aircraft limit separately. Tiny sine or cosine rounding residues at cardinal angles become exact zero, so zero is not labelled as a headwind on one runway and tailwind on the other.
The illustrative bands use the reference thresholds: under 1, 1–10, over 10–20, over 20–30 and over 30 knots. These bands are not aircraft limitations. This tool is an educational vector calculation, not a takeoff or landing clearance. Check the aircraft manual, gusts, runway conditions and current operating procedures. The FAA airport operations guidance explains runway designations and airport operations.