Crosswind Component Formula — How It Works

The Formula

All crosswind calculations reduce to a single trigonometric decomposition. Given:

• W = wind speed (kts, mph, km/h, or m/s)
• θ = wind direction in degrees (direction wind is FROM)
• R = runway heading in degrees

The angle between them:

α = (θ − R + 360) mod 360

Then:

Crosswind = W × sin(α)
Headwind  = W × cos(α)

α stays in the range 0°–360°, which preserves left/right and headwind/tailwind sign naturally.

Sign Conventions

Example: α = 270° → sin(270°) = −1 (full left crosswind), cos(270°) = 0 (no headwind component).

Gust Components

METARs report gusts as a second speed: 180° at 12G22 means steady 12, gust 22. The formula is applied twice — once with steady speed, once with gust speed — using the same angle. The gust crosswind is the relevant number for go/no-go decisions because it is the peak instantaneous load on the aircraft during the approach.

Runway Number to Heading Conversion

Runway numbers are magnetic headings divided by 10, rounded to the nearest 10°. Runway 27 = 270° magnetic. Runway 09 = 090°. Runway 36 = 360° (treated as 0° in calculations).

The opposite runway is always runway number ± 18, corresponding to a heading difference of exactly 180°.

Angle of Incidence and the Clock Method

Pilots use the “clock method” as a mental approximation. It maps sin() to easy fractions:

The approximation error is small enough to be operationally useful. A 30° crosswind angle at 20 kts gives exactly 10 kts crosswind; the clock method says ½ × 20 = 10 — exact in this case.

Unit Conversions Used

The calculator converts all inputs to knots internally, then converts outputs back to the selected unit.