The sine/cosine formula, the pilot’s clock rule of thumb, and what “maximum demonstrated crosswind” actually means for your go/no-go call.
Wind rarely blows straight down the runway. Whatever direction it comes from, you can split it into two parts: the headwind component (along the runway, which shortens your ground roll) and the crosswind component (across the runway, which pushes you sideways and is the part that demands rudder, aileron, and proficiency).
The split depends entirely on the angle between the wind and the runway. A wind straight down the runway is all headwind, no crosswind. A wind 90° to the runway is all crosswind. Everything in between is a mix — and the math below tells you exactly how much of each.
First find the wind angle (the difference between the wind direction and the runway heading), then split the wind with sine and cosine.
Runway heading is the runway number × 10 (Runway 09 = 090°). Subtract the wind direction from it (or vice-versa) and take the difference.
Crosswind = wind speed × sin(angle)
Headwind = wind speed × cos(angle)
Given
Runway heading: 090°
Wind: 120° at 20 kt
Angle: 120 − 90 = 30°
Work
Crosswind = 20 × sin 30° = 10 kt
Headwind = 20 × cos 30° ≈ 17 kt
Clock rule: 30° = half → 10 kt
Crosswind ≈ 10 kt, headwind ≈ 17 kt
Pilots estimate crosswind in their head with the clock rule: read the wind angle like minutes on a clock and take that fraction of the wind speed.
15°
¼
a quarter of the wind speed
30°
½
half the wind speed
45°
¾
about 70% of the wind speed
60°+
all
treat as the full wind speed
Your POH lists a maximum demonstrated crosswind component — the strongest crosswind a test pilot proved during certification. It is not a regulatory limit, but exceeding it puts you beyond what the manufacturer demonstrated and likely beyond your own practiced skill.
Decide with three numbers together: the computed crosswind, the POH demonstrated value, and the gust spread. Then cross-check the whole picture in Go / No-Go.
FlightKit’s crosswind calculator pulls live winds for your airport and gives you the crosswind and headwind components for every runway — and flags any that are closed.
The crosswind component is the part of the wind that blows across the runway, perpendicular to your direction of travel. The rest of the wind is the headwind (or tailwind) component, blowing along the runway. You care about the crosswind because it is what pushes the airplane sideways during takeoff and landing.
Find the angle between the wind and the runway, then: crosswind = wind speed × sine(angle), and headwind = wind speed × cosine(angle). Example: a 30° angle with a 20-knot wind gives a crosswind of 20 × sin 30° = 10 knots and a headwind of 20 × cos 30° ≈ 17 knots. A crosswind calculator or a wind-component chart does this instantly.
Treat the wind angle like minutes on a clock face: 15° ≈ a quarter of the wind, 30° ≈ a half, 45° ≈ three-quarters, and 60° or more ≈ the full wind speed as crosswind. It is close enough for a quick mental check in the run-up area before you commit to a runway.
It is the strongest crosswind a test pilot demonstrated during the aircraft’s certification, published in the POH. It is not a regulatory limitation — but it is a strong guideline, and exceeding it means you are operating beyond what the manufacturer proved and your own demonstrated skill. Treat it, your personal minimums, and gusts together when deciding.
Runway numbers and tower/ATIS winds are referenced to magnetic north, so they match directly. Winds in a METAR or a forecast are referenced to true north. If you mix the two, correct for local magnetic variation first, or the angle — and your crosswind — will be off.
There is no universal number — it depends on the aircraft, your proficiency, the gust spread, and the runway. Build a personal-minimums crosswind limit, check it against the POH max demonstrated value, and add margin for gusts. When in doubt, pick a more favorable runway or wait.