Crosswind calculator

A runway takes only the part of the wind that lies along it. The rest pushes the aeroplane sideways, and that part has a name, a number and a limit. This page splits a wind into the two: how much of it is headwind or tailwind, and how much of it is crosswind. There is no chart to read off and no scale to squint at — the answer is the same trigonometry the chart was drawn from. What it cannot tell you is whether the number is acceptable. That figure lives in the flight manual of the aeroplane you are about to fly, it is different for every type, and this page has never seen it. Everything is worked out in your browser; nothing is fetched and nothing is sent anywhere.

How it is calculated

angle = |wind − runway heading| · crosswind = speed × sin(angle) · headwind = speed × cos(angle)

The runway number is its magnetic heading in tens of degrees, so runway 27 points 270 degrees and runway 9 points 090. Subtract that from the direction the wind is blowing from and you have the angle between them. The sine of that angle times the wind speed is the crosswind; the cosine times the speed is the component along the runway, which is a headwind while the angle is under 90 degrees and a tailwind once it passes it. The one trap is the reference direction: the runway number and the wind the tower reads out are magnetic, while the wind written in a METAR or a TAF is true. Feed this page two directions measured from the same north.

Source: FAA AC 150/5300-13 CHG 6, Appendix 1, paragraph 2, Crosswinds — "The crosswind component of wind direction and velocity is the resultant vector which acts at a right angle to the runway. It is equal to the wind velocity multiplied by the trigonometric sine of the angle between the wind direction and the runway direction"

Questions people ask

The METAR says 210 and the tower says 200. Which one do I use?

Whichever you like, as long as the runway number is measured from the same north — and it is magnetic. The runway number is the nearest ten-degree increment of the magnetic azimuth of the centreline, and the wind the tower gives you is magnetic too, so those two go together without any arithmetic. A METAR or a TAF is not: the FAA and NWS key to the two codes calls that group a "3 digit true-north direction". Where the local variation is a few degrees the difference is lost in the rounding; where it is fifteen or twenty it is a real error, and you have to move the written wind by the variation before comparing it with a runway number.

What crosswind can I actually take?

This page does not know, and neither does any other calculator. Certification only requires an aeroplane to be shown controllable in a 90-degree crosswind of two tenths of its stalling speed, and the figure that came out of that test is placarded and printed in the flight manual for your particular type. It is a demonstrated value rather than a legal ceiling on most light aeroplanes, but it is the only number with any authority behind it, and your own currency sits below it.

Why is the answer a tailwind?

Because the wind is behind you: the angle between the wind and the runway is more than 90 degrees, so the cosine goes negative. The page shows the size of it and calls it a tailwind rather than printing a minus sign you might miss. If that is unexpected, check the reciprocal runway — the same wind on runway 09 instead of 27 turns the same number back into a headwind.

Should I use the mean wind or the gust?

Work out both. The mean tells you what the approach will feel like; the gust tells you what the aeroplane has to survive in the flare, and it is the gust that gets compared against a limit. A report of 21016G28KT is two calculations, not one, and the second is the one that decides whether you go.

Does the runway number always give the exact heading?

No, and that is by design. The number is rounded to the nearest ten degrees, so runway 18 might point anywhere from 175 to 184 degrees magnetic — and it drifts, because magnetic north moves and runways are renumbered years after the fact. For a crosswind estimate the rounding is harmless. If you want the published centreline to the degree, it is in the aerodrome chart, not in the number painted on the threshold.

Why are the components not simply added up?

Because they are at right angles to each other. A 20-knot wind 60 degrees off the runway gives 10 knots of headwind and about 17 knots of crosswind, and 10 plus 17 is not 20 — the two sides of a right-angled triangle only add up through their squares. That is also why a wind almost down the runway can still carry a crosswind worth respecting.

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