Crosswind & Headwind Calculator
The clock rule reads high on crosswind, which is the safe direction — and fails completely on headwind, because cos is flat near zero.
The clock rule against the trigonometry
Why the same idea fails for headwind
Best runways for this wind
The clock rule works for crosswind and fails for headwind — and there's a reason
Taking the crosswind fraction as angle ÷ 60, capped at one, it never under-estimates by more than 4.5% — and only below 30°. That bound is exact rather than sampled: as the angle shrinks the ratio tends to (1/60)·(180/π) = 3/π = 0.955. Above 30° it always over-estimates, by up to 15.5% at 60°. Reading high on crosswind is the conservative error, which is why the rule has survived without anyone minding that it's wrong.
The same linear idea applied to headwind fails catastrophically. Taking the headwind fraction as 1 − angle/60 is 42% low at 30°, and at 60° it says zero where the truth is half the wind. Nobody teaches it that way — and this is why.
The reason explains both at once. Near zero, sin(x) ≈ x — genuinely linear — so a linear crosswind rule tracks it. But cos(x) ≈ 1 − x²/2 is flat near zero, so no linear rule can approximate it. Halve the angle and 1−cos quarters while x−sin eighths: the two components behave differently by a whole order, and the folklore covers only the tractable one.
Which gives the consequence people find surprising: a wind 30° off the nose costs only 13% of the headwind while contributing half the wind as crosswind. Turning 30° away from the wind to use a longer or better runway is far cheaper in headwind terms than it feels — the headwind you give up is almost nothing until well past 30°.
- The limit applies to the gust, not the average. A 15G25 wind at 40° gives 9.6 kt of steady crosswind and 16.1 in the gust — 67% higher, and past a 15 kt figure the steady wind clears easily.
- A demonstrated crosswind component is not a limit for most light aircraft. It's the strongest crosswind available during certification, flown by a test pilot — a statement about the weather that week rather than the aeroplane. And it says nothing about your own currency.
- Runway numbers are magnetic; forecast winds are usually true. Tower and ATIS winds are magnetic and compare directly; a TAF is true and needs variation applied. Where variation runs to 20°, using the wrong one moves the crosswind by a third.
- A tailwind costs about 4.5× what the same headwind saves — roughly 10% more distance per 2 kt of tail against 10% less per 9 kt of head. That asymmetry is why the downwind runway so rarely pays.
How to use
- Check whether the wind is magnetic or true before comparing it to a runway.
- Work the crosswind from the gust, not the steady wind.
- Remember 30 degrees off costs almost no headwind.
- Treat a demonstrated component as guidance, not a limit.
Frequently asked questions
What is the clock rule for crosswind?
Take the angle between the wind and the runway, divide by 60, and multiply by the wind speed — capping the fraction at one. Fifteen degrees gives a quarter, thirty gives a half, forty-five gives three quarters and sixty or more gives the whole wind. It is a linear stand-in for the sine, and it is good enough to do in your head on the downwind leg.
How accurate is the clock rule?
Better than it has any right to be, and wrong in the safe direction where it matters. Below thirty degrees it reads slightly low, never by more than 4.5 per cent — a bound that is exact rather than sampled, since the ratio tends to three over pi as the angle shrinks. Above thirty it always reads high, by up to 15.5 per cent at sixty degrees.
Why does the clock rule not work for headwind?
Because a linear rule can approximate a sine near zero and cannot approximate a cosine. Taking the headwind fraction as one minus angle over sixty is 42 per cent low at thirty degrees, and at sixty it says zero where the truth is half the wind. Nobody teaches it that way, and the reason is worth knowing rather than just the fact.
Why do crosswind and headwind behave so differently at small angles?
Because sin(x) is approximately x near zero — genuinely linear — while cos(x) is approximately one minus x squared over two, which is flat. Halve the angle and the departure from flat quarters, while the departure from linear eighths. The two components differ by a whole order of approximation, which is why one has a usable rule of thumb and the other does not.
How much headwind do I lose by using a crosswind runway?
Far less than it feels. A wind thirty degrees off the nose still gives 87 per cent of its speed as headwind while contributing half as crosswind — so turning thirty degrees away costs about a tenth of the headwind. Even at forty-five degrees you keep 71 per cent. Choosing a longer or better runway slightly off the wind is usually cheaper than the numbers suggest.
Should I use the steady wind or the gust for crosswind?
The gust, because that is what upsets the aeroplane. A 15G25 wind at forty degrees off gives 9.6 knots of steady crosswind and 16.1 in the gust — 67 per cent higher. A fifteen knot demonstrated figure clears the average comfortably and is exceeded by the gust, which is exactly the case that catches people out.
Is the demonstrated crosswind component a limit?
For most light aircraft, no. It is the strongest crosswind that happened to be available during certification flying, demonstrated by a test pilot — a statement about the weather that week rather than about the aeroplane capability. Some types do have a genuine limitation and the flight manual says which. Either way it says nothing about your own currency, which usually matters more.
Are runway numbers magnetic or true?
Magnetic, which matters because forecast winds often are not. A tower or ATIS wind is magnetic and compares to the runway directly, but a TAF or area forecast is true and needs the local variation applied first. Where variation runs to twenty degrees or more, using the wrong one moves the calculated crosswind by roughly a third.
How much does a tailwind cost compared with a headwind?
About four and a half times as much per knot. The usual figures are ten per cent more distance per two knots of tailwind against ten per cent less per nine knots of headwind. That asymmetry is why a downwind departure so rarely repays the taxi it saves, and why a light tailwind on a marginal strip is a much bigger problem than the same wind on the nose is a help.
Which runway should I choose in a crosswind?
Usually the one with the least crosswind, but not always. Since thirty degrees off costs only thirteen per cent of the headwind, a runway that is longer, wider, better lit or has a clearer approach can be worth several degrees of extra crosswind. Work out the components for each rather than assuming the most into-wind runway is automatically right.
How do I work out the angle between the wind and the runway?
Subtract one from the other and take whichever way round gives less than 180 degrees. A runway 27 is a heading of 270, and a wind from 310 is 40 degrees off. The wind is from the right if the difference is positive going clockwise, which decides which way to hold aileron — the magnitude decides how much.
What is a gust factor and how should I use it?
The difference between the steady wind and the gust, and a common practice is to add half of it to the approach speed. A 15G25 wind has a ten knot gust factor, so five knots on the approach speed. That extra speed lengthens the landing roll, which is why gusty conditions squeeze both ends of the problem — more speed to control the aeroplane, less runway to stop it in.
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