Crosswind Calculator – Crosswind and Headwind, Before You Fly

See the wind split into two parts

One wind becomes two components: the part across the runway pushes you sideways, and the part along the runway helps or hurts your takeoff and landing roll. The compass shows the runway heading and where the wind comes from; the bars show how big each part is next to the full wind speed.

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How it works

Understand the result

One wind, two components

A wind is a single speed and direction. A runway only cares about two parts of it: the part across it and the part along it.

The split is a sine and a cosine of the same angle. The angle is the relative angle between the wind direction and the runway heading. Crosswind equals wind speed times sin of the relative angle, and the along-runway component equals wind speed times cos of the same angle. A positive along-runway value is a headwind and a negative one is a tailwind of the same size, as the page’s own FAQ explains. At the defaults, a 20 kt wind from 120 degrees on a runway heading of 90 degrees gives a relative angle of 30 degrees, a crosswind of 10.00 kt from the right, and a headwind of 17.32 kt. The sine of 30 degrees is 0.5, so the crosswind is exactly half the wind speed, and the cosine of 30 degrees is about 0.866, so the headwind is about 87 percent of the wind speed. The two components are not two separate winds; they are one wind described in runway coordinates, and their squares add back to the square of the wind speed.

Every figure in that table was produced by this page’s own calculator and is quoted exactly as displayed. The pure cases are the ones to memorise, because they anchor the whole table. At 90 degrees the entire wind is crosswind and there is no headwind at all. At 0 degrees the entire wind is headwind and there is no crosswind. At 180 degrees the entire wind is a tailwind and there is still no crosswind, which surprises people who expect a tailwind to somehow also push sideways. It does not: a wind exactly along the runway has no across component, whichever way along the runway it blows. The doubling row shows the linearity that makes mental checks easy: doubling the wind speed from 20 kt to 40 kt doubles both components exactly, from 10.00 kt to 20.00 kt of crosswind and from 17.32 kt to 34.64 kt of headwind, because both formulas are the wind speed times a fixed sine or cosine.

The left case needs a careful reading, because the display carries a sign as well as a side. With direction 60 and runway 90, the calculator shows -10.00 kt from the left, with a relative angle of 330 degrees and the same headwind of 17.32 kt as the default case. The geometry is the mirror image of the default: the same 30-degree offset, but on the other side of the runway, so the crosswind pushes from the left instead of the right. The negative sign and the word “left” say the same thing in two ways, and the relative angle of 330 degrees is the page’s way of reporting a 30-degree offset on the left side within a 0-to-360-degree circle, rather than as minus 30 degrees. Neither the sign nor the 330-degree figure is an error; both are the page’s consistent convention for the left side, and the headwind is unchanged because the cosine is the same for a 30-degree offset on either side.

Wind direction: from, not towards

The most common crosswind mistake is reading the direction backwards, and it reverses left and right.

Wind direction is where the wind comes from, measured in degrees clockwise from north, as the page’s own FAQ states. A direction of 120 degrees means the wind comes from between east (90 degrees) and south (180 degrees). It does not mean the wind blows towards 120 degrees. If you enter the towards direction by mistake, you will be 180 degrees out, and the calculator will give you the crosswind for the opposite wind: the side will flip, and a headwind will become a tailwind. The numbers will still look plausible, because the opposite wind has the same crosswind magnitude at a mirrored angle, which is exactly why the mistake survives unnoticed. The check is simple: say the direction as “wind from 120” before typing it, and make sure the “from” is in the sentence.

Runway heading works the same way, as a compass direction in degrees. A runway heading of 90 degrees points east. In everyday aviation talk that runway would be called runway 09, because runway numbers are the heading divided by ten, but this calculator asks for the heading in degrees, so 90 is what you type, not 09. The relative angle is then the difference between the wind direction and the runway heading, wrapped into a full circle. Direction 120 minus runway 90 is 30 degrees, a right crosswind. Direction 60 minus runway 90 wraps to 330 degrees, a left crosswind of the same size. The wrap is why the page never shows a negative relative angle: a left offset appears as an angle in the 270-to-360 range, and the display adds the word “left” and a negative sign to the crosswind itself so the side is unmistakable.

One more directional habit is worth building. Before trusting a crosswind figure, picture the runway from above with north at the top, the runway heading as an arrow, and the wind arrow pointing from its source direction toward the runway. The sideways push is the part of the wind arrow perpendicular to the runway, and its side is the side the wind comes from relative to the direction of travel. If the picture and the calculator disagree about the side, the input direction is the first thing to recheck, not the formula, because the formula has no opinion about left and right beyond the sign convention it was given.

Units: knots, mph and metres per second

The calculator works in whichever unit you pick, and it shows the crosswind in the other two units as well, so unit conversion is never a separate chore.

The page’s own FAQ gives the conversion factors: 1 kt equals 1.15078 mph and 0.51444 metres per second. The displayed figures follow those factors exactly. A crosswind of 10.00 kt is shown as 11.51 mph and 5.14 m/s, which are 10 times 1.15078 and 10 times 0.51444, rounded to two decimal places. A crosswind of 20.00 kt is shown as 23.02 mph and 10.29 m/s, which are 20 times the same factors. In mph mode, a 10.00 mph crosswind is shown as 8.69 kt and 4.47 m/s: 10 divided by 1.15078 is 8.69 kt, and 10 mph in metres per second is 4.47 m/s. The conversions are applied to the crosswind component, not to the total wind speed, which is the figure that matters for the sideways push. If you need the total wind speed in another unit, convert that separately; do not read the crosswind conversion row as if it were the whole wind.

The practical point is to pick the unit you think in and let the page do the rest, rather than converting the wind speed by hand before typing it. Hand conversion introduces rounding at the input stage, and rounding at the input stage propagates through both the sine and the cosine. Typing 20 kt directly and reading 11.51 mph beside the crosswind keeps the calculation exact in the chosen unit, with conversion only at the display stage, where rounding is harmless because the displayed conversions are informational, not inputs to anything else.

What the component does not decide

A crosswind component is a measurement, not a decision. This page is careful about that boundary, and the new sections here keep it.

There is no single universal crosswind limit, as the page’s own FAQ states. Limits depend on the aircraft type, the pilot, the runway and the gusts, so the aircraft manual and the operator limits for the flight are the authority for any go or no-go decision, not this calculator. A component of 10.00 kt may be routine for one aircraft and limiting for another, and a component of 20.00 kt may be acceptable on a long, dry runway and unacceptable on a short, wet one. The calculator gives the component only. It does not know the aircraft, the runway surface, or the pilot, and no number it displays should be read as permission or prohibition.

Gusts are a second, related limit on the page’s scope. The calculator works from a single steady wind speed and direction. Real wind gusts above and below that steady value, and changes direction during the approach, so the component during a gust can be larger than the component computed from the reported steady wind. The page does not model gusts, and no gust factor is added to its figures. If the reported wind includes gusts, the prudent reading is that the steady-wind component is a floor for the gust component, not a ceiling, and the operator limits and manual remain the decision authority. The same caution applies to a wind that is shifting direction: the component should be recomputed for the directions at the extremes of the shift, not just for the mean direction, because the sideways push follows the actual direction at the time, not the average.

Finally, the headwind and tailwind figures deserve the same respect as the crosswind. A headwind shortens the ground roll and a tailwind lengthens it, in general terms, and the along-runway component the page shows is the input to that judgement, not the judgement itself. The page does not compute takeoff or landing distances, and the new sections here do not invent any. The component is the contribution this page makes to a larger performance calculation that lives in the aircraft manual.

Three mistakes, in the order pilots make them

These mistakes are listed in the order they tend to happen, from entering the wind to reading the answer.

1. Entering the towards direction. As described above, wind direction means “from”, and entering the opposite direction flips the side and turns a headwind into a tailwind. The fix is verbal: always say “from” before the number, and check the side against a mental picture before trusting the figure.

2. Using the wind speed as the crosswind. The total wind speed is the crosswind only at a 90-degree relative angle. At the default 30 degrees, a 20 kt wind gives only 10.00 kt of crosswind, with the rest appearing as headwind. Quoting 20 kt as the crosswind overstates the sideways push by a factor of two in that case, and quoting the headwind as the crosswind understates it. The page separates the two components for exactly this reason, and both should be read before either is quoted.

3. Ignoring the sign and the side word. A crosswind of -10.00 kt from the left is not a smaller crosswind than 10.00 kt from the right, and it is not a negative amount of wind. The magnitude is 10.00 kt either way; the sign and the side word together say which way it pushes. For runway selection and for briefing, the side matters as much as the size, because a left crosswind and a right crosswind demand different control inputs, even though the component number, apart from its sign, is identical.

Put together, the safe routine is: direction as “from”, heading in degrees, both components read, side word noted, and the result treated as a measurement to be judged against the aircraft manual and operator limits, not as a decision. That routine uses everything the page computes and nothing it does not, which is the right relationship to have with any single-purpose calculator.

One wind, five runways

The same wind is a different problem on every runway. Holding the wind fixed and changing only the runway heading shows how completely the runway decides the answer.

Take a steady wind of 20 kt from 120 degrees, and try it on five runway headings. On runway 90, the default case, the relative angle is 30 degrees, the crosswind is 10.00 kt from the right, and the headwind is 17.32 kt. On runway 120, the wind is exactly along the runway, the relative angle is 0 degrees, the crosswind is 0.00 kt straight along the runway, and the headwind is the full 20.00 kt. On runway 30, the wind is exactly across the runway, the relative angle is 90 degrees, the crosswind is the full 20.00 kt from the right, and the headwind is 0.00 kt. On runway 180, the relative angle is 300 degrees, the crosswind is -17.32 kt from the left, and the headwind is 10.00 kt. On runway 270, the relative angle is 210 degrees, the crosswind is -10.00 kt from the left, and the along-runway component is a tailwind of 17.32 kt.

Every figure in that table was produced by this page’s own calculator and is quoted exactly as displayed. Read down the crosswind column and the story is the sine curve in runway form: zero when the wind is along the runway, half the wind speed at a 30-degree offset, most of the wind speed at a 60-degree offset, as on runway 180, where the 300-degree relative angle is a 60-degree offset on the left side and the crosswind is 17.32 kt, and the full wind speed at a 90-degree offset. Read down the along-runway column and the story is the cosine curve: full headwind when aligned, half headwind at a 60-degree offset, zero at a right angle, and then a tailwind once the relative angle passes 180 degrees, as on runway 270, where the wind that was a headwind on runway 90 becomes a tailwind of the same size, 17.32 kt, with a left crosswind of 10.00 kt beside it.

The runway 270 row is the most instructive in the table, because it combines the two things pilots most want to avoid at once: a tailwind and a crosswind. A pilot who only checked the crosswind would see 10.00 kt from the left and might judge it acceptable, while missing that the same wind is also pushing from behind at 17.32 kt. A pilot who only checked the headwind would see a tailwind and might reject the runway, while missing that the crosswind is also present. The page shows both components together precisely so that neither check happens alone. Runway selection is a two-component decision, and a table like this one, with both columns read together, is the minimum information needed to make it.

There is also a practical lesson about which runway to prefer when there is a choice. Among the five headings, runway 120 gives no crosswind at all and a full headwind, which is the best combination on both counts. Runway 90 gives a moderate crosswind and a strong headwind. Runway 180 gives a large left crosswind with only a small headwind. Runway 270 gives a left crosswind and a tailwind, the worst combination in the set. The ranking is not a rule, because runway availability, length, surface, traffic and operator limits all constrain the real choice, and this page decides none of those things. But as a pure wind ranking, it shows why the first question at an airfield with a choice of runways is always which heading is closest to the wind direction, and why a runway 30 degrees off the wind is usually a better wind choice than one 60 degrees off, even before any other factor is considered.

A pre-flight crosswind routine

A routine turns a calculator into a habit. This one takes under a minute and uses every figure the page shows.

First, get the wind as “from”, with its speed and direction, and the runway heading in degrees, and enter all three before reading any result. The order matters: entering the wind first and the runway second prevents the common error of typing the runway heading into the wind direction field, which produces a plausible-looking but wrong relative angle. Second, read both components, not just the crosswind. At the defaults that means noting 10.00 kt from the right and a headwind of 17.32 kt together, because the runway decision needs both, and because a tailwind hiding beside an acceptable crosswind, as on the runway 270 case in the previous section, is the error this step exists to catch. Third, read the conversions beside the crosswind, and make sure the unit you are thinking in matches the unit you entered. A pilot thinking in mph who entered knots, or the reverse, will misjudge the component by about fifteen percent, which is the difference between knots and mph, and that is enough to turn a marginal component into an apparently comfortable one.

Fourth, compare the component with the limits that actually apply: the aircraft manual and the operator limits for the flight, as the page’s own FAQ directs. The calculator cannot do this step, and no routine that skips it is complete, however carefully the component was computed. Fifth, if the wind is gusty or shifting, recompute for the gust direction and speed, or for the directions at the extremes of the shift, and judge the flight on the worst credible component, not on the mean. The steady-wind component is the starting point for that judgement, not the end of it. A routine that ends at the steady component has computed a number; a routine that ends at the manual limits, checked against the gust component, has made a decision.

Finally, brief the side out loud. “Crosswind ten knots from the right, headwind seventeen” is a sentence a second pilot can check, while “crosswind ten” is a number that can be misheard, misremembered, or attached to the wrong runway. The side word, right or left, and the headwind or tailwind word, are part of the result, not decorations on it, and the page displays them for that reason. A routine that speaks them is a routine that can be caught when it goes wrong, which is the only kind of routine worth having in aviation.

None of this routine changes the arithmetic, which is a sine, a cosine, and two unit conversions. What it changes is the chance that the arithmetic is applied to the right inputs, read in full, and judged against the right limits. Calculators are good at arithmetic and bad at judgement, and a routine that keeps those two jobs separate, arithmetic to the page, judgement to the manual and the pilot, is the safest way to use a page like this one.

The other component: headwind and tailwind from the same wind

One wind splits into two components, and the calculator shows both, because a pilot needs both. The crosswind component is the wind speed times the sine of the angle between the wind direction and the runway heading, and the headwind component is the wind speed times the cosine of the same angle. A wind straight down the runway gives a full headwind and no crosswind; a wind straight across gives a full crosswind and no headwind; and a wind at 30 degrees to the runway splits into a crosswind of half the wind speed and a headwind of about 87 percent of it. A worked pair: a 20-knot wind at 30 degrees to the runway gives a crosswind of 20 times sine 30, which is 10.0 knots, and a headwind of 20 times cosine 30, which is 17.3 knots.

The sign of the headwind component carries the operational meaning. A positive headwind shortens the takeoff and landing roll and steepens the climb, because the aircraft meets the air sooner; a negative headwind, a tailwind, lengthens both and must be checked against the aircraft’s tailwind limitation, which is usually far smaller than its crosswind capability. That is why the split matters more than either component alone: a 20-knot wind can be a helpful headwind, a testing crosswind, or a limiting tailwind, depending only on the angle, and the angle is set by the runway in use, not by the wind. Choose the runway, read both components, and judge the pair together against the manual.

How much crosswind is too much: demonstrated values, limits, and personal minimums

There is no single safe crosswind number, because the number that appears in most pilot operating handbooks is not a limit. The demonstrated crosswind component is the crosswind in which a test pilot demonstrated a satisfactory landing during certification, and it demonstrates that the aircraft can be landed in that crosswind, not that it cannot be landed in a stronger one, and not that every pilot should attempt it. A limitation, where one exists, is stated separately in the limitations section of the manual, and an operator may impose its own lower limit on top of that. The demonstrated figure is a data point about the aircraft; the limit, where it exists, is a rule; and neither is a personal capability.

Judge the component against four things, in order. First, the manual: the limitation if there is one, and the demonstrated figure as context. Second, the gust: work the component on the gust speed, not the steady speed, because the gust is the wind the aircraft meets at the moment of touchdown, and a steady 12 knots gusting 22 is a 22-knot crosswind problem, not a 12-knot one. Third, the runway: a wet or contaminated surface, a narrow runway, and a strong crosswind together leave less margin than any one of them alone. Fourth, yourself: a personal minimum, set below the demonstrated figure and practised in good conditions first, is the number that actually decides the go-around, and it should be written down before the flight, not negotiated on final approach. The calculator gives the component; the manual and the pilot give the decision.

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