Wind correction angle calculator for the wind triangle

What this calculator does

An aircraft flies through the air and the air moves over the ground, so pointing at where you want to go is almost never the way to get there. The wind triangle resolves the two, and it produces two numbers: the heading that holds your track, and the groundspeed that results.

The second one is the one that matters for fuel. A 25 knot wind at 50 degrees off the nose costs only 9.2 degrees of crab but takes 17.6 knots off a 120 knot true airspeed, which is nearly fifteen per cent of your progress for a wind that does not feel strong.

The formula

FormulaWCA = asin(wind speed × sin(wind angle) ÷ TAS); heading = track + WCA; groundspeed = TAS × cos(WCA) − wind speed × cos(wind angle)

The crosswind component is wind speed × sin(wind angle), where the wind angle is how far the wind direction sits from your track. Dividing that by true airspeed and taking the inverse sine gives the correction angle, which is added to the track to get the heading. The groundspeed is then TAS × cos(WCA) − wind speed × cos(wind angle), the along-track part of what is left.

Term	Meaning
Track	The path over the ground you want to make good.
Heading	Where the nose points. Track plus the wind correction angle.
Wind correction angle	The crab needed to cancel the crosswind. Also called drift correction.
Groundspeed	Speed over the ground, which is what distance and time are measured against.

The inputs explained

Field	What to enter
Track you want to make good (°)	The track you want in degrees true, since winds aloft forecasts are given in true.
True airspeed (kt)	True airspeed rather than indicated. The true airspeed page estimates it.
Wind direction (from) (°)	The direction the wind is coming from, which is the convention in every forecast and report.
Wind speed (kt)	Wind speed in knots.
Leg distance (nm)	Leg distance, used only for the time estimate.

When to use it

Planning a cross-country leg

Work out the heading and groundspeed for each leg before departure, then the times follow. A leg flown on track heading with no correction will drift off at roughly the crosswind component in miles per hour.

Seeing why a crosswind costs speed

Set the wind direction perpendicular to the track. The along-track component is zero so you might expect no cost, but the groundspeed still drops below true airspeed, because some of the airspeed is being spent crabbing rather than progressing.

Checking a leg is flyable

If the crosswind exceeds true airspeed the track cannot be held at all, and the calculator says so rather than returning a number. It is a real situation for a slow aircraft in a strong wind.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How does wind angle change the correction?

The wind speed is constant and only the direction it comes from changes.

120 kt true airspeed, 25 kt wind, track 090

Wind from	Heading to fly	Wind correction angle	Groundspeed
090°	90.0°	0.0° right	95.0 kt
120°	96.0°	6.0° right	97.7 kt
150°	100.4°	10.4° right	105.5 kt
180°	102.0°	12.0° right	117.4 kt
240°	96.0°	6.0° right	141.0 kt
270°	90.0°	0.0° right	145.0 kt

A direct headwind from 090 needs no correction at all and costs the full 25 knots, giving 95. A direct tailwind from 270 also needs no correction and gives 145. The largest crab is at 180, perpendicular to the track, at 12 degrees, and even there the groundspeed is 117.4, barely below the airspeed. Wind angle decides the crab; the along-track component decides the speed, and they peak at opposite ends.

What does a stronger wind do?

The wind direction is fixed 50 degrees off the nose and only the speed changes.

120 kt true airspeed, wind from 140, track 090

Wind speed	Wind correction angle	Groundspeed	Time for the leg
10 kt	3.7° right	113.3 kt	52 min 57 s
25 kt	9.2° right	102.4 kt	58 min 36 s
40 kt	14.8° right	90.3 kt	66 min 26 s
60 kt	22.5° right	72.3 kt	83 min 1 s
90 kt	35.1° right	40.4 kt	148 min 38 s

Ten knots costs 3.7 degrees of crab and brings the groundspeed to 113.3. Ninety knots needs 35.1 degrees and leaves only 40.4, so a hundred mile leg goes from 52 minutes to nearly two and a half hours. The correction angle grows faster than linearly as the wind approaches the airspeed, which is the point at which a flight plan needs rethinking rather than recalculating.

Questions

Is the answer in true or magnetic degrees?

True, because the inputs are. Winds aloft forecasts are given in degrees true while a tower reports magnetic, so apply the local magnetic variation before flying the heading if your compass is magnetic.

Why does a pure crosswind still slow me down?

Because part of your airspeed is spent crabbing into the wind rather than moving along the track. The effect is small at modest wind angles and grows quickly once the crab exceeds about fifteen degrees.

How is this different from the crosswind component for a runway?

The runway crosswind page answers whether you can land in the wind. This one answers where to point to hold a track in flight, and gives the groundspeed that follows.

What if the crosswind exceeds my airspeed?

Then the track cannot be held, and the calculator says so rather than returning a meaningless number. You would need a different track, a different altitude or a different day.

Does this account for a climb or descent?

No. It assumes level flight at one true airspeed in one wind. Legs that climb or descend through changing wind need to be split.

For the airspeed that feeds it, see true airspeed, and for landing in the same wind, runway crosswind component. Fuel against the resulting groundspeed is on fuel burn endurance and range.