geoprimsField-grade geospatial math

The wind triangle explained

Heading, groundspeed, and wind correction angle from your course, airspeed, and the wind, worked exactly and by rule of thumb.

For pilots · updated 2026-09-23

Planning and education aid. Not for primary navigation. Full disclaimer

The wind triangle is the drawing that shows how the wind changes your path over the ground. One side is your airplane moving through the air, on its heading at true airspeed. One side is the air moving over the ground, the wind. The third side is the result: your track and groundspeed. Solve it and you get the heading to fly and the groundspeed you will make.

The Pilot’s Handbook of Aeronautical Knowledge calls it the basis of dead reckoning. It is what the wind side of an E6B flight computer solves, and what a GPS navigator shows you after the fact.

The words

Term Meaning
True course The line you want to follow over the ground, measured from true north
True airspeed (TAS) Your speed through the air
Wind The direction it blows from, true, and its speed
True heading Where the nose points to hold the course
Wind correction angle (WCA) The angle between heading and course: the crab
Groundspeed Your speed over the ground along the course

Winds aloft forecasts are given from true north. That is why the triangle is worked in true degrees, and variation and deviation come after.

Why it matters

Groundspeed sets your time en route and so your fuel burn. The wind correction angle keeps you on the course you drew. Get either wrong and you arrive late, low on fuel, or somewhere else. The same geometry runs backward in flight: from the heading you hold and the track and groundspeed you see, you can work out the real wind.

How it is worked out

The triangle is exact trigonometry, which is why a spinning computer or a calculator can solve it.

  1. Split the wind against the course. The part across the course is the crosswind. The part along it is headwind or tailwind.
  2. Wind correction angle. Turn into the wind until the airplane’s sideways speed cancels the crosswind: sin(WCA) = crosswind ÷ TAS.
  3. Groundspeed. Your speed along the course is TAS × cos(WCA), less the headwind or plus the tailwind.
  4. Heading. True heading = true course + WCA, to the right if the wind is from the right.

The heading and groundspeed tool does these steps exactly and shows each one under “How we got this.”

A worked example

True course 090°, TAS 120 kt, wind 030° at 20 kt:

Item Result
Crosswind on the course 17.3 kt from the left
Headwind on the course 10 kt
Wind correction angle 8.3° left
True heading 81.7°
Groundspeed 108.7 kt

Notice the groundspeed: 11.3 kt below TAS, although the headwind part of the wind is only 10 kt. Pointing the nose 8.3° off the course costs a little speed along it.

The handbook’s own example checks the method. It draws the triangle for a true course of 090°, a wind of 045° at 40 kt, and 120 kt TAS, and measures a true heading of 076°, a wind correction of 14°, and a groundspeed of 88 kt. The tool gives 76.4°, 13.6°, and 88.3 kt: the same answer, to the width of a pencil line.

Rules of thumb, and how far they drift

Two shortcuts carry most pilots through a flight without a computer.

How they compare with the exact triangle at 120 kt TAS:

Case Crosswind Rule of thumb WCA Exact WCA Exact groundspeed
Wind 030° at 20 kt 17.3 kt 8.7° 8.3° 108.7 kt
Wind 045° at 40 kt 28.3 kt 14.1° 13.6° 88.3 kt
Wind 000° at 40 kt, straight across 40 kt 20° 19.5° 113.1 kt
Wind 270° at 20 kt, straight behind 0 kt 140 kt

The rule reads a little high, by about half a degree in these cases, which is well inside what you can hold by hand. It grows as the wind becomes a larger share of your airspeed. For groundspeed, “TAS minus headwind” is close for small crab angles and too high for large ones: a 40 kt wind straight across still costs 6.9 kt.

Running the triangle other ways

The same three sides can be solved for any missing piece.

Common mistakes

Where the numbers come from

The method is the vector triangle in Chapter 16 of the FAA’s Pilot’s Handbook of Aeronautical Knowledge, solved with trigonometry instead of a protractor. Every value above comes from the heading and groundspeed tool and its sibling tools. For the same geometry at the runway, read How to calculate crosswind. This is a planning and education aid; it does not replace your navigation equipment or charts.

Try it: Wind triangle: heading and groundspeed

The calculator below is the real tool, running its worked example. Change any value; nothing leaves your device.

81.7°

Fly heading 81.7° for a groundspeed of 108.7 kt, a wind correction of 8.3° to the left.

Groundspeed
Wind correction angle
Provenance
Computed by
aviation.wind.heading-groundspeed 1.0.1, core 0.1.0
Model
Wind triangle: WCA = asin(W/TAS · sin(WD − TC)), GS = TAS·cos(WCA) − W·cos(WD − TC)
Accuracy
Exact for steady wind and flat-earth geometry over a leg. Planning aid, not certified for navigation.
Notes
None
Cites
Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C; Federal Aviation Administration, Aeronautical Information Manual

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N ↑Heading 81.7°WindGround 108.7 kt

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Sources

Every number on this page comes from the tools above, which cite their sources on their own pages under "How we got this." Found a mistake? Use "Report a problem" at the bottom of the page.