Wind triangle: airspeed and heading for a groundspeed

The true airspeed and heading that make good a course at the groundspeed you need, for a known wind.

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

Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

120kt

Fly 120 kt true airspeed on heading 81.7° to make good the course at that groundspeed.

Heading
Wind correction angle

Provenance

Computed by: aviation.wind.tas-from-groundspeed 1.0.0, core 0.1.0
Model: Air vector = ground vector − wind vector: the ground vector runs along the course at the groundspeed, and the wind vector points where the wind blows to (its direction + 180°). TAS is the air vector's length and the heading its direction
Accuracy: Exact for steady wind and flat-earth geometry over a leg. Planning aid, not certified for navigation.
Notes: 1 shown with the answer
Cites: Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C; Federal Aviation Administration, Aeronautical Information Manual

Something look off?

Your values

Showing an example. Change anything.

Course Like 090 deg · plain numbers mean degrees Groundspeed needed Like 108.7 kt · plain numbers mean kt Wind directionoptional Where the wind blows from, like 300 deg · plain numbers mean degrees Wind speedoptional Like 15 kt · plain numbers mean kt

More options 4

Course referenceoptional true (the default, as plotted on a chart) or magnetic Wind referenceoptional true (the default: METAR, TAF, winds aloft) or magnetic METAR wind groupoptional Instead of direction and speed, like 30015G25KT or VRB05KT (true north) Magnetic variationoptional East positive, like -12 for 12° W; needed to mix true and magnetic · plain numbers mean degrees

Run many at once from a CSV

Loading…

How we got thisFormula, worked example, sources, and proof

Model: Air vector = ground vector − wind vector: the ground vector runs along the course at the groundspeed, and the wind vector points where the wind blows to (its direction + 180°). TAS is the air vector's length and the heading its direction

Show your work

Air vector
air = ground − wind (east, north)
(108.7, 0) − (-10, -17.3) = (118.7, 17.3) kt
Heading
heading = atan2(east, north)
atan2(118.7, 17.3) = 81.7°
True airspeed
$TAS = |air|$
√(118.7² + 17.3²) = 120 kt

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Exact for steady wind and flat-earth geometry over a leg. Planning aid, not certified for navigation.

Worked example: Course 090° at 108.7 kt over the ground, wind 030° at 20 kt. Source: add-aviation-suite heading-and-groundspeed scenario solved the other way: about 120 kt on heading 081.7°. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Course: 90 deg
Groundspeed needed: 108.7 kt
Wind direction: 30 deg
Wind speed: 20 kt

You get

True airspeed: 120 kt
Heading: 81.7°
Wind correction angle: -8.3°

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-19, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Checked against: 8 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C, Federal Aviation Administration, FAA-H-8083-25C. Aircraft Performance and Navigation chapters (pressure and density altitude, wind triangle).
Aeronautical Information Manual, Federal Aviation Administration, Current edition. Chapter 4 (tower and ATIS winds, magnetic) and Chapter 7 (METAR and TAF winds, true).

Terms

METAR: aviation routine weather report: An airport weather observation in a standard code: wind, visibility, weather, clouds, temperature, dew point, and altimeter setting, issued at least hourly. Source: Aviation Weather Handbook
TAF: terminal aerodrome forecast: A forecast for an airport, usually 24 or 30 hours long, coded like a METAR with change groups such as FM, TEMPO, BECMG, and PROB30. Source: Aviation Weather Handbook

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.