Wind triangle: heading and groundspeed

Model: Wind triangle: WCA = asin(W/TAS · sin(WD − TC)), GS = TAS·cos(WCA) − W·cos(WD − TC)

Show your work

1. Wind correction angle

   WCA = asin(wind speed × sin(wind direction − course) / TAS)

   asin(20 × sin -60° / 120) = -8.3°

2. Groundspeed

   GS = TAS × cos WCA − wind speed × cos(wind direction − course)

   120 × cos -8.3° − 20 × cos -60° = 108.7 kt

3. Heading to fly

   $$\mathrm{heading}=\mathrm{course}+\mathrm{WCA}$$

   90° + -8.3° = 81.7°

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.

When to use this: Use this on a leg where you know the course you want to make good, your true airspeed, and the wind: it gives the heading to fly, the wind correction angle, and the groundspeed you will get. It is the wind side of the E6B, solved exactly, and it feeds the time and fuel for the leg.

Limitations: One steady wind over a straight leg, in flat-earth geometry: it does not model wind that changes with altitude or along the route, climbs and descents, or the difference between a great circle and a straight line on a chart. The heading is true unless you convert it; the declination and true-to-magnetic tools do that. Planning aid, not for primary navigation.

Worked example: Course 090°, 120 kt, wind 030° at 20 kt. Source: add-aviation-suite wind scenario: WCA -8.30°, heading 081.7°, groundspeed 108.7 kt.

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 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

• 2026-09-23, fixed: A wind straight across the runway read "0 kt tailwind", and one straight down it read "0 kt crosswind from the none": float noise like −0.0000000000000018 kt was taken as a tailwind. Components under a billionth of a knot are now exactly zero, and the sentence says "no headwind or tailwind" or "No crosswind" whenever a component rounds to zero. The wind triangle said "a wind correction of 0° to the right" with no crosswind; it now says "with no wind correction". Runway wind components and the wind triangle are now version 1.0.1. Changelog
• 2026-09-19, changed: Pressure altitude, density altitude, runway crosswind and headwind, and the wind triangle are now stable. Each matches the worked examples in the FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C) and at least 20 vectors from a separate implementation. Results are unchanged. Changelog

Checked against: 22 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