Wind Triangle Ground Speed Calculator
The aviation wind triangle is the foundational vector problem of navigation: given your true airspeed (TAS), the wind speed and direction, and your desired true course (TC), find the true heading to fly and the resulting ground speed. Solving the wind triangle tells you how much to crab into the wind (wind correction angle) so that your actual track over the ground matches your planned course. This calculator uses the exact trigonometric vector solution: it resolves TAS and wind into northward and eastward components, combines them, and extracts ground speed and wind correction angle. Enter wind direction as the direction the wind is blowing FROM (standard meteorological convention), true course in degrees true, TAS in knots, and wind speed in knots.
Wind triangle formula
Wind Component North = -WS x cos(WD)
Wind Component East = -WS x sin(WD)
Aircraft North = TAS x cos(TC) + Wind North
Aircraft East = TAS x sin(TC) + Wind East
GS = sqrt(North^2 + East^2)
WCA = TC - atan2(East, North)
Wind direction is converted from meteorological (FROM direction) to a vector. The true heading to fly equals the true course plus the wind correction angle. A positive WCA means the nose is pointed right of course (left wind); negative means left of course (right wind).
Using wind triangle results
- Apply variation to convert true heading to magnetic heading, then deviation to get compass heading.
- Ground speed determines ETE (estimated time en route): ETE = distance / GS.
- Fuel burn for the leg uses burn rate x ETE, not TAS-based time.
- In-flight, compare GPS ground speed against the calculated value to detect forecast wind errors.
Wind triangle calculator: frequently asked questions
What is the aviation wind triangle?
The wind triangle is a vector diagram relating true airspeed (TAS), wind velocity, and ground speed/track. TAS is the aircraft's speed through the air, the wind vector shifts that through the air mass, and the resulting vector over the ground is ground speed along the actual track.
What is the difference between true course and true heading?
True course (TC) is the desired track over the ground referenced to true north. True heading (TH) is the direction the nose points, corrected for wind. To maintain the desired course, pilots crab into the wind by the wind correction angle (WCA).
How is ground speed calculated from TAS and wind?
Using the vector law of cosines: GS^2 = TAS^2 + WS^2 - 2 x TAS x WS x cos(angle between TAS heading and wind direction). The wind correction angle is found from the sine rule. This calculator solves the full vector triangle.
What is a wind correction angle?
The wind correction angle (WCA) is the number of degrees the aircraft's nose must be pointed into the wind to track the desired course over the ground. A positive WCA means crabbing left for a wind from the right.
Why does wind speed affect ground speed but not airspeed?
Airspeed is measured relative to the surrounding air mass. Wind moves the air mass itself, so the aircraft's speed over the ground (ground speed) differs from TAS. A tailwind adds to ground speed; a headwind subtracts from it.
Official sources
- FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25B), Chapter 16 Navigation: faa.gov.
- FAA Aeronautical Information Manual: faa.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.