Ground Speed Calculator
The wind triangle relates true airspeed, wind, and the speed and direction the aircraft actually makes good over the ground. Knowing your ground speed lets you compute time en route and fuel; knowing the wind correction angle lets you hold the intended course. This calculator resolves the wind relative to your desired course into a crosswind component and an along-course component, solves the inverse sine for the crab angle, and combines the projection of airspeed with the headwind or tailwind to give ground speed. Enter true airspeed, the desired course, the wind direction, and wind speed, all on the same north reference.
Ground speed (wind triangle) formula
Wind angle = wind direction - course
Headwind = wind speed * cos(wind angle)
Crosswind = wind speed * sin(wind angle)
Wind correction angle = arcsin(crosswind / true airspeed)
Ground speed = TAS * cos(WCA) - headwind
A positive headwind reduces ground speed; a negative value (tailwind) increases it. The crab angle points the nose into the wind by the wind correction angle.
Wind triangle notes
- Keep course and wind direction on the same reference, true with true or magnetic with magnetic.
- Add the wind correction angle to the course on the upwind side to find the heading to fly.
- Time en route equals leg distance divided by the ground speed this tool returns.
- If the crosswind exceeds true airspeed, the course cannot be held and the result is not available.
- Even a pure crosswind lowers ground speed, because some airspeed is spent crabbing into the wind.
Ground speed: frequently asked questions
How is ground speed calculated from the wind?
Resolve the wind into a crosswind component across the course and a headwind component along it. The wind correction angle is the inverse sine of the crosswind divided by true airspeed. Ground speed is the true airspeed multiplied by the cosine of that correction angle, minus the headwind component along the course.
What is the wind correction angle?
The wind correction angle, or crab angle, is how far you must point the nose into the wind so the aircraft tracks the intended course rather than drifting downwind. It is the inverse sine of the crosswind component divided by true airspeed. Apply it to the desired course to get the heading to fly.
Does a headwind always reduce ground speed?
Yes. Any wind component along the course that opposes travel reduces ground speed below true airspeed; a tailwind component increases it. A pure crosswind reduces ground speed slightly too, because part of the airspeed is used to crab into the wind rather than to move along the course.
What units does this use?
True airspeed, wind speed, and ground speed are all in knots; directions are in degrees. As long as the airspeed and wind speed share the same speed unit, the ground speed comes out in that unit. Keep the course and wind direction on the same north reference, both true.
Why might the calculator show no solution?
If the crosswind component is greater than the true airspeed, the aircraft cannot make good the course at all, because no heading produces enough sideways correction. The calculator flags this as not available. In practice this means the wind is too strong relative to airspeed for that track.
Official sources
- FAA: Pilot's Handbook of Aeronautical Knowledge.
- NIST Digital Library of Mathematical Functions: trigonometric functions.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.