By Zencalcy Editorial TeamLast reviewed About us
Ground speed is the speed of an aircraft relative to the ground, not the air around it. Wind adds as a vector: a tailwind increases ground speed, a headwind decreases it, and a crosswind shifts the track. This calculator solves the wind triangle for speed.
Combine airspeed and wind into a ground speed.
v_g = √(v² + w² + 2vw·cos α)
α is the angle between the heading and the wind. At 0° the wind is a pure tailwind, at 90° a pure crosswind and at 180° a pure headwind.
| Symbol | Meaning |
|---|---|
| v | True airspeed, in metres per second. |
| w | Wind speed, in metres per second. |
| α | Angle between heading and wind. |
| v_g | Ground speed, in metres per second. |
A direct tailwind adds fully: ground speed is 120 m/s. The same wind at 90° gives about 102 m/s, and as a headwind it drops the ground speed to 80 m/s.
Continue with the Horizontal Projectile Motion Calculator, Impulse and Momentum Calculator, or the Inclined Plane Calculator — or browse more kinematics tools and all physics calculators.
In this calculator 0° means the wind moves in the same direction as the aircraft, so it is a tailwind. Use 180° for a headwind.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Content updated: September 2026