Ground Speed Calculator — Wind Triangle
Enter true airspeed, wind speed and wind angle to calculate the actual speed of the aircraft over the ground and the wind correction angle.
kt
kt
°
Speed of aircraft relative to the ground
- 1
Headwind component
20 × cos(45°) = 14.14Positive = headwind (opposes motion); negative = tailwind (assists). - 2
Crosswind component
20 × sin(45°) = 14.14 - 3
Forward ground speed component
TAS − headwind = 120 − 14.14 = 105.86 - 4
Ground speed
√(105.86² + 14.14²) = 106.8
How does this calculator work?
Ground speed = √((TAS − W·cos θ)² + (W·sin θ)²), where θ is the wind angle from the aircraft nose (0° = headwind, 180° = tailwind). A 120 kt aircraft in a 20 kt headwind has 100 kt GS; in a 20 kt tailwind it has 140 kt GS; in a 20 kt crosswind about 121 kt GS.
Formula
How this is calculated
An aircraft's ground speed differs from its airspeed whenever wind is present. The wind triangle solves the vector relationship between three speeds: True Airspeed (TAS) is the speed of the aircraft relative to the surrounding air mass, wind speed is the speed of the air mass relative to the ground, and Ground Speed (GS) is the resulting speed of the aircraft relative to the ground — what a GPS measures.
When the wind angle from the nose is 0° the wind opposes forward motion (headwind), reducing GS by the full wind speed. At 180° the wind assists (tailwind), adding to GS. At 90° the wind is a pure crosswind, creating sideways drift without directly reducing forward speed (though GS is slightly higher than TAS by the crosswind Pythagoras effect). For any intermediate angle, the headwind component is W × cos(θ) and the crosswind component is W × sin(θ); the ground speed vector magnitude is found by the Pythagorean theorem on the forward and sideways components.
The wind correction angle (WCA) is how many degrees the pilot turns the nose into the wind to track the desired course despite the crosswind. The formula assumes wings-level, constant-altitude flight and ignores atmospheric effects such as altitude corrections to indicated airspeed. All speeds must be in the same units (knots in the default).
Frequently asked questions
Airspeed is the aircraft speed relative to the air around it — what the airspeed indicator reads. Ground speed is the aircraft speed relative to the ground — what a GPS measures. A headwind lowers ground speed below airspeed; a tailwind raises it above.
A pure crosswind does not add to or subtract from forward motion, but the wind triangle has both a forward component (unchanged from TAS) and a sideways component equal to wind speed. The Pythagorean magnitude √(TAS² + W²) is slightly larger than TAS alone.
Yes — if flying into a headwind equal to TAS the aircraft hovers relative to the ground (GS = 0). In a headwind stronger than TAS the aircraft actually moves backward over the ground. High-altitude jet streams occasionally cause this for small aircraft flying into them.
Also known as
TG we-Calculate Editorial Team. (2026). Ground Speed Calculator — Wind Triangle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/ground-speed-calculator
TG we-Calculate Editorial Team. "Ground Speed Calculator — Wind Triangle." TG we-Calculate. 2026. https://we-calculate.com/calculator/ground-speed-calculator.
TG we-Calculate Editorial Team, "Ground Speed Calculator — Wind Triangle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/ground-speed-calculator
@misc{wecalculate_ground_speed_calculator, title = {Ground Speed Calculator — Wind Triangle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/ground-speed-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?