# Ground Speed Calculator

URL: https://speedycalculator.com/calculators/physics/ground-speed/
Last updated: 2026-10-30

> The ground speed calculator finds an aircraft's ground speed, wind correction angle and heading from the true airspeed, desired course and the wind's speed and direction.

## Inputs

- True airspeed (knots, km/h, mph, m/s)
- Course α (°, rad, arcmin, arcsec, mrad)
- Wind speed (knots, km/h, mph, m/s)
- Wind direction β (from) (°, rad, arcmin, arcsec, mrad)

## Results

- Wind correction angle
- Heading
- Ground speed
- Headwind component
- Crosswind component

## Formula

```
WCA = arcsin(V_w·sin(β − α) / TAS),  heading = α + WCA
GS = TAS·cos(WCA) − V_w·cos(β − α)
```

## Explanation

Pilots fly through moving air. To track a course over the ground, they point the nose slightly into the wind (the wind correction angle), and the wind also speeds up or slows down their ground speed – which sets the flight time and fuel needed.

### How to use the Ground Speed Calculator

- **True airspeed**
- **Course α**
- **Wind speed**
- **Wind direction β (from)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the true airspeed, the course you want to fly over the ground, and the wind (the direction it blows from). Angles are true bearings in degrees.

### Inputs explained

FieldWhat to enterTrue airspeedUnits: knots, km/h, mph, m/sCourse αUnits: °, rad, arcmin, arcsec, mradWind speedUnits: knots, km/h, mph, m/sWind direction β (from)Units: °, rad, arcmin, arcsec, mrad

### What each result means

- **Wind correction angle** = deg(asin([Wind speed]×sin(rad([Wind direction β (from)] - [Course α]))÷[True airspeed]))
- **Heading** = mod([Course α] + [Wind correction angle], 360)
- **Ground speed** = [True airspeed]×cos(rad([Wind correction angle])) - [Wind speed]×cos(rad([Wind direction β (from)] - [Course α]))
- **Headwind component** = [Wind speed]×cos(rad([Wind direction β (from)] - [Course α]))
- **Crosswind component** = [Wind speed]×sin(rad([Wind direction β (from)] - [Course α]))

### Example values

How the main result changes when **True airspeed** changes and everything else stays at the example values above:

True airspeed (knots)Ground speed (knots)6047.459078.32120108.74150139180169.16240229.37

## Worked example

Inputs — True airspeed: 120 knots; Course α: 90 °; Wind speed: 20 knots; Wind direction β (from): 30 °.

Results — Wind correction angle = -8.3 °; Heading = 81.7 °; **Ground speed = 108.74 knots**; Headwind component = 10 knots; Crosswind component = -17.32 knots.

## Key terms

- **True airspeed**: Speed relative to the air mass.
- **Ground speed**: Speed relative to the ground.

## FAQ

**What is the wind correction angle?**
The angle between heading and course needed to cancel the crosswind drift.

**Is wind direction "from" or "to"?**
Aviation winds are reported as the direction they blow from.

**Why is ground speed lower into a headwind?**
The air mass moves backwards relative to the ground.

**What if the crosswind is stronger than the airspeed?**
The course cannot be held – the arcsine has no solution.


## Sources

- [FAA – Pilot's Handbook of Aeronautical Knowledge](https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)