Ground Speed Calculator

What the ground speed calculator does

An aircraft moves through the air, but the air itself is moving over the ground. Your speed across the ground is the combination of the two. This calculator works out that ground speed from your true airspeed and the wind, and along the way it gives the heading you need to hold and the angle you must crab into the wind.

You enter your true airspeed, the wind speed and the direction it comes from, and the course you want to track. Below is how airspeed and wind combine, the equations behind it, and a worked example.

How to use it

1. Enter your true airspeed in knots, km/h, or mph.
2. Enter the wind speed, and the direction the wind blows from, in degrees.
3. Enter your course, the direction you want to travel over the ground, in degrees.
4. Press Calculate for the ground speed, heading, and wind correction angle, or Reset to clear it.

Airspeed, wind, and the wind triangle

Think of three arrows. One is your air vector, pointing where the nose is aimed, as long as your true airspeed. One is the wind vector, pointing where the air is moving, as long as the wind speed. Add them tip to tail and you get the third arrow, the ground vector, pointing where you actually go and as long as your ground speed.

This is the wind triangle, and it is just vector addition. Because the three arrows form a triangle, knowing two of them fixes the third. The calculator takes your airspeed and the wind, then solves the triangle for the ground speed and for the heading that keeps your path along the course you wanted.

Headwind, tailwind, and crosswind

The wind helps or hurts depending on where it comes from. A pure tailwind pushes from behind and adds straight onto your airspeed, so a 120-knot aircraft with a 30-knot tailwind makes 150 knots over the ground. A pure headwind does the reverse, subtracting from your airspeed, so the same aircraft into a 30-knot headwind makes only 90 knots and takes longer to arrive.

A crosswind, blowing from the side, does something subtler. To keep from drifting off course you point the nose slightly into the wind, an angle called the wind correction angle or crab. Holding that crab keeps your path straight, but because some of your airspeed is now spent fighting sideways rather than driving forward, a crosswind trims your ground speed a little below your airspeed. Most real winds are a mix of these, part along your path and part across it.

The equations it uses

With V_a for true airspeed, V_w for wind speed, δ for the course, and ω for the wind direction, the wind correction angle α comes from how much of the wind blows across your path:

α = arcsin( ( V_w ÷ V_a ) · sin( ω − δ ) )

The heading you fly is then your course adjusted by that crab angle, δ + α. The ground speed comes from solving the wind triangle for its third side, combining your airspeed and the wind once the crab is accounted for. When the wind is straight behind you the ground speed rises to airspeed plus wind speed, when it is straight ahead it falls to airspeed minus wind speed, and a crosswind lands somewhere in between.

Units and precision

Airspeed and wind speed can be entered in knots, km/h, or mph, and the calculator converts internally to knots, the standard unit in aviation, so the ground speed is reported in knots. Course and wind direction are in degrees, measured the usual way as a compass bearing. Directions follow the aviation convention that wind is named for where it comes from, so a wind from 270 degrees is blowing out of the west. Results are shown to a few decimal places, finer than the wind is ever truly known.

A worked example: flying into a headwind

Suppose you are tracking a course of 360 degrees, due north, at a true airspeed of 120 knots, straight into a 30-knot wind coming from the north.

The wind is dead ahead, so none of it blows across your path and the wind correction angle is 0 degrees: the nose points straight along the course, with no crab needed. The wind subtracts from your airspeed, giving a ground speed of 120 − 30 = 90 knots. Turn that same wind around to a tailwind and the ground speed would instead climb to 150 knots, the clearest illustration of how much the wind can help or hurt.

Why ground speed matters in flight

Airspeed is what keeps an aircraft flying, but ground speed is what gets it somewhere. The difference decides how long a leg takes and how much fuel it burns. A strong headwind can stretch a flight well past its planned time, while a tailwind can deliver you early, and on a long route the gap between the two can be substantial.

This is why flight planning works in ground speed, not airspeed. Knowing the ground speed for each leg gives the real time en route and the fuel needed, and knowing the wind correction angle tells the pilot how to aim the nose so the aircraft actually tracks the intended line rather than drifting downwind.

Questions people ask

What is the difference between airspeed and ground speed?

Airspeed is how fast the aircraft moves through the air. Ground speed is how fast it moves over the ground. They differ by the wind: the moving air is carried along underneath the aircraft.

What is the wind correction angle?

It is the angle you point the nose into the wind, the crab, to keep from drifting off course in a crosswind. Holding it keeps your track along the line you intended.

Does a headwind really slow you down?

Yes, over the ground. Your airspeed is unchanged, but a headwind subtracts from your speed across the ground, so the trip takes longer and burns more fuel.

Can ground speed be faster than airspeed?

Yes, with a tailwind. When the wind blows from behind, it adds to your airspeed, so your ground speed climbs above the speed you are flying through the air.

References

A quick note on where this comes from. The wind triangle, the vector addition of airspeed and wind to give ground speed and heading, is standard air navigation, set out in the US Federal Aviation Administration's Pilot's Handbook of Aeronautical Knowledge. The knot and the other units follow the US National Institute of Standards and Technology.

1. US Federal Aviation Administration (FAA), Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25), chapter on Navigation. https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak
2. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811