Ground Speed Calculator

Calculate ground speed from airspeed and wind conditions

Compute ground speed, wind correction angle, and heading for flight planning

Last updated: December 22, 2025
Frank Zhao - Creator
CreatorFrank Zhao

Calculation Mode

More info

Wind Direction Convention

More info
More info
kn
More info
kn
More info
deg
More info
deg
More info
kn
More info
kn
More info
deg
More info
deg
More info
kn
🧭

Introduction / Overview

This ground speed calculator is built for flight planning and learning. In Navigation mode, you enter true airspeed, wind, and course — and it returns your ground speed, wind correction angle, and heading. In Wind Finding mode, you do the reverse: enter the flight data and it solves for the wind.

Think of it like walking on a moving walkway at the airport: your walking speed is your “airspeed,” the walkway is the “wind,” and what your friend sees from the terminal is your “ground speed.”

Who is this for?

  • Student pilots and instructors who want to see the wind triangle math in action.
  • Flight sim pilots who want quick, consistent numbers for headings and ETAs.
  • Anyone comparing “still-air” performance to real wind conditions.
💡
Reliability note:

The calculator uses the same wind-triangle relationships taught in basic navigation: vector addition plus a small set of trigonometric identities. You can switch wind direction convention ("from" vs "to") and units, and the results stay consistent.

🌍

What is the ground speed of a flying object?

Ground speed is how fast you’re moving relative to the ground below you. It’s the speed that turns distance into time: if you know the remaining distance, ground speed tells you the ETA.

The one-line idea

Time=Distancevg\text{Time} = \frac{\text{Distance}}{v_g}wherevg is ground speed\quad\text{where}\quad v_g\ \text{is ground speed}

A simple intuition: if you watch the world slide by beneath you (roads, coastline, runway lights), what you’re “seeing” is ground speed. Wind can make those visual cues move faster or slower even if the aircraft performance (true airspeed) hasn’t changed.

✈️

True airspeed vs. ground speed

True airspeed (TAS) is the aircraft’s speed through the air mass. Ground speed is the speed across the Earth. The difference between them is the wind.

Practical differences pilots care about

  • In still air, you’ll see vg=vav_g = v_a.
  • TAS is mostly about performance (stall margins, climb, aircraft capability). Ground speed is about planning (time en route).
  • A strong tailwind can make vg>vav_g > v_a, while a headwind can make vg<vav_g < v_a.

Quick mental check: if the wind is pushing you from behind, your ground speed goes up; if it’s in your face, it goes down. Crosswinds are trickier — they mostly affect heading, but they can also nudge ground speed a bit.

🧮

How do I calculate ground speed from true airspeed?

Conceptually, ground speed is just vector addition: the airspeed vector plus the wind vector.

Vector form

v⃗g=v⃗a+v⃗w\vec v_g = \vec v_a + \vec v_w

If you think in headings and tracks: you’re “aiming” the air vector a little into the wind, and the wind vector shifts the result to land on the planned course.

In flight-planning problems, you typically know the magnitudes vav_a (TAS) and vwv_w (wind speed), and you know the course (track) you want to fly. The calculator uses a wind-triangle approach (law of sines/cosines) to compute heading, wind correction angle, and ground speed.

Wind direction convention (important)

Aviation weather reports usually give wind FROM a direction (for example, wind from 270∘270^{\circ}). Some formulas (and some vector diagrams) use the direction wind blows TO. They differ by 180∘180^{\circ}.

ωto=ωfrom+180∘\omega_{to} = \omega_{from} + 180^{\circ}(then normalize to 0∘–360∘)\quad(\text{then normalize to } 0^{\circ}\text{–}360^{\circ})
🎯

How do we find the wind correction angle of an aircraft?

Wind doesn’t just change how fast you move over the ground — it can also push you sideways. The wind correction angle (WCA) is the amount you “crab” into the wind so your actual ground track stays on the intended course.

Imagine you’re rowing straight across a river, but the current drags you downstream. To land at your target spot, you aim a bit upstream. That “aiming upstream” angle is the same idea as WCA.

Wind correction angle formula

α=sin⁡−1 ⁣(vwva sin⁡(ω−δ))\alpha = \sin^{-1}\!\left(\frac{v_w}{v_a}\,\sin(\omega - \delta)\right)
α\alpha— wind correction angle (WCA)
vav_a— true airspeed (TAS)
vwv_w— wind speed
δ\delta— course (intended ground track)
ω\omega— wind direction (in the convention you’ve selected)

Heading from course + WCA

ψ=δ+α\psi = \delta + \alpha(ψ is heading)\quad(\psi\ \text{is heading})

Positive/negative sign conventions can vary by textbook. The calculator keeps it consistent internally and normalizes angles for you. If the heading looks “wrong way” at first glance, double-check whether wind is set to FROM vs TO.

🚀

How to use ground speed calculator

You can get useful answers in under a minute. Here’s the fastest workflow for the most common task: compute heading, WCA, and ground speed from wind and TAS.

1

Pick the mode and convention

Choose Navigation mode, then decide whether wind direction is reported as FROM (typical aviation) or TO.

2

Enter the four inputs

Fill in TAS, wind speed, course, and wind direction. Units can be mixed — the calculator converts them safely.

3

Read the outputs

The calculator returns WCA, heading, and ground speed. The wind components section also shows crosswind and headwind/tailwind.

4

Use the result for ETA

If you have distance remaining, plug ground speed into time planning:

ETA time=Distancevg\text{ETA time} = \frac{\text{Distance}}{v_g}
EX

Worked example (with real numbers)

Suppose you have va=100 ktv_a = 100\ \text{kt}, course δ=090∘\delta = 090^{\circ}, wind speed vw=20 ktv_w = 20\ \text{kt}, and wind FROM 180∘180^{\circ}.

Step 1: Convert wind FROM → TO

ωto=180∘+180∘=360∘≡0∘\omega_{to} = 180^{\circ} + 180^{\circ} = 360^{\circ} \equiv 0^{\circ}

Step 2: Compute WCA

α=sin⁡−1 ⁣(20100sin⁡(0∘−90∘))=sin⁡−1(−0.2)≈−11.54∘\alpha = \sin^{-1}\!\left(\frac{20}{100}\sin(0^{\circ}-90^{\circ})\right)=\sin^{-1}(-0.2)\approx -11.54^{\circ}

Step 3: Heading

ψ=δ+α=90∘−11.54∘=78.46∘\psi = \delta + \alpha = 90^{\circ} - 11.54^{\circ} = 78.46^{\circ}

Step 4: Ground speed (law of cosines form)

δ−ω+α=90∘−0∘−11.54∘=78.46∘\delta-\omega+\alpha = 90^{\circ}-0^{\circ}-11.54^{\circ}=78.46^{\circ}
vg≈1002+202−2⋅100⋅20cos⁡(78.46∘)v_g \approx \sqrt{100^2 + 20^2 - 2\cdot100\cdot20\cos(78.46^{\circ})}
vg≈97.98 ktv_g \approx 97.98\ \text{kt}

Interpretation: the wind is mostly a crosswind, so you crab into it (negative WCA here), and ground speed ends up a little below TAS.

Mini example: pure tailwind (fast sanity check)

Let va=80 ktv_a=80\ \text{kt}, course δ=090∘\delta=090^{\circ}, and wind FROM 270∘270^{\circ} at vw=20 ktv_w=20\ \text{kt}. That wind blows TO 090∘090^{\circ}, so it acts like a tailwind.

α=0∘\alpha=0^{\circ}ψ=δ\psi=\deltavg=va+vw=100 ktv_g=v_a+v_w=100\ \text{kt}
🧩

Real-world examples / Use cases

Below are a few realistic scenarios. Each one is a little different — that’s the point. Ground speed problems often feel “obvious” until wind direction enters the chat.

🏁

Pure tailwind / headwind check

Background: quick planning sanity check.

va=80 ktv_a=80\ \text{kt}vw=20 ktv_w=20\ \text{kt}α=0∘\alpha=0^{\circ}
vg=va+vw=100 ktv_g = v_a + v_w = 100\ \text{kt}(tailwind)
vg=va−vw=60 ktv_g = v_a - v_w = 60\ \text{kt}(headwind)
🧭

Crosswind on a training leg

Background: you’re flying a planned course and want to avoid drifting off track.

va=100 ktv_a=100\ \text{kt}δ=090∘\delta=090^{\circ}vw=20 ktv_w=20\ \text{kt}ωfrom=180∘\omega_{from}=180^{\circ}
α≈−11.54∘\alpha \approx -11.54^{\circ}ψ≈78.46∘\psi \approx 78.46^{\circ}vg≈97.98 ktv_g \approx 97.98\ \text{kt}
🌬️

Wind finding after the fact

Background: you recorded TAS, heading, course, and groundspeed and want to estimate the wind.

va=110 ktv_a=110\ \text{kt}ψ=075∘\psi=075^{\circ}δ=090∘\delta=090^{\circ}vg=120 ktv_g=120\ \text{kt}
vw≈31.6 ktv_w \approx 31.6\ \text{kt}ωto≈154∘\omega_{to} \approx 154^{\circ}ωfrom≈334∘\omega_{from} \approx 334^{\circ}

Tip: enter the values in Wind Finding mode to reproduce these numbers and to switch between FROM / TO conventions.

🛬

Crosswind awareness

Background: you care about crosswind component for a runway direction.

XW=vwsin⁡(ω−δ)XW = v_w\sin(\omega-\delta)
δ=180∘\delta=180^{\circ}vw=30 ktv_w=30\ \text{kt}ωfrom=240∘\omega_{from}=240^{\circ}
∣XW∣≈26.0 kt|XW|\approx 26.0\ \text{kt}HW≈15.0 ktHW\approx 15.0\ \text{kt}
⏱️

ETA for a leg

Background: you want to estimate time en route quickly.

Time=Dvg\text{Time} = \frac{D}{v_g}
D=150 nmD=150\ \text{nm}vg=120 ktv_g=120\ \text{kt}Time=150120=1.25 h\text{Time}=\frac{150}{120}=1.25\ \text{h}
🧾

Planning with mixed units

Background: your wind is in knots but performance data is in mph or km/h.

Use the unit dropdowns — the calculator will keep the math internally consistent.

🗺️

Common scenarios / When to use

It’s especially useful when…

  • You have a planned course and wind forecast, and you want a realistic ETA.
  • You want to know how much you’ll need to crab into the wind (WCA) before you even taxi.
  • You have track/heading/groundspeed data (e.g., from a GPS log) and want an estimated wind.

When it might not be a good fit

  • •Strong gusts, wind shear, turbulence, or rapidly changing wind with altitude. The calculator assumes a steady wind during the leg.
  • •Situations where you must include magnetic variation, compass deviation, or instrument errors (those are outside the scope here).
💡

Tips & Best practices

1

Be consistent about wind direction

The fastest way to get a surprising result is mixing “wind from” and “wind to.” If your source is METAR/TAF, it’s almost always “from.”

2

Use wind components as a sanity check

If the crosswind component looks huge, you should expect a bigger crab angle. If headwind is strongly negative (tailwind), expect ground speed to increase.

3

Watch the “no solution” warning

If crosswind exceeds true airspeed, maintaining the desired track is physically impossible. Mathematically, that’s when ∣vwvasin⁡(ω−δ)∣>1\left|\frac{v_w}{v_a}\sin(\omega-\delta)\right| > 1.

4

Keep units simple when learning

When you’re first building intuition, use knots and degrees. Once it “clicks,” switch units freely — the calculator is designed to handle it.

📐

Calculation method / Formula explanation

The calculator uses the wind triangle: a geometric picture of how the wind vector and the aircraft’s airspeed vector combine into a ground track.

Core relationships

v⃗g=v⃗a+v⃗w\vec v_g = \vec v_a + \vec v_w
ψ=δ+α\psi = \delta + \alpha

Ground speed via a law-of-cosines style formula

One convenient form expresses ground speed as:

vg=va2+vw2−2vavwcos⁡(δ−ω+α)v_g = \sqrt{v_a^2 + v_w^2 - 2 v_a v_w\cos(\delta - \omega + \alpha)}

Where δ\delta is course, ω\omega is wind direction (in your chosen convention), and α\alpha is WCA.

Wind components (helpful for intuition)

XW=vwsin⁡(ω−δ)XW = v_w\sin(\omega-\delta)HW=−vwcos⁡(ω−δ)HW = -v_w\cos(\omega-\delta)

The signs depend on convention, but the idea is simple: one component pushes you sideways (crosswind) and the other speeds you up or slows you down (headwind/tailwind).

📘

Related concepts / Background info

Course vs. heading vs. track (quick definitions)

  • Course is the intended direction over the ground (δ\delta).
  • Heading is where the nose points (ψ\psi).
  • Track is the path you actually fly over the ground (often equal to course if you fly it accurately).

A tiny but powerful habit: whenever numbers look odd, ask “Am I confusing course (where I want to go) with heading (where I must point)?”

❓

Frequently Asked Questions

Q

What’s the difference between course and heading?

Course (δ\delta) is the direction you want your ground track to follow. Heading (ψ\psi) is the direction the aircraft points. They differ by WCA:

ψ=δ+α\psi = \delta + \alpha
Q

Can ground speed be higher than true airspeed?

Yes — with a tailwind. In the simplest “same direction” case, you get:

vg=va+vwv_g = v_a + v_w(tailwind)\quad(\text{tailwind})

Tip: if you’re seeing vg≫vav_g \gg v_a with only a mild wind, double-check wind direction.

Q

Why does the calculator say “no solution” sometimes?

That happens when the required crosswind component exceeds your available airspeed — meaning you cannot hold the desired course. In terms of the WCA formula, the value inside sin⁡−1\sin^{-1} must be between −1-1 and 11.

∣vwvasin⁡(ω−δ)∣≤1\left|\frac{v_w}{v_a}\sin(\omega-\delta)\right| \le 1
Q

Is “wind direction” the direction wind comes from or goes to?

In aviation, it’s usually the direction the wind comes from. Some math uses the direction the wind blows to. They differ by 180∘180^{\circ}.

ωto=ωfrom+180∘\omega_{to} = \omega_{from} + 180^{\circ}
Q

What does a negative wind correction angle mean?

It simply means the correction points to the “other side” under the chosen sign convention. Practically: you’re crabbing into the wind. The important thing is that heading and course satisfy ψ=δ+α\psi=\delta+\alpha.

Q

Why are angles normalized to 0∘–360∘0^{\circ}\text{–}360^{\circ}?

Because headings wrap around. For example, 370∘370^{\circ} is the same as 10∘10^{\circ}.

⚠️

Limitations / Disclaimers

  • •This calculator provides educational estimates and planning math. It is not a substitute for certified flight planning tools, training, or operational judgment.
  • •It assumes steady wind during the leg and does not model gusts, wind shear, or changes with altitude.
  • •It does not account for magnetic variation, compass deviation, instrument error, or aircraft-specific performance tables.

Related Calculators

Trajectory Calculator

Have a look at the flight path of the object with this trajectory calculator.

Try Now

Free Fall Calculator

Calculate free fall parameters including gravitational acceleration, drop height, fall duration, and impact velocity. Supports bidirectional LRU solving with unit conversions.

Try Now

Free Fall with Air Resistance Calculator

Calculate free fall with quadratic air drag, including terminal velocity, fall time, maximum velocity, and drag force. Supports air resistance coefficient calculation from object properties.

Try Now

Projectile Range Calculator

Calculate the horizontal range of a projectile based on velocity, angle, and initial height. Supports bidirectional calculation with multiple unit systems.

Try Now

Projectile Motion Calculator

Calculate projectile trajectory parameters including launch velocity, angle, distance, maximum height, and flight time with bidirectional solving.

Try Now

Maximum Height Calculator – Projectile Motion

Use this maximum height calculator to figure out what is the maximum vertical position of an object in projectile motion.

Try Now