Ground Speed Calculator works out ground speed, the true heading and the wind correction angle from airspeed and wind. It also converts a distance and time into knots, mph or km/h.
Wind direction is where the wind blows from, as in a winds aloft forecast.
Altitude and Variation
Trip and Units
Step-by-Step Working
- Known values in knots and degrees: TAS = 120, course = 90°, wind from 60° at 25
- Wind angle: wind direction − course = 60° − 90° = −30°
- Crosswind: 25 × sin(−30°) = −12.5 kt. Headwind: 25 × cos(−30°) = 21.65 kt
- Wind correction angle: sin⁻¹(crosswind ÷ TAS) = sin⁻¹(−12.5 ÷ 120) = −5.98°
- Heading: course + correction = 90° + (−5.98°) = 84.02°
- Result: GS = TAS × cos(WCA) − headwind = 119.35 − 21.65 = 97.7 kt
Ground Speed on Every Course
| Course | Heading | Ground Speed |
|---|---|---|
| N, 360° | 010° | 105.53 kt |
| NE, 045° | 048° | 95.68 kt |
| E, 090° | 084° | 97.7 kt |
| SE, 135° | 123° | 111.07 kt |
| S, 180° | 170° | 130.53 kt |
| SW, 225° | 222° | 143.97 kt |
| W, 270° | 276° | 141 kt |
| NW, 315° | 327° | 124.02 kt |
Wind Triangle
Ground Speed Calculator for Wind and Timed Legs
The Ground Speed Calculator works two ways. Airspeed and Wind solves the wind triangle before or during a flight. Distance and Time turns a leg timed between two known points into a ground speed, which is the check pilots make once they are in the air.
The wind method is the aviation flight planning case. It takes a true airspeed, a true course, and the wind direction and speed. Wind direction is where the wind blows from, the way a winds aloft forecast gives it. The course and wind fields have compass presets, and any bearing from 0° to 360° can be typed in.
The headline is the speed over the ground on that course. The cards add the true heading to fly, the magnetic heading, the wind correction angle, the headwind and crosswind parts of the wind, and the time en route for the trip distance. Results can be shown in knots, mph or km/h.
A table in the Ground Speed Calculator lists the ground speed on all eight compass courses for the same airspeed and wind, so the best and worst directions are visible at a glance. The message under the results gives the ground speed on the reciprocal course, which is the return leg.
Ground Speed Formula
Ground speed is the rate of an aircraft’s progress over the ground, and airspeed is its rate of progress through the air, as the FAA Pilot’s Handbook of Aeronautical Knowledge defines them. The wind moves the air itself, so the two differ whenever the wind blows.
To calculate ground speed with wind, the wind is first split into two parts relative to the course. W is the wind speed, and the angle is the wind direction minus the course. The crosswind acts across the course and the headwind acts along it.
$$XW = W \sin(\theta_{wind} – \theta_{course})$$
$$HW = W \cos(\theta_{wind} – \theta_{course})$$
The aircraft must point slightly into the crosswind to stay on course. That crab is the wind correction angle, and adding it to the course gives the true heading. A negative angle means a correction to the left.
$$WCA = \sin^{-1}\left(\frac{XW}{TAS}\right)$$
Ground speed is then the part of the true airspeed that still points along the course, minus the headwind. This is how to calculate ground speed from true airspeed, and a tailwind enters as a negative headwind, which adds speed.
$$GS = TAS \cos(WCA) – HW$$
The Ground Speed Calculator applies these four lines in order. With the default entries of 120 kt, a course of 090° and wind from 060° at 25 kt, the wind sits 30° off the nose. The headwind is 21.65 kt and the crosswind is 12.5 kt from the left. The correction is 5.98° left, the heading is 084° and the ground speed is 97.7 kt.
A published problem makes a fair test. A flight planning exercise from the Aircraft Owners and Pilots Association uses a true course of 080°, winds aloft from 040° at 40 kt and an airspeed of 160 kt. Its answer is a true heading of 071°, a 9° correction and 127 kt, and the Ground Speed Calculator returns 071°, 9.25° and 127.28 kt.
Ground Speed With Distance and Time
In flight, ground speed is measured, not predicted. Note the time when passing one landmark and again at the next, then divide the distance by the time. This is how to calculate ground speed with distance and time, and it is the same formula as any other speed.
$$GS = \frac{distance}{time}$$
Flying 14 NM in 6 minutes is 2.33 NM per minute. Multiplying by 60 gives 140 kt, which is 161.11 mph or 259.28 km/h. The first card shows the miles per minute figure, since that is the quick cockpit version of the same sum.
The Ground Speed Calculator then compares the result with the planned true airspeed. At a planned 150 kt, a measured 140 kt means about 10 kt of headwind along the track. The last card applies the new ground speed to the distance still to go, so 100 NM takes 42 min 51 s in place of the planned 40 min.
| Distance | Time | Speed | In knots |
|---|---|---|---|
| 14 NM | 6 min | 140 kt | 140 kt |
| 250 NM | 2 h | 125 kt | 125 kt |
| 10 NM | 1 h | 10 kt, or 11.51 mph | 10 kt |
| 100 km | 1 h | 100 km/h, or 62.14 mph | 54 kt |
| 12 NM | 8 min | 90 kt, or 166.68 km/h | 90 kt |
These five examples of speed all use the one formula. The Distance and Time setting accepts nautical miles, statute miles or kilometers with minutes, hours or seconds, so it also answers how fast 100 km in 1 hour is in knots. For motion built from several legs, the Displacement Calculator adds velocity and time legs together.
True Airspeed From Altitude
The wind triangle needs true airspeed, and the airspeed indicator does not show it. Thinner air at altitude makes the indicator read low. Under Altitude and Variation, the Ground Speed Calculator takes a calibrated airspeed, a pressure altitude and an outside air temperature and works out the true airspeed first.
| Calibrated airspeed | Pressure altitude | Outside air temperature | True airspeed | Ground speed, default wind |
|---|---|---|---|---|
| 120 kt | Sea level | 15 °C | 120 kt | 97.7 kt |
| 120 kt | 5,000 ft | 5 °C | 129.15 kt | 106.89 kt |
| 120 kt | 10,000 ft | −5 °C | 139.33 kt | 117.12 kt |
| 120 kt | 5,000 ft | 20 °C | 132.58 kt | 110.34 kt |
This is the sense in which a ground speed calculator with altitude differs from a simple one. Altitude does not change ground speed directly. It raises the true airspeed for the same indicated reading, and warmer air raises it a little more, as the last row shows.
The conversion uses the standard subsonic airspeed equation with International Standard Atmosphere constants, including a sea level speed of sound of 661.48 kt. It covers pressure altitudes up to 36,000 ft and stops if the result reaches Mach 1.
Ground Speed in Knots, km/h and mph
The tool works as a ground speed kts calculator by default, and ground speed kts simply means ground speed measured in knots. A knot is one nautical mile per hour, and a nautical mile is exactly 1,852 m, so 1 knot is 1.852 km/h or about 1.15 mph. Knots are a unit and ground speed is the quantity, which is the only difference between the two terms.
| Knots | Kilometers per hour | Miles per hour |
|---|---|---|
| 1 kt | 1.85 km/h | 1.15 mph |
| 10 kt | 18.52 km/h | 11.51 mph |
| 20 kt | 37.04 km/h | 23.02 mph |
| 25 kt | 46.3 km/h | 28.77 mph |
| 30 kt | 55.56 km/h | 34.52 mph |
| 40 kt | 74.08 km/h | 46.03 mph |
| 100 kt | 185.2 km/h | 115.08 mph |
| 500 kt | 926 km/h | 575.39 mph |
To convert ground speed in knots to kilometers per hour, multiply by 1.852. A ground speed of 100 knots is 185.2 km/h, and 500 kts is 926 km/h. The third result card in the Ground Speed Calculator does this for every answer, and Result Units switches the whole tool to an airplane ground speed in km/h.
Whether 20 knots is fast depends on what is moving. For an aircraft it is very slow. As a wind it is a fresh breeze, force 5 on the Beaufort scale of the National Weather Service, and a 25 knot wind is a strong breeze at force 6. That 25 kt wind is the default in the tool.
Ground Speed and Airspeed Compared
Is ground speed faster than airspeed?
It is with a tailwind and slower with a headwind. The FAA handbook gives the simple case of 120 kt of airspeed with a 20 kt tailwind, which makes 140 kt over the ground. In still air the two are equal.
The default wind shows the spread. Flying east at 120 kt, the ground speed is 97.7 kt. On the reciprocal course of 270° the same wind becomes a tailwind and the ground speed is 141 kt, a gap of more than 43 kt on the same day.
How do you calculate the fastest ground speed?
The fastest ground speed comes with the wind directly behind, and it equals true airspeed plus wind speed. The slowest comes with the wind on the nose and equals true airspeed minus wind speed. For 120 kt and a 25 kt wind, the limits are 145 kt and 95 kt.
A pure crosswind sits between them. With a 20 kt wind at right angles to the course, a 120 kt aircraft crabs 9.59° and keeps 118.32 kt. A crosswind costs little speed but a lot of heading, which the every-course table makes plain for any wind.
What is ground velocity?
Ground velocity is ground speed with its direction attached. It is the vector sum of the aircraft’s velocity through the air and the wind velocity. The wind triangle in the Ground Speed Calculator draws those three vectors as heading, wind and track.
Courses, wind directions and headings in the wind triangle are all true, measured from true north. An E6B flight computer solves the same triangle on its wind side, so the tool doubles as a ground speed calculator for E6B practice. More motion tools are listed under Kinematics Calculators.
How is magnetic heading found from true heading?
A compass points to magnetic north, so the true heading is corrected by the magnetic variation printed on the chart. Easterly variation is subtracted and westerly variation is added. The Magnetic Variation field under Altitude and Variation applies this, and the first card then shows the magnetic heading.
The published problem above carries 6° of east variation. Its true heading of 071° becomes a magnetic heading of 065°. Variation changes only the number on the compass, so the ground speed stays at 127.28 kt.